The Scala Language Specification, Version 2.9

24th May 2011


0.1 Preface

Scala is a Java-like programming language which unifies object-oriented and functional programming. It is a pure object-oriented language in the sense that every value is an object. Types and behavior of objects are described by classes. Classes can be composed using mixin composition. Scala is designed to work seamlessly with two less pure but mainstream object-oriented languages -- Java and C#.

Scala is a functional language in the sense that every function is a value. Nesting of function definitions and higher-order functions are naturally supported. Scala also supports a general notion of pattern matching which can model the algebraic types used in many functional languages.

Scala has been designed to interoperate seamlessly with Java (an alternative implementation of Scala also works for .NET). Scala classes can call Java methods, create Java objects, inherit from Java classes and implement Java interfaces. None of this requires interface definitions or glue code.

Scala has been developed from 2001 in the programming methods laboratory at EPFL. Version 1.0 was released in November 2003. This document describes the second version of the language, which was released in March 2006. It acts a reference for the language definition and some core library modules. It is not intended to teach Scala or its concepts; for this there are other documents (Odersky and al. 2004; Odersky 2006; Odersky and Zenger 2005a; Odersky et al. 2003; Odersky and Zenger 2005b)

Scala has been a collective effort of many people. The design and the implementation of version 1.0 was completed by Philippe Altherr, Vincent Cremet, Gilles Dubochet, Burak Emir, Stéphane Micheloud, Nikolay Mihaylov, Michel Schinz, Erik Stenman, Matthias Zenger, and the author. Iulian Dragos, Gilles Dubochet, Philipp Haller, Sean McDirmid, Lex Spoon, and Geoffrey Washburn joined in the effort to develop the second version of the language and tools. Gilad Bracha, Craig Chambers, Erik Ernst, Matthias Felleisen, Shriram Krishnamurti, Gary Leavens, Sebastian Maneth, Erik Meijer, Klaus Ostermann, Didier Rémy, Mads Torgersen, and Philip Wadler have shaped the design of the language through lively and inspiring discussions and comments on previous versions of this document. The contributors to the Scala mailing list have also given very useful feedback that helped us improve the language and its tools.

1 Lexical Syntax

Scala programs are written using the Unicode Basic Multilingual Plane (BMP) character set; Unicode supplementary characters are not presently supported. This chapter defines the two modes of Scala's lexical syntax, the Scala mode and the XML mode. If not otherwise mentioned, the following descriptions of Scala tokens refer to Scala mode, and literal characters ‘c’ refer to the ASCII fragment \u0000-\u007F

In Scala mode, Unicode escapes are replaced by the corresponding Unicode character with the given hexadecimal code.

UnicodeEscape ::= \{\\}u{u} hexDigit hexDigit hexDigit hexDigit
hexDigit      ::= ‘0’ | … | ‘9’ | ‘A’ | … | ‘F’ | ‘a’ | … | ‘f’

To construct tokens, characters are distinguished according to the following classes (Unicode general category given in parentheses):

  1. Whitespace characters. \u0020 | \u0009 | \u000D | \u000A
  2. Letters, which include lower case letters(Ll), upper case letters(Lu), titlecase letters(Lt), other letters(Lo), letter numerals(Nl) and the two characters \u0024 ‘\$’ and \u005F ‘_’, which both count as upper case letters
  3. Digits ‘0’ | … | ‘9’
  4. Parentheses ‘(’ | ‘)’ | ‘[’ | ‘]’ | ‘{’ | ‘}’
  5. Delimiter characters ‘`’ | ‘'’ | ‘"’ | ‘.’ | ‘;’ | ‘,’
  6. Operator characters. These consist of all printable ASCII characters \u0020-\u007F which are in none of the sets above, mathematical symbols(Sm) and other symbols(So).

1.1 Identifiers

op       ::=  opchar {opchar} 
varid    ::=  lower idrest
plainid  ::=  upper idrest
           |  varid
           |  op
id       ::=  plainid
           |  ‘`’ stringLit ‘`’
idrest   ::=  {letter | digit} [‘_’ op]

There are three ways to form an identifier. First, an identifier can start with a letter which can be followed by an arbitrary sequence of letters and digits. This may be followed by underscore ‘_’ characters and another string composed of either letters and digits or of operator characters. Second, an identifier can start with an operator character followed by an arbitrary sequence of operator characters. The preceding two forms are called plain identifiers. Finally, an identifier may also be formed by an arbitrary string between back-quotes (host systems may impose some restrictions on which strings are legal for identifiers). The identifier then is composed of all characters excluding the backquotes themselves.

As usual, a longest match rule applies. For instance, the string

big_bob++=`def`

decomposes into the three identifiers big_bob, ++=, and def. The rules for pattern matching further distinguish between variable identifiers, which start with a lower case letter, and constant identifiers, which do not.

The ‘$’ character is reserved for compiler-synthesized identifiers. User programs should not define identifiers which contain ‘$’ characters.

The following names are reserved words instead of being members of the syntactic class id of lexical identifiers.

abstract    case        catch       class       def
do          else        extends     false       final
finally     for         forSome     if          implicit
import      lazy        match       new         null
object      override    package     private     protected
return      sealed      super       this        throw       
trait       try         true        type        val         
var         while       with        yield
_    :    =    =>    <-    <:    <%     >:    #    @

The Unicode operators \u21D2 ‘’ and \u2190 ‘’, which have the ASCII equivalents ‘=>’ and ‘<-’, are also reserved.

  1. Here are examples of identifiers:

        x         Object        maxIndex   p2p      empty_?
        +         `yield`       αρετη     _y       dot_product_*
        __system  _MAX_LEN_     
  2. Backquote-enclosed strings are a solution when one needs to access Java identifiers that are reserved words in Scala. For instance, the statement Thread.yield() is illegal, since yield is a reserved word in Scala. However, here's a work-around: Thread.`yield`()

1.2 Newline Characters

semi ::= ‘;’ |  nl {nl}

Scala is a line-oriented language where statements may be terminated by semi-colons or newlines. A newline in a Scala source text is treated as the special token “nl” if the three following criteria are satisfied:

  1. The token immediately preceding the newline can terminate a statement.
  2. The token immediately following the newline can begin a statement.
  3. The token appears in a region where newlines are enabled.

The tokens that can terminate a statement are: literals, identifiers and the following delimiters and reserved words:

this    null    true    false    return    type    <xml-start>    
_       )       ]       }

The tokens that can begin a statement are all Scala tokens except the following delimiters and reserved words:

catch    else    extends    finally    forSome    match        
with    yield    ,    .    ;    :    =    =>    <-    <:    <%    
>:    #    [    )    ]    }

A case token can begin a statement only if followed by a class or object token.

Newlines are enabled in:

  1. all of a Scala source file, except for nested regions where newlines are disabled, and
  2. the interval between matching { and } brace tokens, except for nested regions where newlines are disabled.

Newlines are disabled in:

  1. the interval between matching ( and ) parenthesis tokens, except for nested regions where newlines are enabled, and
  2. the interval between matching [ and ] bracket tokens, except for nested regions where newlines are enabled.
  3. The interval between a case token and its matching => token, except for nested regions where newlines are enabled.
  4. Any regions analyzed in XML mode.

Note that the brace characters of {...} escapes in XML and string literals are not tokens, and therefore do not enclose a region where newlines are enabled.

Normally, only a single nl token is inserted between two consecutive non-newline tokens which are on different lines, even if there are multiple lines between the two tokens. However, if two tokens are separated by at least one completely blank line (i.e a line which contains no printable characters), then two nl tokens are inserted.

The Scala grammar (given in full here) contains productions where optional nl tokens, but not semicolons, are accepted. This has the effect that a newline in one of these positions does not terminate an expression or statement. These positions can be summarized as follows:

Multiple newline tokens are accepted in the following places (note that a semicolon in place of the newline would be illegal in every one of these cases):

A single new line token is accepted

  1. The following code contains four well-formed statements, each on two lines. The newline tokens between the two lines are not treated as statement separators.

    if (x > 0)
      x = x - 1
    
    while (x > 0)
      x  = x / 2
    
    for (x <- 1 to 10)
      println(x)
    
    type
      IntList = List[Int]
  2. The following code designates an anonymous class:

    new Iterator[Int]
    {
      private var x = 0
      def hasNext = true
      def next = { x += 1; x }
    }

    With an additional newline character, the same code is interpreted as an object creation followed by a local block:

    new Iterator[Int] 
    
    {
      private var x = 0
      def hasNext = true
      def next = { x += 1; x }
    }
  3. The following code designates a single expression:

      x < 0 ||
      x > 10

    With an additional newline character, the same code is interpreted as two expressions:

      x < 0 ||
    
      x > 10
  4. The following code designates a single, curried function definition:

    def func(x: Int)
            (y: Int) = x + y

    With an additional newline character, the same code is interpreted as an abstract function definition and a syntactically illegal statement:

    def func(x: Int)
    
            (y: Int) = x + y
  5. The following code designates an attributed definition:

    @serializable
    protected class Data { ... }

    With an additional newline character, the same code is interpreted as an attribute and a separate statement (which is syntactically illegal).

    @serializable
    
    protected class Data { ... }

1.3 Literals

There are literals for integer numbers, floating point numbers, characters, booleans, symbols, strings. The syntax of these literals is in each case as in Java.

Literal  ::=  [‘-’] integerLiteral
           |  [‘-’] floatingPointLiteral
           |  booleanLiteral
           |  characterLiteral
           |  stringLiteral
           |  symbolLiteral
           |  ‘null’

1.3.1 Integer Literals

integerLiteral  ::=  (decimalNumeral | hexNumeral | octalNumeral) 
                       [‘L’ | ‘l’]
decimalNumeral  ::=  ‘0’ | nonZeroDigit {digit}
hexNumeral      ::=  ‘0’ ‘x’ hexDigit {hexDigit}
octalNumeral    ::=  ‘0’ octalDigit {octalDigit}
digit           ::=  ‘0’ | nonZeroDigit
nonZeroDigit    ::=  ‘1’ | … | ‘9’
octalDigit      ::=  ‘0’ | … | ‘7’

Integer literals are usually of type Int, or of type Long when followed by a L or l suffix. Values of type Int are all integer numbers between 231 and 2311, inclusive. Values of type Long are all integer numbers between 263 and 2631, inclusive. A compile-time error occurs if an integer literal denotes a number outside these ranges.

However, if the expected type pt of a literal in an expression is either Byte, Short, or Char and the integer number fits in the numeric range defined by the type, then the number is converted to type pt and the literal's type is pt. The numeric ranges given by these types are:

Byte 27 to 271
Short 215 to 2151
Char 0 to 2161
  1. Here are some integer literals:

    0          21          0xFFFFFFFF       0777L

1.3.2 Floating Point Literals

floatingPointLiteral  ::=  digit {digit} ‘.’ {digit} [exponentPart] [floatType]
                        |  ‘.’ digit {digit} [exponentPart] [floatType]
                        |  digit {digit} exponentPart [floatType]
                        |  digit {digit} [exponentPart] floatType
exponentPart          ::=  (‘E’ | ‘e’) [‘+’ | ‘-’] digit {digit}
floatType             ::=  ‘F’ | ‘f’ | ‘D’ | ‘d’

Floating point literals are of type Float when followed by a floating point type suffix F or f, and are of type Double otherwise. The type Float consists of all IEEE 754 32-bit single-precision binary floating point values, whereas the type Double consists of all IEEE 754 64-bit double-precision binary floating point values.

If a floating point literal in a program is followed by a token starting with a letter, there must be at least one intervening whitespace character between the two tokens.

  1. Here are some floating point literals:

    0.0        1e30f      3.14159f      1.0e-100      .1
  2. The phrase 1.toString parses as three different tokens: 1, ., and toString. On the other hand, if a space is inserted after the period, the phrase 1. toString parses as the floating point literal 1. followed by the identifier toString.

1.3.3 Boolean Literals

booleanLiteral  ::=  ‘true’ | ‘false’

The boolean literals true and false are members of type Boolean.

1.3.4 Character Literals

characterLiteral  ::=  ‘'’ printableChar ‘'’
                    |  ‘'’ charEscapeSeq ‘'’

A character literal is a single character enclosed in quotes. The character is either a printable unicode character or is described by an escape sequence.

  1. Here are some character literals:

    'a'    '\u0041'    '\n'    '\t'

Note that '\u000A' is not a valid character literal because Unicode conversion is done before literal parsing and the Unicode character \u000A (line feed) is not a printable character. One can use instead the escape sequence '\n' or the octal escape '\12' (see here).

1.3.5 String Literals

stringLiteral  ::=  ‘\"’ {stringElement} ‘\"’
stringElement  ::=  printableCharNoDoubleQuote  |  charEscapeSeq

A string literal is a sequence of characters in double quotes. The characters are either printable unicode character or are described by escape sequences. If the string literal contains a double quote character, it must be escaped, i.e. "\"". The value of a string literal is an instance of class String.

  1. Here are some string literals:

    "Hello,\nWorld!"       
    "This string contains a \" character."

1.3.5.1 Multi-Line String Literals

stringLiteral   ::=  ‘"""’ multiLineChars ‘"""’
multiLineChars  ::=  {[‘"’] [‘"’] charNoDoubleQuote} {‘"’}

A multi-line string literal is a sequence of characters enclosed in triple quotes """ ... """. The sequence of characters is arbitrary, except that it may contain three or more consuctive quote characters only at the very end. Characters must not necessarily be printable; newlines or other control characters are also permitted. Unicode escapes work as everywhere else, but none of the escape sequences here are interpreted.

  1. Here is a multi-line string literal:

      """the present string
         spans three 
         lines."""

    This would produce the string:

    the present string
         spans three 
         lines.

The Scala library contains a utility method stripMargin which can be used to strip leading whitespace from multi-line strings. The expression

 """the present string
    spans three 
    lines.""".stripMargin

evaluates to

the present string
spans three 
lines.

Method stripMargin is defined in class scala.collection.immutable.StringLike. Because there is a predefined implicit conversion from String to StringLike, the method is applicable to all strings.

1.3.6 Escape Sequences

The following escape sequences are recognized in character and string literals.

\b \u0008: backspace BS
\t \u0009: horizontal tab HT
\n \u000a: linefeed LF
\f \u000c: form feed FF
\r \u000d: carriage return CR
\" \u0022: double quote "
\' \u0027: single quote '
\\ \u005c: backslash \

A character with Unicode between 0 and 255 may also be represented by an octal escape, i.e. a backslash ‘’ followed by a sequence of up to three octal characters.

It is a compile time error if a backslash character in a character or string literal does not start a valid escape sequence.

1.3.7 Symbol literals

symbolLiteral  ::=  ‘'’ plainid

A symbol literal 'x is a shorthand for the expression scala.Symbol("x"). Symbol is a case class, which is defined as follows.

package scala
final case class Symbol private (name: String) {
  override def toString: String = "'" + name
}

The apply method of Symbol's companion object caches weak references to Symbols, thus ensuring that identical symbol literals are equivalent with respect to reference equality.

1.4 Whitespace and Comments

Tokens may be separated by whitespace characters and/or comments. Comments come in two forms:

A single-line comment is a sequence of characters which starts with // and extends to the end of the line.

A multi-line comment is a sequence of characters between /* and */. Multi-line comments may be nested, but are required to be properly nested. Therefore, a comment like /* /* */ will be rejected as having an unterminated comment.

1.5 XML mode

In order to allow literal inclusion of XML fragments, lexical analysis switches from Scala mode to XML mode when encountering an opening angle bracket '<' in the following circumstance: The '<' must be preceded either by whitespace, an opening parenthesis or an opening brace and immediately followed by a character starting an XML name.

 ( whitespace | ‘(’ | ‘{’ ) ‘<’ (XNameStart | ‘!’ | ‘?’)

  XNameStart ::= ‘_’ | BaseChar | Ideographic // as in W3C XML, but without ‘:’

The scanner switches from XML mode to Scala mode if either

Note that no Scala tokens are constructed in XML mode, and that comments are interpreted as text.

  1. The following value definition uses an XML literal with two embedded Scala expressions

    val b = <book>
              <title>The Scala Language Specification</title>
              <version>{scalaBook.version}</version>
              <authors>{scalaBook.authors.mkList("", ", ", "")}</authors>
            </book>

2 Identifiers, Names and Scopes

Names in Scala identify types, values, methods, and classes which are collectively called entities. Names are introduced by local definitions and declarations, inheritance, import clauses, or package clauses which are collectively called bindings.

Bindings of different kinds have a precedence defined on them:

  1. Definitions and declarations that are local, inherited, or made available by a package clause in the same compilation unit where the definition occurs have highest precedence.
  2. Explicit imports have next highest precedence.
  3. Wildcard imports have next highest precedence.
  4. Definitions made available by a package clause not in the compilation unit where the definition occurs have lowest precedence.

There are two different name spaces, one for types and one for terms. The same name may designate a type and a term, depending on the context where the name is used.

A binding has a scope in which the entity defined by a single name can be accessed using a simple name. Scopes are nested. A binding in some inner scope shadows bindings of lower precedence in the same scope as well as bindings of the same or lower precedence in outer scopes.

Note that shadowing is only a partial order. In a situation like

val x = 1;
{ import p.x; 
  x }

neither binding of x shadows the other. Consequently, the reference to x in the third line above would be ambiguous.

A reference to an unqualified (type- or term-) identifier x is bound by the unique binding, which

It is an error if no such binding exists. If x is bound by an import clause, then the simple name x is taken to be equivalent to the qualified name to which x is mapped by the import clause. If x is bound by a definition or declaration, then x refers to the entity introduced by that binding. In that case, the type of x is the type of the referenced entity.

  1. Assume the following two definitions of a objects named X in packages P and Q.

    package P {
      object X { val x = 1; val y = 2 }
    }
    
    package Q {
      object X { val x = true; val y = "" }
    }

    The following program illustrates different kinds of bindings and precedences between them.

    package P {                  // `X' bound by package clause
    import Console._             // `println' bound by wildcard import
    object A {                   
      println("L4: "+X)          // `X' refers to `P.X' here
      object B {
        import Q._               // `X' bound by wildcard import
        println("L7: "+X)        // `X' refers to `Q.X' here
        import X._               // `x' and `y' bound by wildcard import
        println("L8: "+x)        // `x' refers to `Q.X.x' here
        object C {
          val x = 3              // `x' bound by local definition
          println("L12: "+x)     // `x' refers to constant `3' here
          { import Q.X._         // `x' and `y' bound by wildcard import
    //      println("L14: "+x)   // reference to `x' is ambiguous here
            import X.y           // `y' bound by explicit import
            println("L16: "+y)   // `y' refers to `Q.X.y' here
            { val x = "abc"      // `x' bound by local definition
              import P.X._       // `x' and `y' bound by wildcard import
    //        println("L19: "+y) // reference to `y' is ambiguous here
              println("L20: "+x) // `x' refers to string ``abc'' here
    }}}}}}

A reference to a qualified (type- or term-) identifier e.x refers to the member of the type T of e which has the name x in the same namespace as the identifier. It is an error if T is not a value type. The type of e.x is the member type of the referenced entity in T.

3 Types

  Type              ::=  FunctionArgTypes ‘=>’ Type
                      |  InfixType [ExistentialClause]
  FunctionArgTypes  ::=  InfixType
                      |  ‘(’ [ ParamType {‘,’ ParamType } ] ‘)’
  ExistentialClause ::=  ‘forSome’ ‘{’ ExistentialDcl 
                             {semi ExistentialDcl} ‘}’
  ExistentialDcl    ::=  ‘type’ TypeDcl 
                      |  ‘val’ ValDcl
  InfixType         ::=  CompoundType {id [nl] CompoundType}
  CompoundType      ::=  AnnotType {‘with’ AnnotType} [Refinement]
                      |  Refinement
  AnnotType         ::=  SimpleType {Annotation}
  SimpleType        ::=  SimpleType TypeArgs
                      |  SimpleType ‘#’ id
                      |  StableId
                      |  Path ‘.’ ‘type’
                      |  ‘(’ Types ‘)’
  TypeArgs          ::=  ‘[’ Types ‘]’
  Types             ::=  Type {‘,’ Type}

We distinguish between first-order types and type constructors, which take type parameters and yield types. A subset of first-order types called value types represents sets of (first-class) values. Value types are either concrete or abstract.

Every concrete value type can be represented as a class type, i.e. a type designator that refers to a class or a trait,1 or as a compound type representing an intersection of types, possibly with a refinement that further constrains the types of its members. Abstract value types are introduced by type parameters and abstract type bindings. Parentheses in types can be used for grouping.

Non-value types capture properties of identifiers that are not values. For example, a type constructor does not directly specify a type of values. However, when a type constructor is applied to the correct type arguments, it yields a first-order type, which may be a value type.

Non-value types are expressed indirectly in Scala. E.g., a method type is described by writing down a method signature, which in itself is not a real type, although it gives rise to a corresponding method type. Type constructors are another example, as one can write type Swap[m[_, _], a,b] = m[b, a], but there is no syntax to write the corresponding anonymous type function directly.

3.1 Paths

Path            ::=  StableId
                  |  [id ‘.’] this
StableId        ::=  id
                  |  Path ‘.’ id
                  |  [id ‘.’] ‘super’ [ClassQualifier] ‘.’ id
ClassQualifier  ::= ‘[’ id ‘]’

Paths are not types themselves, but they can be a part of named types and in that function form a central role in Scala's type system.

A path is one of the following.

A stable identifier is a path which ends in an identifier.

3.2 Value Types

Every value in Scala has a type which is of one of the following forms.

3.2.1 Singleton Types

SimpleType  ::=  Path ‘.’ type

A singleton type is of the form $p$.type, where p is a path pointing to a value expected to conform to scala.AnyRef. The type denotes the set of values consisting of null and the value denoted by p.

A stable type is either a singleton type or a type which is declared to be a subtype of trait scala.Singleton.

3.2.2 Type Projection

SimpleType  ::=  SimpleType ‘#’ id

A type projection $T$#$x$ references the type member named x of type T.

3.2.3 Type Designators

SimpleType  ::=  StableId

A type designator refers to a named value type. It can be simple or qualified. All such type designators are shorthands for type projections.

Specifically, the unqualified type name t where t is bound in some class, object, or package C is taken as a shorthand for $C$.this.type#$t$. If t is not bound in a class, object, or package, then t is taken as a shorthand for ε.type#$t$.

A qualified type designator has the form p.t where p is a path and t is a type name. Such a type designator is equivalent to the type projection p.type#t.

  1. Some type designators and their expansions are listed below. We assume a local type parameter t, a value maintable with a type member Node and the standard class scala.Int,

    t ε.type#t
    Int scala.type#Int
    scala.Int scala.type#Int
    data.maintable.Node data.maintable.type#Node

3.2.4 Parameterized Types

SimpleType      ::=  SimpleType TypeArgs
TypeArgs        ::=  ‘[’ Types ‘]’

A parameterized type T[U1,,Un] consists of a type designator T and type parameters U1,,Un where n1. T must refer to a type constructor which takes n type parameters a1,,an.

Say the type parameters have lower bounds L1,,Ln and upper bounds U1,,Un. The parameterized type is well-formed if each actual type parameter conforms to its bounds, i.e. σLi<:Ti<:σUi where σ is the substitution [a1:=T1,,an:=Tn].

  1. Given the partial type definitions:

    class TreeMap[A <: Comparable[A], B] { … }
    class List[A] { … }
    class I extends Comparable[I] { … }
    
    class F[M[_], X] { … }
    class S[K <: String] { … }
    class G[M[ Z <: I ], I] { … }

    the following parameterized types are well formed:

      TreeMap[I, String]
      List[I]
      List[List[Boolean]]
    
      F[List, Int]
      G[S, String]
  2. Given the type definitions of (17), the following types are ill-formed:

    TreeMap[I]            // illegal: wrong number of parameters
    TreeMap[List[I], Int] // illegal: type parameter not within bound
    
    F[Int, Boolean]       // illegal: Int is not a type constructor
    F[TreeMap, Int]       // illegal: TreeMap takes two parameters,
                          //   F expects a constructor taking one
    G[S, Int]             // illegal: S constrains its parameter to
                          //   conform to String,
                          // G expects type constructor with a parameter
                          //   that conforms to Int

3.2.5 Tuple Types

SimpleType    ::=   ‘(’ Types ‘)’

A tuple type (T1,,Tn) is an alias for the class scala.Tuple$_n$[$T_1$, … , $T_n$], where n2.

Tuple classes are case classes whose fields can be accessed using selectors _1 , … , _n. Their functionality is abstracted in a corresponding Product trait. The n-ary tuple class and product trait are defined at least as follows in the standard Scala library (they might also add other methods and implement other traits).

case class Tuple$n$[+T1, … , +$T_n$](_1: T1, … , _n: $T_n$) 
extends Product_n[T1, … , $T_n$]

trait Product_n[+T1, … , +$T_n$] {
  override def productArity = $n$
  def _1: T1
  …
  def _n: $T_n$
}

3.2.6 Annotated Types

AnnotType  ::=  SimpleType {Annotation}

An annotated type T $a_1 , \ldots , a_n$ attaches annotations a1,,an to the type T.

  1. The following type adds the @suspendable annotation to the type String:

    String @suspendable

3.2.7 Compound Types

CompoundType    ::=  AnnotType {‘with’ AnnotType} [Refinement]
                  |  Refinement
Refinement      ::=  [nl] ‘{’ RefineStat {semi RefineStat} ‘}’
RefineStat      ::=  Dcl
                  |  ‘type’ TypeDef
                  |

A compound type $T_1$ with … with $T_n$ { $R$ } represents objects with members as given in the component types T1,,Tn and the refinement { $R$ }. A refinement { $R$ } contains declarations and type definitions. If a declaration or definition overrides a declaration or definition in one of the component types T1,,Tn, the usual rules for overriding apply; otherwise the declaration or definition is said to be “structural”.2

Within a method declaration in a structural refinement, the type of any value parameter may only refer to type parameters or abstract types that are contained inside the refinement. That is, it must refer either to a type parameter of the method itself, or to a type definition within the refinement. This restriction does not apply to the function's result type.

If no refinement is given, the empty refinement is implicitly added, i.e.  $T_1$ withwith $T_n$ is a shorthand for $T_1$ withwith $T_n$ {}.

A compound type may also consist of just a refinement { $R$ } with no preceding component types. Such a type is equivalent to AnyRef{ R }.

  1. The following example shows how to declare and use a function which parameter's type contains a refinement with structural declarations.

    case class Bird (val name: String) extends Object {
        def fly(height: Int) = …
    …
    }
    case class Plane (val callsign: String) extends Object {
        def fly(height: Int) = …
    …
    }
    def takeoff(
            runway: Int,
          r: { val callsign: String; def fly(height: Int) }) = {
      tower.print(r.callsign + " requests take-off on runway " + runway)
      tower.read(r.callsign + " is clear for take-off")
      r.fly(1000)
    }
    val bird = new Bird("Polly the parrot"){ val callsign = name }
    val a380 = new Plane("TZ-987")
    takeoff(42, bird)
    takeoff(89, a380)

    Although Bird and Plane do not share any parent class other than Object, the parameter r of function takeoff is defined using a refinement with structural declarations to accept any object that declares a value callsign and a fly function.

3.2.8 Infix Types

InfixType     ::=  CompoundType {id [nl] CompoundType}

An infix type $T_1$ \mathit{op} $T_2$ consists of an infix operator op which gets applied to two type operands T1 and T2. The type is equivalent to the type application $\mathit{op}$[$T_1$, $T_2$]. The infix operator op may be an arbitrary identifier, except for *, which is reserved as a postfix modifier denoting a repeated parameter type.

All type infix operators have the same precedence; parentheses have to be used for grouping. The associativity of a type operator is determined as for term operators: type operators ending in a colon ‘:’ are right-associative; all other operators are left-associative.

In a sequence of consecutive type infix operations t0opt1op_2op_ntn, all operators op1,,opn must have the same associativity. If they are all left-associative, the sequence is interpreted as ((t0op_1t1)op_2)op_ntn, otherwise it is interpreted as t0op_1(t1op_2(op_ntn)).

3.2.9 Function Types

Type              ::=  FunctionArgs ‘=>’ Type
FunctionArgs      ::=  InfixType
                    |  ‘(’ [ ParamType {‘,’ ParamType } ] ‘)’

The type (T1,,Tn)U represents the set of function values that take arguments of types T1,,Tn and yield results of type U. In the case of exactly one argument type TU is a shorthand for (T)U.
An argument type of the form T represents a call-by-name parameter of type T.

Function types associate to the right, e.g. STU is the same as S(TU).

Function types are shorthands for class types that define apply functions. Specifically, the n-ary function type (T1,,Tn)U is a shorthand for the class type Function$_n$[T1 , … , $T_n$, U]. Such class types are defined in the Scala library for n between 0 and 9 as follows.

package scala 
trait Function_n[-T1 , … , -T$_n$, +R] {
  def apply(x1: T1 , … , x$_n$: T$_n$): R 
  override def toString = "<function>" 
}

Hence, function types are covariant in their result type and contravariant in their argument types.

3.2.10 Existential Types

Type               ::= InfixType ExistentialClauses
ExistentialClauses ::= ‘forSome’ ‘{’ ExistentialDcl 
                       {semi ExistentialDcl} ‘}’
ExistentialDcl     ::= ‘type’ TypeDcl 
                    |  ‘val’ ValDcl

An existential type has the form $T$ forSome { $Q$ } where Q is a sequence of type declarations.

Let t1[tps1]>:L1<:U1,,tn[tpsn]>:Ln<:Un be the types declared in Q (any of the type parameter sections [ $\mathit{tps}_i$ ] might be missing). The scope of each type ti includes the type T and the existential clause Q. The type variables ti are said to be bound in the type $T$ forSome { $Q$ }. Type variables which occur in a type T but which are not bound in T are said to be free in T.

A type instance of $T$ forSome { $Q$ } is a type σT where σ is a substitution over t1,,tn such that, for each i, σLi<:σti<:σUi. The set of values denoted by the existential type $T$ forSome {$\,Q\,$} is the union of the set of values of all its type instances.

A skolemization of $T$ forSome { $Q$ } is a type instance σT, where σ is the substitution [tʹ1/t1,,tʹn/tn] and each tʹi is a fresh abstract type with lower bound σLi and upper bound σUi.

3.2.10.1 Simplification Rules

Existential types obey the following four equivalences:

  1. Multiple for-clauses in an existential type can be merged. E.g., $T$ forSome { $Q$ } forSome { $Q'$ } is equivalent to $T$ forSome { $Q$ ; $Q'$}.
  2. Unused quantifications can be dropped. E.g., $T$ forSome { $Q$ ; $Q'$} where none of the types defined in Qʹ are referred to by T or Q, is equivalent to $T$ forSome {$ Q $}.
  3. An empty quantification can be dropped. E.g., $T$ forSome { } is equivalent to T.
  4. An existential type $T$ forSome { $Q$ } where Q contains a clause type $t[\mathit{tps}] >: L <: U$ is equivalent to the type $T'$ forSome { $Q$ } where Tʹ results from T by replacing every covariant occurrence of t in T by U and by replacing every contravariant occurrence of t in T by L.

3.2.10.2 Existential Quantification over Values

As a syntactic convenience, the bindings clause in an existential type may also contain value declarations val $x$: $T$. An existential type $T$ forSome { $Q$; val $x$: $S\,$;$\,Q'$ } is treated as a shorthand for the type $T'$ forSome { $Q$; type $t$ <: $S$ with Singleton; $Q'$ }, where t is a fresh type name and Tʹ results from T by replacing every occurrence of $x$.type with t.

3.2.10.3 Placeholder Syntax for Existential Types

WildcardType   ::=  ‘_’ TypeBounds

Scala supports a placeholder syntax for existential types. A wildcard type is of the form _$\;$>:$\,L\,$<:$\,U$. Both bound clauses may be omitted. If a lower bound clause >:$\,L$ is missing, >:$\,$scala.Nothing is assumed. If an upper bound clause <:$\,U$ is missing, <:$\,$scala.Any is assumed. A wildcard type is a shorthand for an existentially quantified type variable, where the existential quantification is implicit.

A wildcard type must appear as type argument of a parameterized type. Let T=p.c[targs,T,targsʹ] be a parameterized type where targs,targsʹ may be empty and T is a wildcard type _$\;$>:$\,L\,$<:$\,U$. Then T is equivalent to the existential type

$p.c[\mathit{targs},t,\mathit{targs}']$ forSome { type $t$ >: $L$ <: $U$ }

where t is some fresh type variable. Wildcard types may also appear as parts of infix types , function types, or tuple types. Their expansion is then the expansion in the equivalent parameterized type.

  1. Assume the class definitions

    class Ref[T]
    abstract class Outer { type T } .

    Here are some examples of existential types:

    Ref[T] forSome { type T <: java.lang.Number }
    Ref[x.T] forSome { val x: Outer }
    Ref[x_type # T] forSome { type x_type <: Outer with Singleton }

    The last two types in this list are equivalent. An alternative formulation of the first type above using wildcard syntax is:

    Ref[_ <: java.lang.Number]
  2. The type List[List[_]] is equivalent to the existential type

    List[List[t] forSome { type t }] . 
  3. Assume a covariant type

    class List[+T]

    The type

    List[T] forSome { type T <: java.lang.Number }

    is equivalent (by simplification rule 4 above) to

    List[java.lang.Number] forSome { type T <: java.lang.Number }

    which is in turn equivalent (by simplification rules 2 and 3 above) to List[java.lang.Number].

3.3 Non-Value Types

The types explained in the following do not denote sets of values, nor do they appear explicitly in programs. They are introduced in this report as the internal types of defined identifiers.

3.3.1 Method Types

A method type is denoted internally as (Ps)U, where (Ps) is a sequence of parameter names and types (p1:T1,,pn:Tn) for some n0 and U is a (value or method) type. This type represents named methods that take arguments named p1,,pn of types T1,,Tn and that return a result of type U.

Method types associate to the right: (Ps1)(Ps2)U is treated as (Ps1)((Ps2)U).

A special case are types of methods without any parameters. They are written here => T. Parameterless methods name expressions that are re-evaluated each time the parameterless method name is referenced.

Method types do not exist as types of values. If a method name is used as a value, its type is implicitly converted to a corresponding function type.

  1. The declarations

    def a: Int
    def b (x: Int): Boolean
    def c (x: Int) (y: String, z: String): String

    produce the typings

    a: => Int
    b: (Int) Boolean
    c: (Int) (String, String) String

3.3.2 Polymorphic Method Types

A polymorphic method type is denoted internally as [$\mathit{tps}\,$]$T$ where [$\mathit{tps}\,$] is a type parameter section [$a_1$ >: $L_1$ <: $U_1 , \ldots , a_n$ >: $L_n$ <: $U_n$] for some n0 and T is a (value or method) type. This type represents named methods that take type arguments $S_1 , \ldots , S_n$ which conform to the lower bounds $L_1 , \ldots , L_n$ and the upper bounds $U_1 , \ldots , U_n$ and that yield results of type T.

  1. The declarations

    def empty[A]: List[A]
    def union[A <: Comparable[A]] (x: Set[A], xs: Set[A]): Set[A]

    produce the typings

    empty : [A >: Nothing <: Any] List[A]
    union : [A >: Nothing <: Comparable[A]] (x: Set[A], xs: Set[A]) Set[A]  .

3.3.3 Type Constructors

A type constructor is represented internally much like a polymorphic method type. [$\pm$ $a_1$ >: $L_1$ <: $U_1 , \ldots , \pm a_n$ >: $L_n$ <: $U_n$] $T$ represents a type that is expected by a type constructor parameter or an abstract type constructor binding with the corresponding type parameter clause.

  1. Consider this fragment of the Iterable[+X] class:

    trait Iterable[+X] {
      def flatMap[newType[+X] <: Iterable[X], S](f: X => newType[S]): newType[S]
    }

    Conceptually, the type constructor Iterable is a name for the anonymous type [+X] Iterable[X], which may be passed to the newType type constructor parameter in flatMap.

3.4 Base Types and Member Definitions

Types of class members depend on the way the members are referenced. Central here are three notions, namely: #. the notion of the set of base types of a type T, #. the notion of a type T in some class C seen from some prefix type S, #. the notion of the set of member bindings of some type T.

These notions are defined mutually recursively as follows.

  1. The set of base types of a type is a set of class types, given as follows.

    • The base types of a class type C with parents T1,,Tn are C itself, as well as the base types of the compound type $T_1$ with … with $T_n$ { $R$ }.
    • The base types of an aliased type are the base types of its alias.
    • The base types of an abstract type are the base types of its upper bound.
    • The base types of a parameterized type $C$[$T_1 , \ldots , T_n$] are the base types of type C, where every occurrence of a type parameter ai of C has been replaced by the corresponding parameter type Ti.
    • The base types of a singleton type $p$.type are the base types of the type of p.
    • The base types of a compound type $T_1$ with $\ldots$ with $T_n$ { $R$ } are the reduced union of the base classes of all Ti's. This means: Let the multi-set 𝒮 be the multi-set-union of the base types of all Ti's. If 𝒮 contains several type instances of the same class, say $S^i$#$C$[$T^i_1 , \ldots , T^i_n$] (iI), then all those instances are replaced by one of them which conforms to all others. It is an error if no such instance exists. It follows that the reduced union, if it exists, produces a set of class types, where different types are instances of different classes.
    • The base types of a type selection $S$#$T$ are determined as follows. If T is an alias or abstract type, the previous clauses apply. Otherwise, T must be a (possibly parameterized) class type, which is defined in some class B. Then the base types of $S$#$T$ are the base types of T in B seen from the prefix type S.
    • The base types of an existential type $T$ forSome { $Q$ } are all types $S$ forSome { $Q$ } where S is a base type of T.
  2. The notion of a type T in class C seen from some prefix type S makes sense only if the prefix type S has a type instance of class C as a base type, say $S'$#$C$[$T_1 , \ldots , T_n$]. Then we define as follows.
    • If $S$ = $\epsilon$.type, then T in C seen from S is T itself.
    • Otherwise, if S is an existential type $S'$ forSome { $Q$ }, and T in C seen from Sʹ is Tʹ, then T in C seen from S is $T'$ forSome {$\,Q\,$}.
    • Otherwise, if T is the i'th type parameter of some class D, then
      • If S has a base type $D$[$U_1 , \ldots , U_n$], for some type parameters [$U_1 , \ldots , U_n$], then T in C seen from S is Ui.
      • Otherwise, if C is defined in a class Cʹ, then T in C seen from S is the same as T in Cʹ seen from Sʹ.
      • Otherwise, if C is not defined in another class, then
        T in C seen from S is T itself.
    • Otherwise, if T is the singleton type $D$.this.type for some class D then
      • If D is a subclass of C and S has a type instance of class D among its base types, then T in C seen from S is S.
      • Otherwise, if C is defined in a class Cʹ, then T in C seen from S is the same as T in Cʹ seen from Sʹ.
      • Otherwise, if C is not defined in another class, then
        T in C seen from S is T itself.
    • If T is some other type, then the described mapping is performed to all its type components.

    If T is a possibly parameterized class type, where T's class is defined in some other class D, and S is some prefix type, then we use $T$ seen from $S$'' as a shorthand forT in D seen from S''.

  3. The member bindings of a type T are (1) all bindings d such that there exists a type instance of some class C among the base types of T and there exists a definition or declaration dʹ in C such that d results from dʹ by replacing every type Tʹ in dʹ by Tʹ in C seen from T, and (2) all bindings of the type's refinement, if it has one.

The definition of a type projection $S$#$t$ is the member binding dt of the type t in S. In that case, we also say that ~S#t` is defined by dt. share a to

3.5 Relations between types

We define two relations between types.

Type equivalence TU T and U are interchangeable in all contexts.
Conformance T<:U Type T conforms to type U.

3.5.1 Type Equivalence

Equivalence () between types is the smallest congruence3 such that the following holds:

3.5.2 Conformance

The conformance relation (<:) is the smallest transitive relation that satisfies the following conditions.

A declaration or definition in some compound type of class type C subsumes another declaration of the same name in some compound type or class type Cʹ, if one of the following holds.

The (<:) relation forms pre-order between types, i.e. it is transitive and reflexive. least upper bounds and greatest lower bounds of a set of types are understood to be relative to that order.

Note: The least upper bound or greatest lower bound of a set of types does not always exist. For instance, consider the class definitions

class A[+T] {}
class B extends A[B]
class C extends A[C]

Then the types A[Any], A[A[Any]], A[A[A[Any]]], ... form a descending sequence of upper bounds for B and C. The least upper bound would be the infinite limit of that sequence, which does not exist as a Scala type. Since cases like this are in general impossible to detect, a Scala compiler is free to reject a term which has a type specified as a least upper or greatest lower bound, and that bound would be more complex than some compiler-set limit.4

The least upper bound or greatest lower bound might also not be unique. For instance A with B and B with A are both greatest lower of A and B. If there are several least upper bounds or greatest lower bounds, the Scala compiler is free to pick any one of them.

3.5.3 Weak Conformance

In some situations Scala uses a more general conformance relation. A type S weakly conforms to a type T, written S<:wT, if S<:T or both S and T are primitive number types and S precedes T in the following ordering.

Byte  $<:_w$ Short 
Short $<:_w$ Int
Char  $<:_w$ Int
Int   $<:_w$ Long
Long  $<:_w$ Float
Float $<:_w$ Double

A weak least upper bound is a least upper bound with respect to weak conformance.

3.6 Volatile Types

Type volatility approximates the possibility that a type parameter or abstract type instance of a type does not have any non-null values. A value member of a volatile type cannot appear in a path.

A type is volatile if it falls into one of four categories:

A compound type $T_1$ with … with $T_n$ {$R\,$} is volatile if one of the following two conditions hold.

  1. One of T2,,Tn is a type parameter or abstract type, or
  2. T1 is an abstract type and and either the refinement R or a type Tj for j>1 contributes an abstract member to the compound type, or
  3. one of T1,,Tn is a singleton type.

Here, a type S contributes an abstract member to a type T if S contains an abstract member that is also a member of T. A refinement R contributes an abstract member to a type T if R contains an abstract declaration which is also a member of T.

A type designator is volatile if it is an alias of a volatile type, or if it designates a type parameter or abstract type that has a volatile type as its upper bound.

A singleton type $p$.type is volatile, if the underlying type of path p is volatile.

An existential type $T$ forSome {$\,Q\,$} is volatile if T is volatile.

3.7 Type Erasure

A type is called generic if it contains type arguments or type variables. Type erasure is a mapping from (possibly generic) types to non-generic types. We write T for the erasure of type T. The erasure mapping is defined as follows.

The intersection dominator of a list of types T1,,Tn is computed as follows. Let Ti1,,Tim be the subsequence of types Ti
which are not supertypes of some other type Tj. If this subsequence contains a type designator Tc that refers to a class which is not a trait, the intersection dominator is Tc. Otherwise, the intersection dominator is the first element of the subsequence, Ti1.

4 Basic Declarations and Definitions

Dcl         ::=  ‘val’ ValDcl
              |  ‘var’ VarDcl
              |  ‘def’ FunDcl
              |  ‘type’ {nl} TypeDcl
PatVarDef   ::=  ‘val’ PatDef
              |  ‘var’ VarDef
Def         ::=  PatVarDef
              |  ‘def’ FunDef
              |  ‘type’ {nl} TypeDef
              |  TmplDef

A declaration introduces names and assigns them types. It can form part of a class definition or of a refinement in a compound type.

A definition introduces names that denote terms or types. It can form part of an object or class definition or it can be local to a block. Both declarations and definitions produce bindings that associate type names with type definitions or bounds, and that associate term names with types.

The scope of a name introduced by a declaration or definition is the whole statement sequence containing the binding. However, there is a restriction on forward references in blocks: In a statement sequence s1sn making up a block, if a simple name in si refers to an entity defined by sj where ji, then for all sk between and including si and sj,

4.1 Value Declarations and Definitions

Dcl          ::=  ‘val’ ValDcl
ValDcl       ::=  ids ‘:’ Type
PatVarDef    ::=  ‘val’ PatDef 
PatDef       ::=  Pattern2 {‘,’ Pattern2} [‘:’ Type] ‘=’ Expr
ids          ::=  id {‘,’ id}

A value declaration val $x$: $T$ introduces x as a name of a value of type T.

A value definition val $x$: $T$ = $e$ defines x as a name of the value that results from the evaluation of e. If the value definition is not recursive, the type T may be omitted, in which case the packed type of expression e is assumed. If a type T is given, then e is expected to conform to it.

Evaluation of the value definition implies evaluation of its right-hand side e, unless it has the modifier lazy. The effect of the value definition is to bind x to the value of e converted to type T. A lazy value definition evaluates its right hand side e the first time the value is accessed.

A constant value definition is of the form

final val x = e

where e is a constant expression. The final modifier must be present and no type annotation may be given. References to the constant value x are themselves treated as constant expressions; in the generated code they are replaced by the definition's right-hand side e.

Value definitions can alternatively have a pattern as left-hand side. If p is some pattern other than a simple name or a name followed by a colon and a type, then the value definition val $p$ = $e$ is expanded as follows:

  1. If the pattern p has bound variables x1,,xn, where n>1:
val $\$ x$ = $e$ match {case $p$ => ($x_1 , \ldots , x_n$)}
val $x_1$ = $\$ x$._1
$\ldots$
val $x_n$ = $\$ x$._n  .

Here, $x is a fresh name.

  1. If p has a unique bound variable x:
val $x$ = $e$ match { case $p$ => $x$ }
  1. If p has no bound variables:
$e$ match { case $p$ => ()}
  1. The following are examples of value definitions

    val pi = 3.1415 
    val pi: Double = 3.1415   // equivalent to first definition
    val Some(x) = f()         // a pattern definition
    val x :: xs = mylist      // an infix pattern definition

    The last two definitions have the following expansions.

    val x = f() match { case Some(x) => x }
    
    val x$\$$ = mylist match { case x :: xs => (x, xs) }
    val x = x$\$$._1 
    val xs = x$\$$._2 

The name of any declared or defined value may not end in _=.

A value declaration val $x_1 , \ldots , x_n$: $T$ is a shorthand for the sequence of value declarations val $x_1$: $T$; ...; val $x_n$: $T$. A value definition val $p_1 , \ldots , p_n$ = $e$ is a shorthand for the sequence of value definitions val $p_1$ = $e$; ...; val $p_n$ = $e$. A value definition val $p_1 , \ldots , p_n: T$ = $e$ is a shorthand for the sequence of value definitions val $p_1: T$ = $e$; ...; val $p_n: T$ = $e$.

4.2 Variable Declarations and Definitions

Dcl            ::=  ‘var’ VarDcl
PatVarDef      ::=  ‘var’ VarDef
VarDcl         ::=  ids ‘:’ Type
VarDef         ::=  PatDef
                 |  ids ‘:’ Type ‘=’ ‘_’

A variable declaration var $x$: $T$ is equivalent to declarations of a getter function x and a setter function $x$_=, defined as follows:

def $x$: $T$ 
def $x$_= ($y$: $T$): Unit

An implementation of a class containing variable declarations may define these variables using variable definitions, or it may define setter and getter functions directly.

A variable definition var $x$: $T$ = $e$ introduces a mutable variable with type T and initial value as given by the expression e. The type T can be omitted, in which case the type of e is assumed. If T is given, then e is expected to conform to it.

Variable definitions can alternatively have a pattern as left-hand side. A variable definition var $p$ = $e$ where p is a pattern other than a simple name or a name followed by a colon and a type is expanded in the same way as a value definition val $p$ = $e$, except that the free names in p are introduced as mutable variables, not values.

The name of any declared or defined variable may not end in _=.

A variable definition var $x$: $T$ = _ can appear only as a member of a template. It introduces a mutable field with type  T and a default initial value. The default value depends on the type T as follows:

0 if T is Int or one of its subrange types
0L if T is Long
0.0f if T is Float
0.0d if T is Double
false if T is Boolean
() if T is Unit
null for all other types T

When they occur as members of a template, both forms of variable definition also introduce a getter function x which returns the value currently assigned to the variable, as well as a setter function $x$_= which changes the value currently assigned to the variable. The functions have the same signatures as for a variable declaration. The template then has these getter and setter functions as members, whereas the original variable cannot be accessed directly as a template member.

  1. The following example shows how properties can be simulated in Scala. It defines a class TimeOfDayVar of time values with updatable integer fields representing hours, minutes, and seconds. Its implementation contains tests that allow only legal values to be assigned to these fields. The user code, on the other hand, accesses these fields just like normal variables.

    class TimeOfDayVar {
      private var h: Int = 0 
      private var m: Int = 0 
      private var s: Int = 0 
    
      def hours              =  h 
      def hours_= (h: Int)   =  if (0 <= h && h < 24) this.h = h 
                                else throw new DateError() 
    
      def minutes            =  m 
      def minutes_= (m: Int) =  if (0 <= m && m < 60) this.m = m
                                else throw new DateError() 
    
      def seconds            =  s 
      def seconds_= (s: Int) =  if (0 <= s && s < 60) this.s = s
                                else throw new DateError() 
    }
    val d = new TimeOfDayVar 
    d.hours = 8; d.minutes = 30; d.seconds = 0 
    d.hours = 25                  // throws a DateError exception

A variable declaration var $x_1 , \ldots , x_n$: $T$ is a shorthand for the sequence of variable declarations var $x_1$: $T$; ...; var $x_n$: $T$. A variable definition var $x_1 , \ldots , x_n$ = $e$ is a shorthand for the sequence of variable definitions var $x_1$ = $e$; ...; var $x_n$ = $e$. A variable definition var $x_1 , \ldots , x_n: T$ = $e$ is a shorthand for the sequence of variable definitions var $x_1: T$ = $e$; ...; var $x_n: T$ = $e$.

4.3 Type Declarations and Type Aliases

Dcl        ::=  ‘type’ {nl} TypeDcl
TypeDcl    ::=  id [TypeParamClause] [‘>:’ Type] [‘<:’ Type]
Def        ::=  type {nl} TypeDef
TypeDef    ::=  id [TypeParamClause] ‘=’ Type

A type declaration type $t$[$\mathit{tps}\,$] >: $L$ <: $U$ declares t to be an abstract type with lower bound type L and upper bound type U. If the type parameter clause [$\mathit{tps}\,$] is omitted, t abstracts over a first-order type, otherwise t stands for a type constructor that accepts type arguments as described by the type parameter clause.

If a type declaration appears as a member declaration of a type, implementations of the type may implement t with any type T for which L<:T<:U. It is a compile-time error if L does not conform to U. Either or both bounds may be omitted. If the lower bound L is absent, the bottom type scala.Nothing is assumed. If the upper bound U is absent, the top type scala.Any is assumed.

A type constructor declaration imposes additional restrictions on the concrete types for which t may stand. Besides the bounds L and U, the type parameter clause may impose higher-order bounds and variances, as governed by the conformance of type constructors.

The scope of a type parameter extends over the bounds >: $L$ <: $U$ and the type parameter clause tps itself. A higher-order type parameter clause (of an abstract type constructor tc) has the same kind of scope, restricted to the declaration of the type parameter tc.

To illustrate nested scoping, these declarations are all equivalent: type t[m[x] <: Bound[x], Bound[x]], type t[m[x] <: Bound[x], Bound[y]] and type t[m[x] <: Bound[x], Bound[_]], as the scope of, e.g., the type parameter of m is limited to the declaration of m. In all of them, t is an abstract type member that abstracts over two type constructors: m stands for a type constructor that takes one type parameter and that must be a subtype of Bound, t's second type constructor parameter. t[MutableList, Iterable] is a valid use of t.

A type alias type $t$ = $T$ defines t to be an alias name for the type T. The left hand side of a type alias may have a type parameter clause, e.g. type $t$[$\mathit{tps}\,$] = $T$. The scope of a type parameter extends over the right hand side T and the type parameter clause tps itself.

The scope rules for definitions and type parameters make it possible that a type name appears in its own bound or in its right-hand side. However, it is a static error if a type alias refers recursively to the defined type constructor itself.
That is, the type T in a type alias type $t$[$\mathit{tps}\,$] = $T$ may not refer directly or indirectly to the name t. It is also an error if an abstract type is directly or indirectly its own upper or lower bound.

  1. The following are legal type declarations and definitions:

    type IntList = List[Integer]
    type T <: Comparable[T]
    type Two[A] = Tuple2[A, A]
    type MyCollection[+X] <: Iterable[X]

    The following are illegal:

    type Abs = Comparable[Abs]      // recursive type alias
    
    type S <: T                     // S, T are bounded by themselves.
    type T <: S
    
    type T >: Comparable[T.That]    // Cannot select from T.
                                    // T is a type, not a value
    type MyCollection <: Iterable   // Type constructor members must explicitly 
                                    // state their type parameters.

If a type alias type $t$[$\mathit{tps}\,$] = $S$ refers to a class type S, the name t can also be used as a constructor for objects of type S.

  1. The Predef object contains a definition which establishes Pair as an alias of the parameterized class Tuple2:

    type Pair[+A, +B] = Tuple2[A, B] 
    object Pair {
      def apply[A, B](x: A, y: B) = Tuple2(x, y)
      def unapply[A, B](x: Tuple2[A, B]): Option[Tuple2[A, B]] = Some(x)
    }

    As a consequence, for any two types S and T, the type Pair[$S$, $T\,$] is equivalent to the type Tuple2[$S$, $T\,$]. Pair can also be used as a constructor instead of Tuple2, as in:

    val x: Pair[Int, String] = new Pair(1, "abc")

4.4 Type Parameters

TypeParamClause  ::= ‘[’ VariantTypeParam {‘,’ VariantTypeParam} ‘]’
VariantTypeParam ::= {Annotation} [‘+’ | ‘-’] TypeParam
TypeParam        ::= (id | ‘_’) [TypeParamClause] [‘>:’ Type] [‘<:’ Type] [‘:’ Type]

Type parameters appear in type definitions, class definitions, and function definitions. In this section we consider only type parameter definitions with lower bounds >: $L$ and upper bounds <: $U$ whereas a discussion of context bounds : $U$ and view bounds <% $U$ is deferred to here.

The most general form of a first-order type parameter is $@a_1 \ldots @a_n$ $\pm$ $t$ >: $L$ <: $U$. Here, L, and U are lower and upper bounds that constrain possible type arguments for the parameter. It is a compile-time error if L does not conform to U. ± is a variance, i.e. an optional prefix of either +, or -. One or more annotations may precede the type parameter.

The names of all type parameters must be pairwise different in their enclosing type parameter clause. The scope of a type parameter includes in each case the whole type parameter clause. Therefore it is possible that a type parameter appears as part of its own bounds or the bounds of other type parameters in the same clause. However, a type parameter may not be bounded directly or indirectly by itself.
A type constructor parameter adds a nested type parameter clause to the type parameter. The most general form of a type constructor parameter is $@a_1\ldots@a_n$ $\pm$ $t[\mathit{tps}\,]$ >: $L$ <: $U$.

The above scoping restrictions are generalized to the case of nested type parameter clauses, which declare higher-order type parameters. Higher-order type parameters (the type parameters of a type parameter t) are only visible in their immediately surrounding parameter clause (possibly including clauses at a deeper nesting level) and in the bounds of t. Therefore, their names must only be pairwise different from the names of other visible parameters. Since the names of higher-order type parameters are thus often irrelevant, they may be denoted with a ‘_’, which is nowhere visible.

  1. Here are some well-formed type parameter clauses:

    [S, T]
    [@specialized T, U]
    [Ex <: Throwable]
    [A <: Comparable[B], B <: A]
    [A, B >: A, C >: A <: B]
    [M[X], N[X]]
    [M[_], N[_]] // equivalent to previous clause
    [M[X <: Bound[X]], Bound[_]]
    [M[+X] <: Iterable[X]]

    The following type parameter clauses are illegal:

    [A >: A]                  // illegal, `A' has itself as bound
    [A <: B, B <: C, C <: A]  // illegal, `A' has itself as bound
    [A, B, C >: A <: B]       // illegal lower bound `A' of `C' does
                              // not conform to upper bound `B'.

4.5 Variance Annotations

Variance annotations indicate how instances of parameterized types vary with respect to subtyping. A ‘+’ variance indicates a covariant dependency, a ‘-’ variance indicates a contravariant dependency, and a missing variance indication indicates an invariant dependency.

A variance annotation constrains the way the annotated type variable may appear in the type or class which binds the type parameter. In a type definition type $T$[$\mathit{tps}\,$] = $S$, or a type declaration type $T$[$\mathit{tps}\,$] >: $L$ <: $U$ type parameters labeled ‘+’ must only appear in covariant position whereas type parameters labeled ‘-’ must only appear in contravariant position. Analogously, for a class definition class $C$[$\mathit{tps}\,$]($\mathit{ps}\,$) extends $T$ { $x$: $S$ => ...}, type parameters labeled ‘+’ must only appear in covariant position in the self type S and the template T, whereas type parameters labeled ‘-’ must only appear in contravariant position.

The variance position of a type parameter in a type or template is defined as follows. Let the opposite of covariance be contravariance, and the opposite of invariance be itself. The top-level of the type or template is always in covariant position. The variance position changes at the following constructs.

References to the type parameters in object-private or object-protected values, variables, or methods of the class are not checked for their variance position. In these members the type parameter may appear anywhere without restricting its legal variance annotations.

  1. The following variance annotation is legal.

    abstract class P[+A, +B] {
      def fst: A; def snd: B
    }

    With this variance annotation, type instances of P subtype covariantly with respect to their arguments. For instance,

    P[IOException, String] <: P[Throwable, AnyRef]

    If the members of P are mutable variables, the same variance annotation becomes illegal.

    abstract class Q[+A, +B](x: A, y: B) { 
      var fst: A = x           // **** error: illegal variance:
      var snd: B = y           // `A', `B' occur in invariant position.
    }

    If the mutable variables are object-private, the class definition becomes legal again:

    abstract class R[+A, +B](x: A, y: B) { 
      private[this] var fst: A = x        // OK
      private[this] var snd: B = y        // OK
    }
  2. The following variance annotation is illegal, since a appears in contravariant position in the parameter of append:

    abstract class Sequence[+A] {
      def append(x: Sequence[A]): Sequence[A]  
                      // **** error: illegal variance: 
                      // `A' occurs in contravariant position.
    }

    The problem can be avoided by generalizing the type of append by means of a lower bound:

    abstract class Sequence[+A] {
      def append[B >: A](x: Sequence[B]): Sequence[B] 
    }
  3. Here is a case where a contravariant type parameter is useful.

    abstract class OutputChannel[-A] {
      def write(x: A): Unit
    }

    With that annotation, we have that OutputChannel[AnyRef] conforms to OutputChannel[String].
    That is, a channel on which one can write any object can substitute for a channel on which one can write only strings.

4.6 Function Declarations and Definitions

Dcl                ::=  ‘def’ FunDcl
FunDcl             ::=  FunSig ‘:’ Type
Def                ::=  ‘def’ FunDef
FunDef             ::=  FunSig [‘:’ Type] ‘=’ Expr 
FunSig             ::=  id [FunTypeParamClause] ParamClauses
FunTypeParamClause ::=  ‘[’ TypeParam {‘,’ TypeParam} ‘]’ 
ParamClauses       ::=  {ParamClause} [[nl] ‘(’ ‘implicit’ Params ‘)’]
ParamClause        ::=  [nl] ‘(’ [Params] ‘)’} 
Params             ::=  Param {‘,’ Param}
Param              ::=  {Annotation} id [‘:’ ParamType] [‘=’ Expr]
ParamType          ::=  Type 
                     |  ‘=>’ Type 
                     |  Type ‘*’

A function declaration has the form def $f\,\mathit{psig}$: $T$, where f is the function's name, psig is its parameter signature and T is its result type. A function definition def $f\,\mathit{psig}$: $T$ = $e$ also includes a function body e, i.e. an expression which defines the function's result. A parameter signature consists of an optional type parameter clause [$\mathit{tps}\,$], followed by zero or more value parameter clauses ($\mathit{ps}_1$)$\ldots$($\mathit{ps}_n$). Such a declaration or definition introduces a value with a (possibly polymorphic) method type whose parameter types and result type are as given.

The type of the function body is expected to conform to the function's declared result type, if one is given. If the function definition is not recursive, the result type may be omitted, in which case it is determined from the packed type of the function body.

A type parameter clause tps consists of one or more type declarations, which introduce type parameters, possibly with bounds. The scope of a type parameter includes the whole signature, including any of the type parameter bounds as well as the function body, if it is present.

A value parameter clause ps consists of zero or more formal parameter bindings such as $x$: $T$ or $x: T = e$, which bind value parameters and associate them with their types. Each value parameter declaration may optionally define a default argument. The default argument expression e is type-checked with an expected type Tʹ obtained by replacing all occurences of the function's type parameters in T by the undefined type.

For every parameter pi,j with a default argument a method named $f\$$default$\$$n is generated which computes the default argument expression. Here, n denotes the parameter's position in the method declaration. These methods are parametrized by the type parameter clause [$\mathit{tps}\,$] and all value parameter clauses ($\mathit{ps}_1$)$\ldots$($\mathit{ps}_{i-1}$) preceeding pi,j. The $f\$$default$\$$n methods are inaccessible for user programs.

The scope of a formal value parameter name x comprises all subsequent parameter clauses, as well as the method return type and the function body, if they are given.5 Both type parameter names and value parameter names must be pairwise distinct.

  1. In the method

    def compare[T](a: T = 0)(b: T = a) = (a == b)

    the default expression 0 is type-checked with an undefined expected type. When applying compare(), the default value 0 is inserted and T is instantiated to Int. The methods computing the default arguments have the form:

    def compare$\$$default$\$$1[T]: Int = 0
    def compare$\$$default$\$$2[T](a: T): T = a

4.6.1 By-Name Parameters

ParamType          ::=  ‘=>’ Type

The type of a value parameter may be prefixed by =>, e.g.
$x$: => $T$. The type of such a parameter is then the parameterless method type => $T$. This indicates that the corresponding argument is not evaluated at the point of function application, but instead is evaluated at each use within the function. That is, the argument is evaluated using call-by-name.

The by-name modifier is disallowed for parameters of classes that carry a val or var prefix, including parameters of case classes for which a val prefix is implicitly generated. The by-name modifier is also disallowed for implicit parameters.

  1. The declaration

    def whileLoop (cond: => Boolean) (stat: => Unit): Unit

    indicates that both parameters of whileLoop are evaluated using call-by-name.

4.6.2 Repeated Parameters

ParamType          ::=  Type ‘*’

The last value parameter of a parameter section may be suffixed by “*”, e.g. (..., $x$:$T$*). The type of such a repeated parameter inside the method is then the sequence type scala.Seq[$T$]. Methods with repeated parameters $T$* take a variable number of arguments of type T. That is, if a method m with type ($p_1:T_1 , \ldots , p_n:T_n, p_s:S$*)$U$ is applied to arguments (e1,,ek) where kn, then m is taken in that application to have type (p1:T1,,pn:Tn,ps:S,,psʹS)U, with kn occurrences of type S where any parameter names beyond ps are fresh. The only exception to this rule is if the last argument is marked to be a sequence argument via a _* type annotation. If m above is applied to arguments ($e_1 , \ldots , e_n, e'$: _*), then the type of m in that application is taken to be ($p_1:T_1, \ldots , p_n:T_n,p_{s}:$scala.Seq[$S$]).

It is not allowed to define any default arguments in a parameter section with a repeated parameter.

  1. The following method definition computes the sum of the squares of a variable number of integer arguments.

    def sum(args: Int*) = {
      var result = 0
      for (arg <- args) result += arg * arg
      result
    }

    The following applications of this method yield 0, 1, 6, in that order.

    sum()
    sum(1)
    sum(1, 2, 3)

    Furthermore, assume the definition:

    val xs = List(1, 2, 3)

    The following application of method sum is ill-formed:

    sum(xs)       // ***** error: expected: Int, found: List[Int]

    By contrast, the following application is well formed and yields again the result 6:

    sum(xs: _*) 

4.6.3 Procedures

FunDcl   ::=  FunSig
FunDef   ::=  FunSig [nl] ‘{’ Block ‘}’

Special syntax exists for procedures, i.e. functions that return the Unit value (). A procedure declaration is a function declaration where the result type is omitted. The result type is then implicitly completed to the Unit type. E.g., def $f$($\mathit{ps}$) is equivalent to def $f$($\mathit{ps}$): Unit.

A procedure definition is a function definition where the result type and the equals sign are omitted; its defining expression must be a block. E.g., def $f$($\mathit{ps}$) {$\mathit{stats}$} is equivalent to def $f$($\mathit{ps}$): Unit = {$\mathit{stats}$}.

  1. Here is a declaration and a definition of a procedure named write:

    trait Writer { 
      def write(str: String)
    }
    object Terminal extends Writer {
      def write(str: String) { System.out.println(str) }
    }

    The code above is implicitly completed to the following code:

    trait Writer { 
      def write(str: String): Unit
    }
    object Terminal extends Writer {
      def write(str: String): Unit = { System.out.println(str) }
    }

4.6.4 Method Return Type Inference

A class member definition m that overrides some other function mʹ in a base class of C may leave out the return type, even if it is recursive. In this case, the return type Rʹ of the overridden function mʹ, seen as a member of C, is taken as the return type of m for each recursive invocation of m. That way, a type R for the right-hand side of m can be determined, which is then taken as the return type of m. Note that R may be different from Rʹ, as long as R conforms to Rʹ.

  1. Assume the following definitions:

    trait I {
      def factorial(x: Int): Int
    }
    class C extends I {
      def factorial(x: Int) = if (x == 0) 1 else x * factorial(x - 1)
    }

    Here, it is OK to leave out the result type of factorial in C, even though the method is recursive.

4.7 Import Clauses

Import          ::= ‘import’ ImportExpr {‘,’ ImportExpr}
ImportExpr      ::= StableId ‘.’ (id | ‘_’ | ImportSelectors)
ImportSelectors ::= ‘{’ {ImportSelector ‘,’} 
                    (ImportSelector | ‘_’) ‘}’
ImportSelector  ::= id [‘=>’ id | ‘=>’ ‘_’]

An import clause has the form import $p$.$I$ where p is a stable identifier and I is an import expression. The import expression determines a set of names of importable members of p which are made available without qualification. A member m of p is importable if it is not object-private. The most general form of an import expression is a list of {}

{ $x_1$ => $y_1 , \ldots , x_n$ => $y_n$, _ } 

for n0, where the final wildcard ‘_’ may be absent. It makes available each importable member $p$.$x_i$ under the unqualified name yi. I.e. every import selector $x_i$ => $y_i$ renames $p$.$x_i$ to yi. If a final wildcard is present, all importable members z of p other than $x_1 , \ldots , x_n,y_1 , \ldots , y_n$ are also made available under their own unqualified names.

Import selectors work in the same way for type and term members. For instance, an import clause import $p$.{$x$ => $y\,$} renames the term name $p$.$x$ to the term name y and the type name $p$.$x$ to the type name y. At least one of these two names must reference an importable member of p.

If the target in an import selector is a wildcard, the import selector hides access to the source member. For instance, the import selector $x$ => _ “renames” x to the wildcard symbol (which is unaccessible as a name in user programs), and thereby effectively prevents unqualified access to x. This is useful if there is a final wildcard in the same import selector list, which imports all members not mentioned in previous import selectors.

The scope of a binding introduced by an import-clause starts immediately after the import clause and extends to the end of the enclosing block, template, package clause, or compilation unit, whichever comes first.

Several shorthands exist. An import selector may be just a simple name x. In this case, x is imported without renaming, so the import selector is equivalent to $x$ => $x$. Furthermore, it is possible to replace the whole import selector list by a single identifier or wildcard. The import clause import $p$.$x$ is equivalent to import $p$.{$x\,$}, i.e. it makes available without qualification the member x of p. The import clause import $p$._ is equivalent to import $p$.{_}, i.e. it makes available without qualification all members of p (this is analogous to import $p$.* in Java).

An import clause with multiple import expressions import $p_1$.$I_1 , \ldots , p_n$.$I_n$ is interpreted as a sequence of import clauses import $p_1$.$I_1$; $\ldots$; import $p_n$.$I_n$.

  1. Consider the object definition:

    object M { 
      def z = 0, one = 1  
      def add(x: Int, y: Int): Int = x + y 
    }

    Then the block

    { import M.{one, z => zero, _}; add(zero, one) }

    is equivalent to the block

    { M.add(M.z, M.one) } 

5 Classes and Objects

TmplDef          ::= [`case'] `class' ClassDef
                  |  [`case'] `object' ObjectDef
                  |  `trait' TraitDef

Classes and objects are both defined in terms of templates.

5.1 Templates

ClassTemplate   ::=  [EarlyDefs] ClassParents [TemplateBody]
TraitTemplate   ::=  [EarlyDefs] TraitParents [TemplateBody]
ClassParents    ::=  Constr {`with' AnnotType}
TraitParents    ::=  AnnotType {`with' AnnotType}
TemplateBody    ::=  [nl] `{' [SelfType] TemplateStat {semi TemplateStat} `}'
SelfType        ::=  id [`:' Type] `=>'
                 |   this `:' Type `=>'

A template defines the type signature, behavior and initial state of a trait or class of objects or of a single object. Templates form part of instance creation expressions, class definitions, and object definitions. A template $sc$ with $mt_1$ with $\ldots$ with $mt_n$ { $\mathit{stats}$ } consists of a constructor invocation sc which defines the template's superclass, trait references $mt_1 , \ldots , mt_n$ (n0), which define the template's traits, and a statement sequence stats which contains initialization code and additional member definitions for the template.

Each trait reference mti must denote a trait. By contrast, the superclass constructor sc normally refers to a class which is not a trait. It is possible to write a list of parents that starts with a trait reference, e.g. $mt_1$ with $\ldots$ with $mt_n$. In that case the list of parents is implicitly extended to include the supertype of mt1 as first parent type. The new supertype must have at least one constructor that does not take parameters. In the following, we will always assume that this implicit extension has been performed, so that the first parent class of a template is a regular superclass constructor, not a trait reference.

The list of parents of every class is also always implicitly extended by a reference to the scala.ScalaObject trait as last mixin. E.g.

$sc$ with $mt_1$ with $\ldots$ with $mt_n$ { $\mathit{stats}$ }

becomes

$mt_1$ with $\ldots$ with $mt_n$ with ScalaObject { $\mathit{stats}$ }.

The list of parents of a template must be well-formed. This means that the class denoted by the superclass constructor sc must be a subclass of the superclasses of all the traits mt1,,mtn. In other words, the non-trait classes inherited by a template form a chain in the inheritance hierarchy which starts with the template's superclass.

The least proper supertype of a template is the class type or compound type consisting of all its parent class types.

The statement sequence stats contains member definitions that define new members or overwrite members in the parent classes. If the template forms part of an abstract class or trait definition, the statement part stats may also contain declarations of abstract members. If the template forms part of a concrete class definition, stats may still contain declarations of abstract type members, but not of abstract term members. Furthermore, stats may in any case also contain expressions; these are executed in the order they are given as part of the initialization of a template.

The sequence of template statements may be prefixed with a formal parameter definition and an arrow, e.g. $x$ =>, or $x$:$T$ =>. If a formal parameter is given, it can be used as an alias for the reference this throughout the body of the template.
If the formal parameter comes with a type T, this definition affects the self type S of the underlying class or object as follows: Let C be the type of the class or trait or object defining the template. If a type T is given for the formal self parameter, S is the greatest lower bound of T and C. If no type T is given, S is just C. Inside the template, the type of this is assumed to be S.

The self type of a class or object must conform to the self types of all classes which are inherited by the template t.

A second form of self type annotation reads just this: $S$ =>. It prescribes the type S for this without introducing an alias name for it.

  1. Consider the following class definitions:

    class Base extends Object {}
    trait Mixin extends Base {}
    object O extends Mixin {}

    In this case, the definition of O is expanded to:

    object O extends Base with Mixin {}

Inheriting from Java Types
A template may have a Java class as its superclass and Java interfaces as its mixins.

Template Evaluation
Consider a template $sc$ with $mt_1$ with $mt_n$ { $\mathit{stats}$ }.

If this is the template of a trait then its mixin-evaluation consists of an evaluation of the statement sequence stats.

If this is not a template of a trait, then its evaluation consists of the following steps.

Delayed Initializaton
The initialization code of an object or class (but not a trait) that follows the superclass constructor invocation and the mixin-evaluation of the template's base classes is passed to a special hook, which is inaccessible from user code. Normally, that hook simply executes the code that is passed to it. But templates inheriting the scala.DelayedInit trait can override the hook by re-implementing the delayedInit method, which is defined as follows:

def delayedInit(body: => Unit)

5.1.1 Constructor Invocations

Constr  ::=  AnnotType {`(' [Exprs] `)'}

Constructor invocations define the type, members, and initial state of objects created by an instance creation expression, or of parts of an object's definition which are inherited by a class or object definition. A constructor invocation is a function application $x$.$c$[$\mathit{targs}$]($\mathit{args}_1$)$\ldots$($\mathit{args}_n$), where x is a stable identifier, c is a type name which either designates a class or defines an alias type for one, targs is a type argument list, args1,,argsn are argument lists, and there is a constructor of that class which is applicable to the given arguments. If the constructor invocation uses named or default arguments, it is transformed into a block expression using the same transformation as described here.

The prefix `$x$.' can be omitted. A type argument list can be given only if the class c takes type parameters. Even then it can be omitted, in which case a type argument list is synthesized using local type inference. If no explicit arguments are given, an empty list () is implicitly supplied.

An evaluation of a constructor invocation $x$.$c$[$\mathit{targs}$]($\mathit{args}_1$)$\ldots$($\mathit{args}_n$) consists of the following steps:

5.1.2 Class Linearization

The classes reachable through transitive closure of the direct inheritance relation from a class C are called the base classes of C. Because of mixins, the inheritance relationship on base classes forms in general a directed acyclic graph. A linearization of this graph is defined as follows.

Let C be a class with template $C_1$ with ... with $C_n$ { $\mathit{stats}$ }. The linearization of C, (C) is defined as follows:

(C)=C,(Cn)++(C1)

Here + denotes concatenation where elements of the right operand replace identical elements of the left operand:

\[
\begin{array}{lcll}
\{a, A\} \;\vec{+}\; B &=& a, (A \;\vec{+}\; B)  &{\bf if} \; a \not\in B \\
                       &=& A \;\vec{+}\; B       &{\bf if} \; a \in B
\end{array}
\]
  1. Consider the following class definitions.

    abstract class AbsIterator extends AnyRef { ... }
    trait RichIterator extends AbsIterator { ... }
    class StringIterator extends AbsIterator { ... }
    class Iter extends StringIterator with RichIterator { ... }

    Then the linearization of class Iter is

    { Iter, RichIterator, StringIterator, AbsIterator, ScalaObject, AnyRef, Any }

    Trait ScalaObject appears in this list because it is added as last mixin to every Scala class ( see here ).

    Note that the linearization of a class refines the inheritance relation: if C is a subclass of D, then C precedes D in any linearization where both C and D occur. also satisfies the property that a linearization of a class always contains the linearization of its direct superclass as a suffix. For instance, the linearization of StringIterator is

    { StringIterator, AbsIterator, ScalaObject, AnyRef, Any }

    which is a suffix of the linearization of its subclass Iter. The same is not true for the linearization of mixins. For instance, the linearization of RichIterator is

    { RichIterator, AbsIterator, ScalaObject, AnyRef, Any }

    which is not a suffix of the linearization of Iter.

5.1.3 Class Members

A class C defined by a template $C_1$ with $\ldots$ with $C_n$ { $\mathit{stats}$ } can define members in its statement sequence stats and can inherit members from all parent classes. Scala adopts Java and C#'s conventions for static overloading of methods. It is thus possible that a class defines and/or inherits several methods with the same name. To decide whether a defined member of a class C overrides a member of a parent class, or whether the two co-exist as overloaded variants in C, Scala uses the following definition of matching on members:

Definition
A member definition M matches a member definition Mʹ, if M and Mʹ bind the same name, and one of following holds.

  1. Neither M nor Mʹ is a method definition.
  2. M and Mʹ define both monomorphic methods with equivalent argument types.
  3. M defines a parameterless method and Mʹ defines a method with an empty parameter list () or vice versa.
  4. M and Mʹ define both polymorphic methods with equal number of argument types T¯, T¯ʹ and equal numbers of type parameters t¯, t¯ʹ, say, and T¯ʹ=[t¯ʹ/t¯]T¯. by the corresponding type parameter t of M.

Member definitions fall into two categories: concrete and abstract. Members of class C are either directly defined (i.e. they appear in C's statement sequence stats) or they are inherited. There are two rules that determine the set of members of a class, one for each category:

A concrete member of a class C is any concrete definition M in some class Ci(C), except if there is a preceding class Cj(C) where j<i which directly defines a concrete member Mʹ matching M.

An abstract member of a class C is any abstract definition M in some class Ci(C), except if C contains already a concrete member Mʹ matching M, or if there is a preceding class Cj(C) where j<i which directly defines an abstract member Mʹ matching M.

This definition also determines the overriding relationships between matching members of a class C and its parents.
First, a concrete definition always overrides an abstract definition. Second, for definitions M and M' which are both concrete or both abstract, M overrides Mʹ if M appears in a class that precedes (in the linearization of C) the class in which Mʹ is defined.

It is an error if a template directly defines two matching members. It is also an error if a template contains two members (directly defined or inherited) with the same name and the same erased type. Finally, a template is not allowed to contain two methods (directly defined or inherited) with the same name which both define default arguments.

  1. Consider the trait definitions:

    trait A { def f: Int }
    trait B extends A { def f: Int = 1 ; def g: Int = 2 ; def h: Int = 3 }
    trait C extends A { override def f: Int = 4 ; def g: Int }
    trait D extends B with C { def h: Int }

    Then trait D has a directly defined abstract member h. It inherits member f from trait C and member g from trait B.

5.1.4 Overriding

A member M of class C that matches a non-private member Mʹ of a base class of C is said to override that member. In this case the binding of the overriding member M must subsume the binding of the overridden member Mʹ. Furthermore, the following restrictions on modifiers apply to M and Mʹ:

A special rule concerns parameterless methods. If a paramterless method defined as def $f$: $T$ = ... or def $f$ = ... overrides a method of type ()Tʹ which has an empty parameter list, then f is also assumed to have an empty parameter list.

Another restriction applies to abstract type members: An abstract type member with a volatile type as its upper bound may not override an abstract type member which does not have a volatile upper bound.

An overriding method inherits all default arguments from the definition in the superclass. By specifying default arguments in the overriding method it is possible to add new defaults (if the corresponding parameter in the superclass does not have a default) or to override the defaults of the superclass (otherwise).

  1. Consider the definitions:

    trait Root { type T <: Root }
    trait A extends Root { type T <: A }
    trait B extends Root { type T <: B }
    trait C extends A with B 

    Then the class definition C is not well-formed because the binding of T in C is type T <: B, which fails to subsume the binding type T <: A of T in type A. The problem can be solved by adding an overriding definition of type T in class C:

    class C extends A with B { type T <: C }

5.1.5 Inheritance Closure

Let C be a class type. The inheritance closure of C is the smallest set 𝒮 of types such that

It is a static error if the inheritance closure of a class type consists of an infinite number of types. (This restriction is necessary to make subtyping decidable (Kennedy and Pierce 2007)).

5.1.6 Early Definitions

EarlyDefs         ::= `{' [EarlyDef {semi EarlyDef}] `}' `with'
EarlyDef          ::=  {Annotation} {Modifier} PatVarDef

A template may start with an early field definition clause, which serves to define certain field values before the supertype constructor is called. In a template

{ val $p_1$: $T_1$ = $e_1$
  ...
  val $p_n$: $T_n$ = $e_n$
} with $sc$ with $mt_1$ with $mt_n$ { $\mathit{stats}$ }

The initial pattern definitions of p1,,pn are called early definitions. They define fields which form part of the template. Every early definition must define at least one variable.

An early definition is type-checked and evaluated in the scope which is in effect just before the template being defined, augmented by any type parameters of the enclosing class and by any early definitions preceding the one being defined. In particular, any reference to this in the right-hand side of an early definition refers to the identity of this just outside the template. Consequently, it is impossible that an early definition refers to the object being constructed by the template, or refers to one of its fields and methods, except for any other preceding early definition in the same section. Furthermore, references to preceding early definitions always refer to the value that's defined there, and do not take into account overriding definitions. In other words, a block of early definitions is evaluated exactly as if it was a local bock containing a number of value definitions.

Early definitions are evaluated in the order they are being defined before the superclass constructor of the template is called.

  1. Early definitions are particularly useful for traits, which do not have normal constructor parameters. Example:

    trait Greeting {
      val name: String
      val msg = "How are you, "+name
    }
    class C extends {
      val name = "Bob"
    } with Greeting {
      println(msg)
    }

    In the code above, the field name is initialized before the constructor of Greeting is called. Therefore, field msg in class Greeting is properly initialized to "How are you, Bob".

    If name had been initialized instead in C's normal class body, it would be initialized after the constructor of Greeting. In that case, msg would be initialized to "How are you, <null>".

5.2 Modifiers

Modifier          ::=  LocalModifier 
                    |  AccessModifier
                    |  `override'
LocalModifier     ::=  `abstract'
                    |  `final'
                    |  `sealed'
                    |  `implicit'
                    |  `lazy'
AccessModifier    ::=  (`private' | `protected') [AccessQualifier]
AccessQualifier   ::=  `[' (id | `this') `]'

Member definitions may be preceded by modifiers which affect the accessibility and usage of the identifiers bound by them. If several modifiers are given, their order does not matter, but the same modifier may not occur more than once. Modifiers preceding a repeated definition apply to all constituent definitions. The rules governing the validity and meaning of a modifier are as follows.

The modifier can be qualified with an identifier C (e.g. private[$C$]) that must denote a class or package enclosing the definition. Members labeled with such a modifier are accessible respectively only from code inside the package C or only from code inside the class C and its companion module. Such members are also inherited only from templates inside C.

An different form of qualification is private[this]. A member M marked with this modifier is called {}; it can be accessed only from within the object in which it is defined. That is, a selection p.M is only legal if the prefix is this or $O$.this, for some class O enclosing the reference. In addition, the restrictions for unqualified private apply.

Members marked private without a qualifier are called class-private, whereas members labeled with private[this] are called object-private. A member is private if it is either class-private or object-private, but not if it is marked private[$C$] where C is an identifier; in the latter case the member is called qualified private.

Class-private or object-private members may not be abstract, and may not have protected or override modifiers.

A protected identifier x may be used as a member name in a selection $r$.$x$ only if one of the following applies: - The access is within the template defining the member, or, if a qualification C is given, inside the package C, or the class C, or its companion module, or - r is one of the reserved words this and super, or - r's type conforms to a type-instance of the class which contains the access.

A different form of qualification is protected[this]. A member M marked with this modifier can be accessed only from within the object in which it is defined. That is, a selection p.M is only legal if the prefix is this or $O$.this, for some class O enclosing the reference. In addition, the restrictions for unqualified protected apply.

We call a member M of a template incomplete if it is either abstract (i.e. defined by a declaration), or it is labeled abstract and override and every member overridden by M is again incomplete.

Note that the abstract override modifier combination does not influence the concept whether a member is concrete or abstract. A member is abstract if only a declaration is given for it; it is concrete if a full definition is given.

The abstract modifier can also be used in conjunction with override for class member definitions. In that case the previous discussion applies.

  1. The following code illustrates the use of qualified private:

    package outerpkg.innerpkg
    class Outer {
      class Inner {
        private[Outer] def f()
        private[innerpkg] def g()
        private[outerpkg] def h()
      }
    }

    Here, accesses to the method f can appear anywhere within OuterClass, but not outside it. Accesses to method g can appear anywhere within the package outerpkg.innerpkg, as would be the case for package-private methods in Java. Finally, accesses to method h can appear anywhere within package outerpkg, including packages contained in it.

  2. A useful idiom to prevent clients of a class from constructing new instances of that class is to declare the class abstract and sealed:

    object m {
      abstract sealed class C (x: Int) {
        def nextC = new C(x + 1) {}
      }
      val empty = new C(0) {}
    }

    For instance, in the code above clients can create instances of class m.C only by calling the nextC method of an existing m.C object; it is not possible for clients to create objects of class m.C directly. Indeed the following two lines are both in error:

    new m.C(0)    // **** error: C is abstract, so it cannot be instantiated.
    new m.C(0) {} // **** error: illegal inheritance from sealed class.

    A similar access restriction can be achieved by marking the primary constructor private (see ).

5.3 Class Definitions

TmplDef           ::=  `class' ClassDef 
ClassDef          ::=  id [TypeParamClause] {Annotation} 
                       [AccessModifier] ClassParamClauses ClassTemplateOpt 
ClassParamClauses ::=  {ClassParamClause} 
                       [[nl] `(' implicit ClassParams `)']
ClassParamClause  ::=  [nl] `(' [ClassParams] ')'
ClassParams       ::=  ClassParam {`,' ClassParam}
ClassParam        ::=  {Annotation} [{Modifier} (`val' | `var')] 
                       id [`:' ParamType] [`=' Expr]
ClassTemplateOpt  ::=  `extends' ClassTemplate | [[`extends'] TemplateBody]

The most general form of class definition is

class $c$[$\mathit{tps}\,$] $as$ $m$($\mathit{ps}_1$)$\ldots$($\mathit{ps}_n$) extends $t$    $\gap(n \geq 0)$.

Here,

This class definition defines a type $c$[$\mathit{tps}\,$] and a constructor which when applied to parameters conforming to types ps initializes instances of type $c$[$\mathit{tps}\,$] by evaluating the template t.

  1. The following example illustrates val and var parameters of a class C:

    class C(x: Int, val y: String, var z: List[String])
    val c = new C(1, "abc", List())
    c.z = c.y :: c.z
  2. The following class can be created only from its companion module.

    object Sensitive {
      def makeSensitive(credentials: Certificate): Sensitive = 
        if (credentials == Admin) new Sensitive() 
        else throw new SecurityViolationException
    }
    class Sensitive private () {
      ...
    }

5.3.1 Constructor Definitions

FunDef         ::= `this' ParamClause ParamClauses 
                   (`=' ConstrExpr | [nl] ConstrBlock)
ConstrExpr     ::= SelfInvocation
                |  ConstrBlock
ConstrBlock    ::= `{' SelfInvocation {semi BlockStat} `}'
SelfInvocation ::= `this' ArgumentExprs {ArgumentExprs}

A class may have additional constructors besides the primary constructor. These are defined by constructor definitions of the form def this($\mathit{ps}_1$)$\ldots$($\mathit{ps}_n$) = $e$. Such a definition introduces an additional constructor for the enclosing class, with parameters as given in the formal parameter lists ps1,,psn, and whose evaluation is defined by the constructor expression e. The scope of each formal parameter is the subsequent parameter sections and the constructor expression e. A constructor expression is either a self constructor invocation this($\mathit{args}_1$)$\ldots$($\mathit{args}_n$) or a block which begins with a self constructor invocation. The self constructor invocation must construct a generic instance of the class. I.e. if the class in question has name C and type parameters [$\mathit{tps}\,$], then a self constructor invocation must generate an instance of $C$[$\mathit{tps}\,$]; it is not permitted to instantiate formal type parameters.

The signature and the self constructor invocation of a constructor definition are type-checked and evaluated in the scope which is in effect at the point of the enclosing class definition, augmented by any type parameters of the enclosing class and by any early definitions of the enclosing template. The rest of the constructor expression is type-checked and evaluated as a function body in the current class.

If there are auxiliary constructors of a class C, they form together with C's primary constructor an overloaded constructor definition. The usual rules for overloading resolution apply for constructor invocations of C, including for the self constructor invocations in the constructor expressions themselves. However, unlike other methods, constructors are never inherited. To prevent infinite cycles of constructor invocations, there is the restriction that every self constructor invocation must refer to a constructor definition which precedes it (i.e. it must refer to either a preceding auxiliary constructor or the primary constructor of the class).

  1. Consider the class definition

    class LinkedList[A]() {
      var head = _ 
      var tail = null 
      def isEmpty = tail != null   
      def this(head: A) = { this(); this.head = head }
      def this(head: A, tail: List[A]) = { this(head); this.tail = tail }
    }

    This defines a class LinkedList with three constructors. The second constructor constructs an singleton list, while the third one constructs a list with a given head and tail.

5.4 Case Classes

TmplDef  ::=  `case' `class' ClassDef

If a class definition is prefixed with case, the class is said to be a case class.

The formal parameters in the first parameter section of a case class are called elements; they are treated specially. First, the value of such a parameter can be extracted as a field of a constructor pattern. Second, a val prefix is implicitly added to such a parameter, unless the parameter carries already a val or var modifier. Hence, an accessor definition for the parameter is generated.

A case class definition of $c$[$\mathit{tps}\,$]($\mathit{ps}_1\,$)$\ldots$($\mathit{ps}_n$) with type parameters tps and value parameters ps implicitly generates an extractor object which is defined as follows:

object $c$ {
  def apply[$\mathit{tps}\,$]($\mathit{ps}_1\,$)$\ldots$($\mathit{ps}_n$): $c$[$\mathit{tps}\,$] = new $c$[$\mathit{Ts}\,$]($\mathit{xs}_1\,$)$\ldots$($\mathit{xs}_n$)
  def unapply[$\mathit{tps}\,$]($x$: $c$[$\mathit{tps}\,$]) =
    if (x eq null) scala.None
    else scala.Some($x.\mathit{xs}_{11}, \ldots , x.\mathit{xs}_{1k}$)
}

Here, Ts stands for the vector of types defined in the type parameter section tps, each xsi denotes the parameter names of the parameter section psi, and xs11,,xs1k denote the names of all parameters in the first parameter section xs1. If a type parameter section is missing in the class, it is also missing in the apply and unapply methods. The definition of apply is omitted if class c is abstract.

If the case class definition contains an empty value parameter list, the unapply method returns a Boolean instead of an Option type and is defined as follows:

def unapply[$\mathit{tps}\,$]($x$: $c$[$\mathit{tps}\,$]) = x ne null

The name of the unapply method is changed to unapplySeq if the first parameter section ps1 of c ends in a repeated parameter. If a companion object c exists already, no new object is created, but the apply and unapply methods are added to the existing object instead.

A method named copy is implicitly added to every case class unless the class already has a member (directly defined or inherited) with that name. The method is defined as follows:

def copy[$\mathit{tps}\,$]($\mathit{ps}'_1\,$)$\ldots$($\mathit{ps}'_n$): $c$[$\mathit{tps}\,$] = new $c$[$\mathit{Ts}\,$]($\mathit{xs}_1\,$)$\ldots$($\mathit{xs}_n$)

Again, Ts stands for the vector of types defined in the type parameter section tps and each xsi denotes the parameter names of the parameter section psʹi. Every value parameter psʹi,j of the copy method has the form $x_{i,j}$:$T_{i,j}$=this.$x_{i,j}$, where xi,j and Ti,j refer to the name and type of the corresponding class parameter psi,j.

Every case class implicitly overrides some method definitions of class scala.AnyRef unless a definition of the same method is already given in the case class itself or a concrete definition of the same method is given in some base class of the case class different from AnyRef. In particular:

  1. Here is the definition of abstract syntax for lambda calculus:

    class Expr 
    case class Var   (x: String)          extends Expr
    case class Apply (f: Expr, e: Expr)   extends Expr
    case class Lambda(x: String, e: Expr) extends Expr 

    This defines a class Expr with case classes Var, Apply and Lambda. A call-by-value evaluator for lambda expressions could then be written as follows.

    type Env = String => Value 
    case class Value(e: Expr, env: Env) 
    
    def eval(e: Expr, env: Env): Value = e match {
      case Var (x) =>
        env(x)
      case Apply(f, g) =>
        val Value(Lambda (x, e1), env1) = eval(f, env) 
        val v = eval(g, env) 
        eval (e1, (y => if (y == x) v else env1(y)))
      case Lambda(_, _) =>
        Value(e, env)
    }

    It is possible to define further case classes that extend type Expr in other parts of the program, for instance

    case class Number(x: Int) extends Expr 

    This form of extensibility can be excluded by declaring the base class Expr sealed; in this case, all classes that directly extend Expr must be in the same source file as Expr.

5.4.1 Traits

TmplDef          ::=  `trait' TraitDef
TraitDef         ::=  id [TypeParamClause] TraitTemplateOpt
TraitTemplateOpt ::=  `extends' TraitTemplate | [[`extends'] TemplateBody]

A trait is a class that is meant to be added to some other class as a mixin. Unlike normal classes, traits cannot have constructor parameters. Furthermore, no constructor arguments are passed to the superclass of the trait. This is not necessary as traits are initialized after the superclass is initialized.

Assume a trait D defines some aspect of an instance x of type C (i.e. D is a base class of C). Then the {} of D in x is the compound type consisting of all the base classes in (C) that succeed D. The actual supertype gives the context for resolving a super reference in a trait. Note that the actual supertype depends on the type to which the trait is added in a mixin composition; it is not statically known at the time the trait is defined.

If D is not a trait, then its actual supertype is simply its least proper supertype (which is statically known).

  1. The following trait defines the property of being comparable to objects of some type. It contains an abstract method < and default implementations of the other comparison operators <=, >, and >=.

    trait Comparable[T <: Comparable[T]] { self: T =>
      def < (that: T): Boolean
      def <=(that: T): Boolean = this < that || this == that
      def > (that: T): Boolean = that < this 
      def >=(that: T): Boolean = that <= this
    }
  2. Consider an abstract class Table that implements maps from a type of keys A to a type of values B. The class has a method set to enter a new key / value pair into the table, and a method get that returns an optional value matching a given key. Finally, there is a method apply which is like get, except that it returns a given default value if the table is undefined for the given key. This class is implemented as follows.

    abstract class Table[A, B](defaultValue: B) {
      def get(key: A): Option[B]
      def set(key: A, value: B)
      def apply(key: A) = get(key) match {
        case Some(value) => value
        case None => defaultValue
      }
    }

    Here is a concrete implementation of the Table class.

    class ListTable[A, B](defaultValue: B) extends Table[A, B](defaultValue) {
      private var elems: List[(A, B)]
      def get(key: A) = elems.find(._1.==(key)).map(._2)
      def set(key: A, value: B) = { elems = (key, value) :: elems }
    }

    Here is a trait that prevents concurrent access to the get and set operations of its parent class:

    trait SynchronizedTable[A, B] extends Table[A, B] {
      abstract override def get(key: A): B = 
        synchronized { super.get(key) }
      abstract override def set((key: A, value: B) = 
        synchronized { super.set(key, value) }
    }

    Note that SynchronizedTable does not pass an argument to its superclass, Table, even though Table is defined with a formal parameter. Note also that the super calls in SynchronizedTable's get and set methods statically refer to abstract methods in class Table. This is legal, as long as the calling method is labeled abstract override.

    Finally, the following mixin composition creates a synchronized list table with strings as keys and integers as values and with a default value 0:

    object MyTable extends ListTable[String, Int](0) with SynchronizedTable

    The object MyTable inherits its get and set method from SynchronizedTable. The super calls in these methods are re-bound to refer to the corresponding implementations in ListTable, which is the actual supertype of SynchronizedTable in MyTable.

5.5 Object Definitions

ObjectDef       ::=  id ClassTemplate

An object definition defines a single object of a new class. Its most general form is object $m$ extends $t$. Here, m is the name of the object to be defined, and t is a template of the form

$sc$ with $mt_1$ with $\ldots$ with $mt_n$ { $\mathit{stats}$ }

which defines the base classes, behavior and initial state of m. The extends clause extends $sc$ with $mt_1$ with $\ldots$ with $mt_n$ can be omitted, in which case extends scala.AnyRef is assumed. The class body { $\mathit{stats}$ } may also be omitted, in which case the empty body {} is assumed.

The object definition defines a single object (or: module) conforming to the template t. It is roughly equivalent to the following definition of a lazy value:

lazy val $m$ = new $sc$ with $mt_1$ with $\ldots$ with $mt_n$ { this: $m.type$ => $\mathit{stats}$ }

Note that the value defined by an object definition is instantiated lazily. The new $m$\$cls constructor is evaluated not at the point of the object definition, but is instead evaluated the first time m is dereferenced during execution of the program (which might be never at all). An attempt to dereference m again in the course of evaluation of the constructor leads to a infinite loop or run-time error.
Other threads trying to dereference m while the constructor is being evaluated block until evaluation is complete.

The expansion given above is not accurate for top-level objects. It cannot be because variable and method definition cannot appear on the top-level outside of a package object. Instead, top-level objects are translated to static fields.

  1. Classes in Scala do not have static members; however, an equivalent effect can be achieved by an accompanying object definition E.g.

    abstract class Point {
      val x: Double 
      val y: Double 
      def isOrigin = (x == 0.0 && y == 0.0) 
    }
    object Point {
      val origin = new Point() { val x = 0.0; val y = 0.0 }
    }

    This defines a class Point and an object Point which contains origin as a member. Note that the double use of the name Point is legal, since the class definition defines the name Point in the type name space, whereas the object definition defines a name in the term namespace.

    This technique is applied by the Scala compiler when interpreting a Java class with static members. Such a class C is conceptually seen as a pair of a Scala class that contains all instance members of C and a Scala object that contains all static members of C.

    Generally, a companion module of a class is an object which has the same name as the class and is defined in the same scope and compilation unit. Conversely, the class is called the companion class of the module.

6 Expressions

  Expr              ::=  (Bindings | id | `_') `=>' Expr
                      |  Expr1
  Expr1             ::=  `if' `(' Expr `)' {nl} Expr [[semi] else Expr]
                      |  `while' `(' Expr `)' {nl} Expr
                      |  `try' `{' Block `}' [`catch'  `{' CaseClauses `}'] 
                         [`finally' Expr]
                      |  `do' Expr [semi] `while' `(' Expr ')'
                      |  `for' (`(' Enumerators `)' | `{' Enumerators `}') 
                         {nl} [`yield'] Expr
                      |  `throw' Expr
                      |  `return' [Expr]
                      |  [SimpleExpr `.'] id `=' Expr
                      |  SimpleExpr1 ArgumentExprs `=' Expr
                      |  PostfixExpr
                      |  PostfixExpr Ascription
                      |  PostfixExpr `match' `{' CaseClauses `}'
  PostfixExpr       ::=  InfixExpr [id [nl]]
  InfixExpr         ::=  PrefixExpr
                      |  InfixExpr id [nl] InfixExpr
  PrefixExpr        ::=  [`-' | `+' | `~' | `!'] SimpleExpr 
  SimpleExpr        ::=  `new' (ClassTemplate | TemplateBody)
                      |  BlockExpr
                      |  SimpleExpr1 [`_']
  SimpleExpr1       ::=  Literal
                      |  Path
                      |  `_'
                      |  `(' [Exprs] `)'
                      |  SimpleExpr `.' id s
                      |  SimpleExpr TypeArgs
                      |  SimpleExpr1 ArgumentExprs
                      |  XmlExpr
  Exprs             ::=  Expr {`,' Expr}
  BlockExpr         ::=  `{' CaseClauses `}'
                      |  `{' Block `}'
  Block             ::=  {BlockStat semi} [ResultExpr]
  ResultExpr        ::=  Expr1
                      |  (Bindings | ([`implicit'] id | `_') `:' CompoundType) `=>' Block
  Ascription        ::=  `:' InfixType
                      |  `:' Annotation {Annotation} 
                      |  `:' `_' `*'

Expressions are composed of operators and operands. Expression forms are discussed subsequently in decreasing order of precedence.

6.1 Expression Typing

The typing of expressions is often relative to some expected type (which might be undefined). When we write ``expression e is expected to conform to type T'', we mean: (1) the expected type of e is T, and (2) the type of expression e must conform to T.

The following skolemization rule is applied universally for every expression: If the type of an expression would be an existential type T, then the type of the expression is assumed instead to be a skolemization of T.

Skolemization is reversed by type packing. Assume an expression e of type T and let t1[tps1]>:L1<:U1,,tn[tpsn]>:Ln<:Un be all the type variables created by skolemization of some part of e which are free in T. Then the packed type of e is

$T$ forSome { type $t_1[\mathit{tps}_1] >: L_1 <: U_1$; $\ldots$; type $t_n[\mathit{tps}_n] >: L_n <: U_n$ }.

6.2 Literals

SimpleExpr    ::=  Literal

Typing of literals is as described here; their evaluation is immediate.

6.3 The Null Value

The null value is of type scala.Null, and is thus compatible with every reference type. It denotes a reference value which refers to a special “null” object. This object implements methods in class scala.AnyRef as follows:

A reference to any other member of the `null'' object causes aNullPointerException` to be thrown.

6.4 Designators

SimpleExpr  ::=  Path
              |  SimpleExpr `.' id

A designator refers to a named term. It can be a simple name or a selection.

A simple name x refers to a value as specified here. If x is bound by a definition or declaration in an enclosing class or object C, it is taken to be equivalent to the selection $C$.this.$x$ where C is taken to refer to the class containing x even if the type name C is shadowed at the occurrence of x.

If r is a stable identifier of type T, the selection r.x refers statically to a term member m of r that is identified in T by the name x.

For other expressions e, e.x is typed as if it was { val $y$ = $e$; $y$.$x$ }, for some fresh name y.

The expected type of a designator's prefix is always undefined. The type of a designator is the type T of the entity it refers to, with the following exception: The type of a path p which occurs in a context where a stable type is required is the singleton type $p$.type.

The contexts where a stable type is required are those that satisfy one of the following conditions:

  1. The path p occurs as the prefix of a selection and it does not designate a constant, or
  2. The expected type pt is a stable type, or
  3. The expected type pt is an abstract type with a stable type as lower bound, and the type T of the entity referred to by p does not conform to pt, or
  4. The path p designates a module.

The selection e.x is evaluated by first evaluating the qualifier expression e, which yields an object r, say. The selection's result is then the member of r that is either defined by m or defined by a definition overriding m. If that member has a type which conforms to scala.NotNull, the member's value must be initialized to a value different from null, otherwise a scala.UnitializedError is thrown.

6.5 This and Super

SimpleExpr  ::=  [id `.'] `this'
              |  [id '.'] `super' [ClassQualifier] `.' id

The expression this can appear in the statement part of a template or compound type. It stands for the object being defined by the innermost template or compound type enclosing the reference. If this is a compound type, the type of this is that compound type. If it is a template of a class or object definition with simple name C, the type of this is the same as the type of $C$.this.

The expression $C$.this is legal in the statement part of an enclosing class or object definition with simple name C. It stands for the object being defined by the innermost such definition. If the expression's expected type is a stable type, or $C$.this occurs as the prefix of a selection, its type is $C$.this.type, otherwise it is the self type of class C.

A reference super.$m$ refers statically to a method or type m in the least proper supertype of the innermost template containing the reference. It evaluates to the member mʹ in the actual supertype of that template which is equal to m or which overrides m. The statically referenced member m must be a type or a method.

If it is a method, it must be concrete, or the template containing the reference must have a member mʹ which overrides m and which is labeled abstract override.

A reference $C$.super.$m$ refers statically to a method or type m in the least proper supertype of the innermost enclosing class or object definition named C which encloses the reference. It evaluates to the member mʹ in the actual supertype of that class or object which is equal to m or which overrides m. The statically referenced member m must be a type or a method. If the statically referenced member m is a method, it must be concrete, or the innermost enclosing class or object definition named C must have a member mʹ which overrides m and which is labeled abstract override.

The super prefix may be followed by a trait qualifier [$T\,$], as in $C$.super[$T\,$].$x$. This is called a static super reference. In this case, the reference is to the type or method of x in the parent trait of C whose simple name is T. That member must be uniquely defined. If it is a method, it must be concrete.

  1. Consider the following class definitions

    class Root { def x = "Root" }
    class A extends Root { override def x = "A" ; def superA = super.x }
    trait B extends Root { override def x = "B" ; def superB = super.x }
    class C extends Root with B { 
      override def x = "C" ; def superC = super.x
    }
    class D extends A with B {
      override def x = "D" ; def superD = super.x
    }

    The linearization of class C is {C, B, Root} and the linearization of class D is {D, B, A, Root}. Then we have:

    (new A).superA == "Root", 
                              (new C).superB = "Root", (new C).superC = "B",
    (new D).superA == "Root", (new D).superB = "A",    (new D).superD = "B",

    Note that the superB function returns different results depending on whether B is mixed in with class Root or A.

6.6 Function Applications

SimpleExpr    ::=  SimpleExpr1 ArgumentExprs
ArgumentExprs ::=  `(' [Exprs] `)'
                |  `(' [Exprs `,'] PostfixExpr `:' `_' `*' ')'
                |  [nl] BlockExpr
Exprs         ::=  Expr {`,' Expr}

An application $f$($e_1 , \ldots , e_m$) applies the function f to the argument expressions e1,,em. If f has a method type ($p_1$:$T_1 , \ldots , p_n$:$T_n$)$U$, the type of each argument expression ei is typed with the corresponding parameter type Ti as expected type. Let Si be type type of argument ei (i=1,,m). If f is a polymorphic method, local type inference is used to determine type arguments for f. If f has some value type, the application is taken to be equivalent to $f$.apply($e_1 , \ldots , e_m$), i.e. the application of an apply method defined by f.

The function f must be applicable to its arguments e1,,en of types S1,,Sn.

If f has a method type (p1:T1,,pn:Tn)U we say that an argument expression ei is a named argument if it has the form xi=eʹi and xi is one of the parameter names p1,,pn. The function f is applicable if all of the follwing conditions hold:

If f is a polymorphic method it is applicable if local type inference can determine type arguments so that the instantiated method is applicable. If f has some value type it is applicable if it has a method member named apply which is applicable.

Evaluation of $f$($e_1 , \ldots , e_n$) usually entails evaluation of f and e1,,en in that order. Each argument expression is converted to the type of its corresponding formal parameter. After that, the application is rewritten to the function's right hand side, with actual arguments substituted for formal parameters. The result of evaluating the rewritten right-hand side is finally converted to the function's declared result type, if one is given.

The case of a formal parameter with a parameterless method type =>$T$ is treated specially. In this case, the corresponding actual argument expression e is not evaluated before the application. Instead, every use of the formal parameter on the right-hand side of the rewrite rule entails a re-evaluation of e. In other words, the evaluation order for =>-parameters is call-by-name whereas the evaluation order for normal parameters is call-by-value. Furthermore, it is required that e's packed type conforms to the parameter type T. The behavior of by-name parameters is preserved if the application is transformed into a block due to named or default arguments. In this case, the local value for that parameter has the form val $y_i$ = () => $e$ and the argument passed to the function is $y_i$().

The last argument in an application may be marked as a sequence argument, e.g. $e$: _*. Such an argument must correspond to a repeated parameter of type $S$* and it must be the only argument matching this parameter (i.e. the number of formal parameters and actual arguments must be the same). Furthermore, the type of e must conform to scala.Seq[$T$], for some type T which conforms to S. In this case, the argument list is transformed by replacing the sequence e with its elements. When the application uses named arguments, the vararg parameter has to be specified exactly once.

A function application usually allocates a new frame on the program's run-time stack. However, if a local function or a final method calls itself as its last action, the call is executed using the stack-frame of the caller.

  1. Assume the following function which computes the sum of a variable number of arguments:

    def sum(xs: Int*) = (0 /: xs) ((x, y) => x + y)

    Then

    sum(1, 2, 3, 4)
    sum(List(1, 2, 3, 4): _*)

    both yield 10 as result. On the other hand,

    sum(List(1, 2, 3, 4))

    would not typecheck.

6.6.1 Named and Default Arguments

If an application might uses named arguments p=e or default arguments, the following conditions must hold.

If the application uses named or default arguments the following transformation is applied to convert it into an application without named or default arguments.

If the function f has the form $p.m$[$\mathit{targs}$] it is transformed into the block

{ val q = $p$
  q.$m$[$\mathit{targs}$]
}

If the function f is itself an application expression the transformation is applied recursively on f. The result of transforming f is a block of the form

{ val q = $p$
  val $x_1$ = expr$_1$
  $\ldots$
  val $x_k$ = expr$_k$
  q.$m$[$\mathit{targs}$]($\mathit{args}_1$)$, \ldots ,$($\mathit{args}_l$)
}

where every argument in (args1),,(argsl) is a reference to one of the values x1,,xk. To integrate the current application into the block, first a value definition using a fresh name yi is created for every argument in e1,,em, which is initialised to ei for positional arguments and to eʹi for named arguments of the form $x_i=e'_i$. Then, for every parameter which is not specified by the argument list, a value definition using a fresh name zi is created, which is initialized using the method computing the default argument of this parameter.

Let args be a permutation of the generated names yi and zi such such that the position of each name matches the position of its corresponding parameter in the method type ($p_1:T_1 , \ldots , p_n:T_n$)$U$. The final result of the transformation is a block of the form

{ val q = $p$
  val $x_1$ = expr$_1$
  $\ldots$
  val $x_l$ = expr$_k$
  val $y_1$ = $e_1$
  $\ldots$
  val $y_m$ = $e_m$
  val $z_1$ = q.$m$\$default\$i[$\mathit{targs}$]($\mathit{args}_1$)$, \ldots ,$($\mathit{args}_l$)
  $\ldots$
  val $z_d$ = q.$m$\$default\$j[$\mathit{targs}$]($\mathit{args}_1$)$, \ldots ,$($\mathit{args}_l$)
  q.$m$[$\mathit{targs}$]($\mathit{args}_1$)$, \ldots ,$($\mathit{args}_l$)($\mathit{args}$)
}

6.7 Method Values

SimpleExpr    ::=  SimpleExpr1 `_'

The expression $e$ _ is well-formed if e is of method type or if e is a call-by-name parameter. If e is a method with parameters, $e$ _~ represents e converted to a function type by eta expansion. If e is a parameterless method or call-by-name parameter of type =>$T$, $e$ _~ represents the function of type () => $T$, which evaluates e when it is applied to the empty parameterlist ().

  1. The method values in the left column are each equivalent to the anonymous functions on their right.

    Math.sin _ x => Math.sin(x)
    Array.range _ (x1, x2) => Array.range(x1, x2)
    List.map2 _ (x1, x2) => (x3) => List.map2(x1, x2)(x3)
    List.map2(xs, ys)_ x => List.map2(xs, ys)(x)

    Note that a space is necessary between a method name and the trailing underscore because otherwise the underscore would be considered part of the name.

6.8 Type Applications

SimpleExpr    ::=  SimpleExpr TypeArgs

A type application $e$[$T_1 , \ldots , T_n$] instantiates a polymorphic value e of type [$a_1$ >: $L_1$ <: $U_1, \ldots , a_n$ >: $L_n$ <: $U_n$]$S$ with argument types $T_1 , \ldots , T_n$. Every argument type Ti must obey the corresponding bounds Li and Ui. That is, for each i=1,,n, we must have σLi<:Ti<:σUi, where σ is the substitution [a1:=T1,,an:=Tn]. The type of the application is σS.

If the function part e is of some value type, the type application is taken to be equivalent to $e$.apply[$T_1 , \ldots ,$ T$_n$], i.e. the application of an apply method defined by e.

Type applications can be omitted if local type inference can infer best type parameters for a polymorphic functions from the types of the actual function arguments and the expected result type.

6.9 Tuples

SimpleExpr   ::=  `(' [Exprs] `)'

A tuple expression ($e_1 , \ldots , e_n$) is an alias for the class instance creation scala.Tuple$n$($e_1 , \ldots , e_n$), where n2.
The empty tuple () is the unique value of type scala.Unit.

6.10 Instance Creation Expressions

SimpleExpr     ::=  `new' (ClassTemplate | TemplateBody)

A simple instance creation expression is of the form new $c$ where c is a constructor invocation. Let T be the type of c. Then T must denote a (a type instance of) a non-abstract subclass of scala.AnyRef. Furthermore, the concrete self type of the expression must conform to the self type of the class denoted by T. The concrete self type is normally T, except if the expression new $c$ appears as the right hand side of a value definition

val $x$: $S$ = new $c$

(where the type annotation : $S$ may be missing). In the latter case, the concrete self type of the expression is the compound type $T$ with $x$.type.

The expression is evaluated by creating a fresh object of type T which is is initialized by evaluating c. The type of the expression is T.

A general instance creation expression is of the form new $t$ for some class template t. Such an expression is equivalent to the block

{ class $a$ extends $t$; new $a$ }

where a is a fresh name of an anonymous class which is inaccessible to user programs.

There is also a shorthand form for creating values of structural types: If {$D$} is a class body, then new {$D$} is equivalent to the general instance creation expression new AnyRef{$D$}.

  1. Consider the following structural instance creation expression:

    new { def getName() = "aaron" }

    This is a shorthand for the general instance creation expression

    new AnyRef{ def getName() = "aaron" }

    The latter is in turn a shorthand for the block

    { class anon\$X extends AnyRef{ def getName() = "aaron" }; new anon\$X }

    where anon\$X is some freshly created name.

6.11 Blocks

BlockExpr   ::=  `{' Block `}'
Block       ::=  {BlockStat semi} [ResultExpr]

A block expression {$s_1$; $\ldots$; $s_n$; $e\,$} is constructed from a sequence of block statements s1,,sn and a final expression e. The statement sequence may not contain two definitions or declarations that bind the same name in the same namespace. The final expression can be omitted, in which case the unit value () is assumed.

The expected type of the final expression e is the expected type of the block. The expected type of all preceding statements is undefined.

The type of a block $s_1$; $\ldots$; $s_n$; $e$ is $T$ forSome {$\,Q\,$}, where T is the type of e and Q contains existential clauses for every value or type name which is free in T and which is defined locally in one of the statements s1,,sn. We say the existential clause binds the occurrence of the value or type name. Specifically,

Evaluation of the block entails evaluation of its statement sequence, followed by an evaluation of the final expression e, which defines the result of the block.

  1. Assuming a class Ref[T](x: T), the block

    { class C extends B {$\ldots$} ; new Ref(new C) }

    has the type Ref[_1] forSome { type _1 <: B }. The block

    { class C extends B {$\ldots$} ; new C }

    simply has type B, because with the rules here the existentially quantified type _1 forSome { type _1 <: B } can be simplified to B.

6.12 Prefix, Infix, and Postfix Operations

PostfixExpr     ::=  InfixExpr [id [nl]]
InfixExpr       ::=  PrefixExpr
                  |  InfixExpr id [nl] InfixExpr
PrefixExpr      ::=  [`-' | `+' | `!' | `~'] SimpleExpr 

Expressions can be constructed from operands and operators.

6.12.1 Prefix Operations

A prefix operation op;e consists of a prefix operator op, which must be one of the identifiers ‘+’, ‘-’, ‘!’ or ‘~’. The expression op;e is equivalent to the postfix method application e.unary_$\mathit{op}$.

Prefix operators are different from normal function applications in that their operand expression need not be atomic. For instance, the input sequence -sin(x) is read as -(sin(x)), whereas the function application negate sin(x) would be parsed as the application of the infix operator sin to the operands negate and (x).

6.12.2 Postfix Operations

A postfix operator can be an arbitrary identifier. The postfix operation e;op is interpreted as e.op.

6.12.3 Infix Operations

An infix operator can be an arbitrary identifier. Infix operators have precedence and associativity defined as follows:

The precedence of an infix operator is determined by the operator's first character. Characters are listed below in increasing order of precedence, with characters on the same line having the same precedence.

$\mbox{\rm\sl(all letters)}$
|
^
&
< >
= !
:
+ -
* / %
$\mbox{\rm\sl(all other special characters)}$

That is, operators starting with a letter have lowest precedence, followed by operators starting with `|', etc.

There's one exception to this rule, which concerns assignment operators. The precedence of an assigment operator is the same as the one of simple assignment (=). That is, it is lower than the precedence of any other operator.

The associativity of an operator is determined by the operator's last character. Operators ending in a colon `:' are right-associative. All other operators are left-associative.

Precedence and associativity of operators determine the grouping of parts of an expression as follows.

The right-hand operand of a left-associative operator may consist of several arguments enclosed in parentheses, e.g. e;op;(e1,,en). This expression is then interpreted as e.op(e1,,en).

A left-associative binary operation e1;op;e2 is interpreted as e1.op(e2). If op is right-associative, the same operation is interpreted as { val $x$=$e_1$; $e_2$.$\mathit{op}$($x\,$) }, where x is a fresh name.

6.12.4 Assignment Operators

An assignment operator is an operator symbol (syntax category op in Identifiers) that ends in an equals character “=”, with the exception of operators for which one of the following conditions holds:

  1. the operator also starts with an equals character, or
  2. the operator is one of (<=), (>=), (!=).

Assignment operators are treated specially in that they can be expanded to assignments if no other interpretation is valid.

Let's consider an assignment operator such as += in an infix operation $l$ += $r$, where l, r are expressions.
This operation can be re-interpreted as an operation which corresponds to the assignment

$l$ = $l$ + $r$

except that the operation's left-hand-side l is evaluated only once.

The re-interpretation occurs if the following two conditions are fulfilled.

  1. The left-hand-side l does not have a member named +=, and also cannot be converted by an implicit conversion to a value with a member named +=.
  2. The assignment $l$ = $l$ + $r$ is type-correct. In particular this implies that l refers to a variable or object that can be assigned to, and that is convertible to a value with a member named +.

6.13 Typed Expressions

Expr1              ::=  PostfixExpr `:' CompoundType

The typed expression e:T has type T. The type of expression e is expected to conform to T. The result of the expression is the value of e converted to type T.

  1. Here are examples of well-typed and illegally typed expressions.

    1: Int               // legal, of type Int
    1: Long              // legal, of type Long
    // 1: string         // ***** illegal

6.14 Annotated Expressions

Expr1              ::=  PostfixExpr `:' Annotation {Annotation} 

An annotated expression $e$: @$a_1$ $\ldots$ @$a_n$ attaches annotations a1,,an to the expression e.

6.15 Assignments

Expr1        ::=  [SimpleExpr `.'] id `=' Expr
               |  SimpleExpr1 ArgumentExprs `=' Expr

The interpretation of an assignment to a simple variable $x$ = $e$ depends on the definition of x. If x denotes a mutable variable, then the assignment changes the current value of x to be the result of evaluating the expression e. The type of e is expected to conform to the type of x. If x is a parameterless function defined in some template, and the same template contains a setter function $x$_= as member, then the assignment $x$ = $e$ is interpreted as the invocation $x$_=($e\,$) of that setter function. Analogously, an assignment $f.x$ = $e$ to a parameterless function x is interpreted as the invocation $f.x$_=($e\,$).

An assignment $f$($\mathit{args}\,$) = $e$ with a function application to the left of the ‘=’ operator is interpreted as $f.$update($\mathit{args}$, $e\,$), i.e.
the invocation of an update function defined by f.

  1. Here are some assignment expressions and their equivalent expansions.

    x.f = e x.f_=(e)
    x.f() = e x.f.update(e)
    x.f(i) = e x.f.update(i, e)
    x.f(i, j) = e x.f.update(i, j, e)
  2. Here is the usual imperative code for matrix multiplication.

    def matmul(xss: Array[Array[Double]], yss: Array[Array[Double]]) = {
      val zss: Array[Array[Double]] = new Array(xss.length, yss(0).length) 
      var i = 0 
      while (i < xss.length) {
        var j = 0 
        while (j < yss(0).length) {
          var acc = 0.0 
          var k = 0 
          while (k < yss.length) {
            acc = acc + xss(i)(k) * yss(k)(j) 
            k += 1
          }
          zss(i)(j) = acc 
          j += 1
        }
        i += 1
      }
      zss
    }

    Desugaring the array accesses and assignments yields the following expanded version:

    def matmul(xss: Array[Array[Double]], yss: Array[Array[Double]]) = {
      val zss: Array[Array[Double]] = new Array(xss.length, yss.apply(0).length) 
      var i = 0 
      while (i < xss.length) {
        var j = 0 
        while (j < yss.apply(0).length) {
          var acc = 0.0 
          var k = 0 
          while (k < yss.length) {
            acc = acc + xss.apply(i).apply(k) * yss.apply(k).apply(j) 
            k += 1
          }
          zss.apply(i).update(j, acc) 
          j += 1
        }
        i += 1
      }
      zss
    }

6.16 Conditional Expressions

Expr1          ::=  `if' `(' Expr `)' {nl} Expr [[semi] `else' Expr]

The conditional expression if ($e_1$) $e_2$ else $e_3$ chooses one of the values of e2 and e3, depending on the value of e1. The condition e1 is expected to conform to type Boolean. The then-part e2 and the else-part e3 are both expected to conform to the expected type of the conditional expression. The type of the conditional expression is the weak least upper bound of the types of e2 and e3. A semicolon preceding the else symbol of a conditional expression is ignored.

The conditional expression is evaluated by evaluating first e1. If this evaluates to true, the result of evaluating e2 is returned, otherwise the result of evaluating e3 is returned.

A short form of the conditional expression eliminates the else-part. The conditional expression if ($e_1$) $e_2$ is evaluated as if it was if ($e_1$) $e_2$ else ().

6.17 While Loop Expressions

Expr1          ::=  `while' `(' Expr ')' {nl} Expr

The while loop expression while ($e_1$) $e_2$ is typed and evaluated as if it was an application of whileLoop ($e_1$) ($e_2$) where the hypothetical function whileLoop is defined as follows.

def whileLoop(cond: => Boolean)(body: => Unit): Unit  =
  if (cond) { body ; whileLoop(cond)(body) } else {}

6.18 Do Loop Expressions

Expr1          ::=  `do' Expr [semi] `while' `(' Expr ')'

The do loop expression do $e_1$ while ($e_2$) is typed and evaluated as if it was the expression ($e_1$ ; while ($e_2$) $e_1$). A semicolon preceding the while symbol of a do loop expression is ignored.

6.19 For Comprehensions and For Loops

Expr1          ::=  `for' (`(' Enumerators `)' | `{' Enumerators `}') 
                       {nl} [`yield'] Expr
Enumerators    ::=  Generator {semi Enumerator}
Enumerator     ::=  Generator 
                 |  Guard
                 |  `val' Pattern1 `=' Expr
Generator      ::=  Pattern1 `<-' Expr [Guard]
Guard          ::=  `if' PostfixExpr

A for loop for ($\mathit{enums}\,$) $e$ executes expression e for each binding generated by the enumerators enums. A for comprehension for ($\mathit{enums}\,$) yield $e$ evaluates expression e for each binding generated by the enumerators enums and collects the results. An enumerator sequence always starts with a generator; this can be followed by further generators, value definitions, or guards. A generator $p$ <- $e$ produces bindings from an expression e which is matched in some way against pattern p. A value definition $p$ = $e$ binds the value name p (or several names in a pattern p) to the result of evaluating the expression e. A guard if $e$ contains a boolean expression which restricts enumerated bindings. The precise meaning of generators and guards is defined by translation to invocations of four methods: map, withFilter, flatMap, and foreach. These methods can be implemented in different ways for different carrier types.

The translation scheme is as follows. In a first step, every generator $p$ <- $e$, where p is not irrefutable for the type of e is replaced by

$p$ <- $e$.withFilter { case $p$ => true; case _ => false }

Then, the following rules are applied repeatedly until all comprehensions have been eliminated.

  1. The following code produces all pairs of numbers between 1 and n1 whose sums are prime.

    for  { i <- 1 until n 
           j <- 1 until i 
           if isPrime(i+j)
    } yield (i, j)

    The for comprehension is translated to:

    (1 until n)
      .flatMap {
         case i => (1 until i)
           .withFilter { j => isPrime(i+j) }
           .map { case j => (i, j) } }
  2. For comprehensions can be used to express vector and matrix algorithms concisely. For instance, here is a function to compute the transpose of a given matrix:

    def transpose[A](xss: Array[Array[A]]) = {
      for (i <- Array.range(0, xss(0).length)) yield
        for (xs <- xss) yield xs(i)
    }

    Here is a function to compute the scalar product of two vectors:

    def scalprod(xs: Array[Double], ys: Array[Double]) = {
      var acc = 0.0 
      for ((x, y) <- xs zip ys) acc = acc + x * y  
      acc
    }

    Finally, here is a function to compute the product of two matrices. Compare with the imperative version of .

    def matmul(xss: Array[Array[Double]], yss: Array[Array[Double]]) = {
      val ysst = transpose(yss) 
      for (xs <- xss) yield
        for (yst <- ysst) yield 
          scalprod(xs, yst)
    }

    The code above makes use of the fact that map, flatMap, withFilter, and foreach are defined for instances of class scala.Array.

6.20 Return Expressions

Expr1      ::=  `return' [Expr]

A return expression return $e$ must occur inside the body of some enclosing named method or function. The innermost enclosing named method or function in a source program, f, must have an explicitly declared result type, and the type of e must conform to it.
The return expression evaluates the expression e and returns its value as the result of f. The evaluation of any statements or expressions following the return expression is omitted. The type of a return expression is scala.Nothing.

The expression e may be omitted. The return expression return is type-checked and evaluated as if it was return ().

An apply method which is generated by the compiler as an expansion of an anonymous function does not count as a named function in the source program, and therefore is never the target of a return expression.

Returning from a nested anonymous function is implemented by throwing and catching a scala.runtime.NonLocalReturnException. Any exception catches between the point of return and the enclosing methods might see the exception. A key comparison makes sure that these exceptions are only caught by the method instance which is terminated by the return.

If the return expression is itself part of an anonymous function, it is possible that the enclosing instance of f has already returned before the return expression is executed. In that case, the thrown scala.runtime.NonLocalReturnException will not be caught, and will propagate up the call stack.

6.21 Throw Expressions

Expr1      ::=  `throw' Expr

A throw expression throw $e$ evaluates the expression e. The type of this expression must conform to Throwable. If e evaluates to an exception reference, evaluation is aborted with the thrown exception. If e evaluates to null, evaluation is instead aborted with a NullPointerException. If there is an active try expression which handles the thrown exception, evaluation resumes with the handler; otherwise the thread executing the throw is aborted. The type of a throw expression is scala.Nothing.

6.22 Try Expressions

Expr1 ::=  `try' `{' Block `}' [`catch' `{' CaseClauses `}'] 
           [`finally' Expr]

A try expression is of the form try { $b$ } catch $h$ where the handler h is a pattern matching anonymous function

{ case $p_1$ => $b_1$ $\ldots$ case $p_n$ => $b_n$ }

This expression is evaluated by evaluating the block b. If evaluation of b does not cause an exception to be thrown, the result of b is returned. Otherwise the handler h is applied to the thrown exception.
If the handler contains a case matching the thrown exception, the first such case is invoked. If the handler contains no case matching the thrown exception, the exception is re-thrown.

Let pt be the expected type of the try expression. The block b is expected to conform to pt. The handler h is expected conform to type scala.PartialFunction[scala.Throwable, $\mathit{pt}\,$]. The type of the try expression is the weak least upper bound of the type of b and the result type of h.

A try expression try { $b$ } finally $e$ evaluates the block b. If evaluation of b does not cause an exception to be thrown, the expression e is evaluated. If an exception is thrown during evaluation of e, the evaluation of the try expression is aborted with the thrown exception. If no exception is thrown during evaluation of e, the result of b is returned as the result of the try expression.

If an exception is thrown during evaluation of b, the finally block e is also evaluated. If another exception e is thrown during evaluation of e, evaluation of the try expression is aborted with the thrown exception. If no exception is thrown during evaluation of e, the original exception thrown in b is re-thrown once evaluation of e has completed. The block b is expected to conform to the expected type of the try expression. The finally expression e is expected to conform to type Unit.

A try expression try { $b$ } catch $e_1$ finally $e_2$ is a shorthand for try { try { $b$ } catch $e_1$ } finally $e_2$.

6.23 Anonymous Functions

Expr            ::=  (Bindings | [`implicit'] id | `_') `=>' Expr
ResultExpr      ::=  (Bindings | ([`implicit'] id | `_') `:' CompoundType) `=>' Block
Bindings        ::=  `(' Binding {`,' Binding} `)'
Binding         ::=  (id | `_') [`:' Type]

The anonymous function ($x_1$: $T_1 , \ldots , x_n$: $T_n$) => e maps parameters xi of types Ti to a result given by expression e. The scope of each formal parameter xi is e. Formal parameters must have pairwise distinct names.

If the expected type of the anonymous function is of the form scala.Function$n$[$S_1 , \ldots , S_n$, $R\,$], the expected type of e is R and the type Ti of any of the parameters xi can be omitted, in which case$T_i$ = $S_i$ is assumed. If the expected type of the anonymous function is some other type, all formal parameter types must be explicitly given, and the expected type of e is undefined. The type of the anonymous function isscala.Function$n$[$S_1 , \ldots , S_n$, $T\,$], where T is the packed type of e. T must be equivalent to a type which does not refer to any of the formal parameters xi.

The anonymous function is evaluated as the instance creation expression

new scala.Function$n$[$T_1 , \ldots , T_n$, $T$] {
  def apply($x_1$: $T_1 , \ldots , x_n$: $T_n$): $T$ = $e$
}

In the case of a single untyped formal parameter, ($x\,$) => $e$ can be abbreviated to $x$ => $e$. If an anonymous function ($x$: $T\,$) => $e$ with a single typed parameter appears as the result expression of a block, it can be abbreviated to $x$: $T$ => e.

A formal parameter may also be a wildcard represented by an underscore _. In that case, a fresh name for the parameter is chosen arbitrarily.

A named parameter of an anonymous function may be optionally preceded by an implicit modifier. In that case the parameter is labeled implicit; however the parameter section itself does not count as an implicit parameter section in the sense defined here. Hence, arguments to anonymous functions always have to be given explicitly.

  1. Examples of anonymous functions:

    x => x                             // The identity function
    
    f => g => x => f(g(x))             // Curried function composition
    
    (x: Int,y: Int) => x + y           // A summation function
    
    () => { count += 1; count }        // The function which takes an
                                       // empty parameter list $()$, 
                                       // increments a non-local variable 
                                       // `count' and returns the new value.
    
    _ => 5                             // The function that ignores its argument
                                       // and always returns 5.

6.23.1 Placeholder Syntax for Anonymous Functions

SimpleExpr1  ::=  `_'

An expression (of syntactic category Expr) may contain embedded underscore symbols _ at places where identifiers are legal. Such an expression represents an anonymous function where subsequent occurrences of underscores denote successive parameters.

Define an underscore section to be an expression of the form _:$T$ where T is a type, or else of the form _, provided the underscore does not appear as the expression part of a type ascription _:$T$.

An expression e of syntactic category Expr binds an underscore section u, if the following two conditions hold: (1) e properly contains u, and (2) there is no other expression of syntactic category Expr which is properly contained in e and which itself properly contains u.

If an expression e binds underscore sections u1,,un, in this order, it is equivalent to the anonymous function ($u'_1$, ... $u'_n$) => $e'$ where each uiʹ results from ui by replacing the underscore with a fresh identifier and eʹ results from e by replacing each underscore section ui by uiʹ.

  1. The anonymous functions in the left column use placeholder syntax. Each of these is equivalent to the anonymous function on its right.

    _ + 1 x => x + 1
    _ * _ (x1, x2) => x1 * x2
    (_: Int) * 2 (x: Int) => (x: Int) * 2
    if (_) x else y z => if (z) x else y
    _.map(f) x => x.map(f)
    _.map(_ + 1) x => x.map(y => y + 1)

6.24 Constant Expressions

Constant expressions are expressions that the Scala compiler can evaluate to a constant. The definition of ``constant expression'' depends on the platform, but they include at least the expressions of the following forms:

6.25 Statements

BlockStat    ::=  Import
               |  {Annotation} [`implicit'] Def
               |  {Annotation} {LocalModifier} TmplDef
               |  Expr1
               | 
TemplateStat ::=  Import
               |  {Annotation} {Modifier} Def
               |  {Annotation} {Modifier} Dcl
               |  Expr
               | 

Statements occur as parts of blocks and templates. A statement can be an import, a definition or an expression, or it can be empty. Statements used in the template of a class definition can also be declarations. An expression that is used as a statement can have an arbitrary value type. An expression statement e is evaluated by evaluating e and discarding the result of the evaluation.

Block statements may be definitions which bind local names in the block. The only modifier allowed in all block-local definitions is implicit. When prefixing a class or object definition, modifiers abstract, final, and sealed are also permitted.

Evaluation of a statement sequence entails evaluation of the statements in the order they are written.

6.26 Implicit Conversions

Implicit conversions can be applied to expressions whose type does not match their expected type, to qualifiers in selections, and to unapplied methods. The available implicit conversions are given in the next two sub-sections.

We say, a type T is compatible to a type U if T conforms to U after applying eta-expansion and view applications.

6.26.1 Value Conversions

The following five implicit conversions can be applied to an expression e which has some value type T and which is type-checked with some expected type pt.

Overloading Resolution
If an expression denotes several possible members of a class, overloading resolution is applied to pick a unique member.

Type Instantiation
An expression e of polymorphic type

[$a_1$ >: $L_1$ <: $U_1 , \ldots , a_n$ >: $L_n$ <: $U_n$]$T$

which does not appear as the function part of a type application is converted to a type instance of T by determining with local type inference instance types $T_1 , \ldots , T_n$ for the type variables $a_1 , \ldots , a_n$ and implicitly embedding e in the type application $e$[$T_1 , \ldots , T_n$].

Numeric Widening
If e has a primitive number type which weakly conforms to the expected type, it is widened to the expected type using one of the numeric conversion methods toShort, toChar, toInt, toLong, toFloat, toDouble defined here.

Numeric Literal Narrowing
If the expected type is Byte, Short or Char, and the expression e is an integer literal fitting in the range of that type, it is converted to the same literal in that type.

Value Discarding
If e has some value type and the expected type is Unit, e is converted to the expected type by embedding it in the term { $e$; () }.

View Application
If none of the previous conversions applies, and e's type does not conform to the expected type pt, it is attempted to convert e to the expected type with a view.

Dynamic Member Selection
If none of the previous conversions applies, and e is a prefix of a selection e.x, and e's type conforms to class scala.Dynamic, then the selection is rewritten according to the rules for dynamic member selection.

6.26.2 Method Conversions

The following four implicit conversions can be applied to methods which are not applied to some argument list.

Evaluation
A parameterless method m of type => $T$ is always converted to type T by evaluating the expression to which m is bound.

Implicit Application
If the method takes only implicit parameters, implicit arguments are passed following the rules here.

Eta Expansion
Otherwise, if the method is not a constructor, and the expected type pt is a function type (Tsʹ)Tʹ, eta-expansion is performed on the expression e.

Empty Application
Otherwise, if e has method type ()T, it is implicitly applied to the empty argument list, yielding e().

6.26.3 Overloading Resolution

If an identifier or selection e references several members of a class, the context of the reference is used to identify a unique member. The way this is done depends on whether or not e is used as a function. Let 𝒜 be the set of members referenced by e.

Assume first that e appears as a function in an application, as in $e$($e_1 , \ldots , e_m$).

One first determines the set of functions that is potentially applicable based on the shape of the arguments.

The shape of an argument expression e, written shape(e), is a type that is defined as follows:

Let be the set of alternatives in 𝒜 that are applicable to expressions (e1,,en) of types (shape(e1),,shape(en)). If there is precisely one alternative in , that alternative is chosen.

Otherwise, let S1,,Sm be the vector of types obtained by typing each argument with an undefined expected type. For every member m in one determines whether it is applicable to expressions (e1,,em) of types S1,,Sm. It is an error if none of the members in is applicable. If there is one single applicable alternative, that alternative is chosen. Otherwise, let 𝒞𝒞 be the set of applicable alternatives which don't employ any default argument in the application to e1,,em. It is again an error if 𝒞𝒞 is empty. Otherwise, one chooses the most specific alternative among the alternatives in 𝒞𝒞, according to the following definition of being as specific as'', andmore specific than'':

The relative weight of an alternative A over an alternative B is a number from 0 to 2, defined as the sum of

A class or object C is derived from a class or object D if one of the following holds:

An alternative A is more specific than an alternative B if the relative weight of A over B is greater than the relative weight of B over A.

It is an error if there is no alternative in 𝒞𝒞 which is more specific than all other alternatives in 𝒞𝒞.

Assume next that e appears as a function in a type application, as in $e$[$\mathit{targs}\,$]. Then all alternatives in 𝒜 which take the same number of type parameters as there are type arguments in targs are chosen. It is an error if no such alternative exists. If there are several such alternatives, overloading resolution is applied again to the whole expression $e$[$\mathit{targs}\,$].

Assume finally that e does not appear as a function in either an application or a type application. If an expected type is given, let be the set of those alternatives in 𝒜 which are compatible to it. Otherwise, let be the same as 𝒜. We choose in this case the most specific alternative among all alternatives in . It is an error if there is no alternative in which is more specific than all other alternatives in .

  1. Consider the following definitions:

    class A extends B {}
    def f(x: B, y: B) = $\ldots$
    def f(x: A, y: B) = $\ldots$
    val a: A 
    val b: B

    Then the application f(b, b) refers to the first definition of f whereas the application f(a, a) refers to the second. Assume now we add a third overloaded definition

    def f(x: B, y: A) = $\ldots$

    Then the application f(a, a) is rejected for being ambiguous, since no most specific applicable signature exists.

6.26.4 Local Type Inference

Local type inference infers type arguments to be passed to expressions of polymorphic type. Say e is of type [a1 >: L1 <: U1,,an >: Ln <: Un]T and no explicit type parameters are given.

Local type inference converts this expression to a type application $e$[$T_1 , \ldots , T_n$]. The choice of the type arguments T1,,Tn depends on the context in which the expression appears and on the expected type pt. There are three cases.

Case 1: Selections
If the expression appears as the prefix of a selection with a name x, then type inference is deferred to the whole expression e.x. That is, if e.x has type S, it is now treated as having type [a1 >: L1 <: U1,,an >: Ln <: Un]S, and local type inference is applied in turn to infer type arguments for a1,,an, using the context in which e.x appears.

Case 2: Values
If the expression e appears as a value without being applied to value arguments, the type arguments are inferred by solving a constraint system which relates the expression's type T with the expected type pt. Without loss of generality we can assume that T is a value type; if it is a method type we apply eta-expansion to convert it to a function type. Solving means finding a substitution σ of types Ti for the type parameters ai such that

It is a compile time error if no such substitution exists.
If several substitutions exist, local-type inference will choose for each type variable ai a minimal or maximal type Ti of the solution space. A maximal type Ti will be chosen if the type parameter ai appears contravariantly in the type T of the expression. A minimal type Ti will be chosen in all other situations, i.e. if the variable appears covariantly, non-variantly or not at all in the type T. We call such a substitution an optimal solution of the given constraint system for the type T.

Case 3: Methods
The last case applies if the expression e appears in an application e(d1,,dm). In that case T is a method type (p1:R1,,pm:Rm)Tʹ. Without loss of generality we can assume that the result type Tʹ is a value type; if it is a method type we apply eta-expansion to convert it to a function type. One computes first the types Sj of the argument expressions dj, using two alternative schemes. Each argument expression dj is typed first with the expected type Rj, in which the type parameters a1,,an are taken as type constants. If this fails, the argument dj is typed instead with an expected type Rjʹ which results from Rj by replacing every type parameter in a1,,an with {}.

In a second step, type arguments are inferred by solving a constraint system which relates the method's type with the expected type pt and the argument types S1,,Sm. Solving the constraint system means finding a substitution σ of types Ti for the type parameters ai such that

It is a compile time error if no such substitution exists. If several solutions exist, an optimal one for the type Tʹ is chosen.

All or parts of an expected type pt may be undefined. The rules for conformance are extended to this case by adding the rule that for any type T the following two statements are always true: undefined<:T and T<:undefined

It is possible that no minimal or maximal solution for a type variable exists, in which case a compile-time error results. Because <: is a pre-order, it is also possible that a solution set has several optimal solutions for a type. In that case, a Scala compiler is free to pick any one of them.

  1. Consider the two methods:

    def cons[A](x: A, xs: List[A]): List[A] = x :: xs
    def nil[B]: List[B] = Nil

    and the definition

    val xs = cons(1, nil)

    The application of cons is typed with an undefined expected type. This application is completed by local type inference to cons[Int](1, nil). Here, one uses the following reasoning to infer the type argument Int for the type parameter a:

    First, the argument expressions are typed. The first argument 1 has type Int whereas the second argument nil is itself polymorphic. One tries to type-check nil with an expected type List[a]. This leads to the constraint system

    List[b?] <: List[a]

    where we have labeled b? with a question mark to indicate that it is a variable in the constraint system. Because class List is covariant, the optimal solution of this constraint is

    b = scala.Nothing

    In a second step, one solves the following constraint system for the type parameter a of cons:

    Int <: a?
    List[scala.Nothing] <: List[a?]
    List[a?] <: $\mbox{\sl undefined}$

    The optimal solution of this constraint system is

    a = Int

    so Int is the type inferred for a.

  2. Consider now the definition

    val ys = cons("abc", xs)

    where xs is defined of type List[Int] as before. In this case local type inference proceeds as follows.

    First, the argument expressions are typed. The first argument "abc" has type String. The second argument xs is first tried to be typed with expected type List[a]. This fails, as List[Int] is not a subtype of List[a]. Therefore, the second strategy is tried; xs is now typed with expected type List[$\mbox{\sl undefined}$]. This succeeds and yields the argument type List[Int].

    In a second step, one solves the following constraint system for the type parameter a of cons:

    String <: a?
    List[Int] <: List[a?]
    List[a?] <: $\mbox{\sl undefined}$

    The optimal solution of this constraint system is

    a = scala.Any 

    so scala.Any is the type inferred for a.

6.26.5 Eta Expansion

Eta-expansion converts an expression of method type to an equivalent expression of function type. It proceeds in two steps.

First, one identifes the maximal sub-expressions of e; let's say these are e1,,em. For each of these, one creates a fresh name xi. Let eʹ be the expression resulting from replacing every maximal subexpression ei in e by the corresponding fresh name xi. Second, one creates a fresh name yi for every argument type Ti of the method (i=1,,n). The result of eta-conversion is then:

{ val $x_1$ = $e_1$; 
  $\ldots$ 
  val $x_m$ = $e_m$; 
  ($y_1: T_1 , \ldots , y_n: T_n$) => $e'$($y_1 , \ldots , y_n$) 
}

6.26.6 Dynamic Member Selection

The standard Scala library defines a trait scala.Dynamic which defines a member @invokeDynamic@ as follows:

package scala
trait Dynamic {
  def applyDynamic (name: String, args: Any*): Any
  ...
}

Assume a selection of the form e.x where the type of e conforms to scala.Dynamic. Further assuming the selection is not followed by any function arguments, such an expression can be rewitten under the conditions given here to:

$e$.applyDynamic("$x$")

If the selection is followed by some arguments, e.g. e.x(args), then that expression is rewritten to

$e$.applyDynamic("$x$", $\mathit{args}$)

7 Implicit Parameters and Views

7.1 The Implicit Modifier

LocalModifier  ::= ‘implicit’
ParamClauses   ::= {ParamClause} [nl] ‘(’ ‘implicit’ Params ‘)’

Template members and parameters labeled with an implicit modifier can be passed to implicit parameters and can be used as implicit conversions called views. The implicit modifier is illegal for all type members, as well as for top-level objects.

  1. The following code defines an abstract class of monoids and two concrete implementations, StringMonoid and IntMonoid. The two implementations are marked implicit.

    abstract class Monoid[A] extends SemiGroup[A] {
      def unit: A
      def add(x: A, y: A): A
    }
    object Monoids {
      implicit object stringMonoid extends Monoid[String] {
        def add(x: String, y: String): String = x.concat(y)
        def unit: String = ""
      }
      implicit object intMonoid extends Monoid[Int] {
        def add(x: Int, y: Int): Int = x + y
        def unit: Int = 0
      }
    }

7.2 Implicit Parameters

An implicit parameter list (implicit $p_1$,$\ldots$,$p_n$) of a method marks the parameters p1,,pn as implicit. A method or constructor can have only one implicit parameter list, and it must be the last parameter list given.

A method with implicit parameters can be applied to arguments just like a normal method. In this case the implicit label has no effect. However, if such a method misses arguments for its implicit parameters, such arguments will be automatically provided.

The actual arguments that are eligible to be passed to an implicit parameter of type T fall into two categories. First, eligible are all identifiers x that can be accessed at the point of the method call without a prefix and that denote an implicit definition or an implicit parameter. An eligible identifier may thus be a local name, or a member of an enclosing template, or it may be have been made accessible without a prefix through an import clause. If there are no eligible identifiers under this rule, then, second, eligible are also all implicit members of some object that belongs to the implicit scope of the implicit parameter's type, T.

The implicit scope of a type T consists of all companion modules of classes that are associated with the implicit parameter's type. Here, we say a class C is associated with a type T, if it is a base class of some part of T. The parts of a type T are:

If there are several eligible arguments which match the implicit parameter's type, a most specific one will be chosen using the rules of static overloading resolution. If the parameter has a default argument and no implicit argument can be found the default argument is used.

  1. Assuming the classes from , here is a method which computes the sum of a list of elements using the monoid's add and unit operations.

    def sum[A](xs: List[A])(implicit m: Monoid[A]): A = 
      if (xs.isEmpty) m.unit
      else m.add(xs.head, sum(xs.tail))

    The monoid in question is marked as an implicit parameter, and can therefore be inferred based on the type of the list. Consider for instance the call sum(List(1, 2, 3)) in a context where stringMonoid and intMonoid are visible. We know that the formal type parameter a of sum needs to be instantiated to Int. The only eligible object which matches the implicit formal parameter type Monoid[Int] is intMonoid so this object will be passed as implicit parameter.

This discussion also shows that implicit parameters are inferred after any type arguments are inferred.

Implicit methods can themselves have implicit parameters. An example is the following method from module scala.List, which injects lists into the scala.Ordered class, provided the element type of the list is also convertible to this type.

implicit def list2ordered[A](x: List[A])
  (implicit elem2ordered: A => Ordered[A]): Ordered[List[A]] = 
  ...

Assume in addition a method

implicit def int2ordered(x: Int): Ordered[Int]

that injects integers into the Ordered class. We can now define a sort method over ordered lists:

def sort[A](xs: List[A])(implicit a2ordered: A => Ordered[A]) = ...

We can apply sort to a list of lists of integers yss: List[List[Int]] as follows:

sort(yss)

The call above will be completed by passing two nested implicit arguments:

sort(yss)(xs: List[Int] => list2ordered[Int](xs)(int2ordered)) .

The possibility of passing implicit arguments to implicit arguments raises the possibility of an infinite recursion. For instance, one might try to define the following method, which injects every type into the Ordered class:

implicit def magic[A](x: A)(implicit a2ordered: A => Ordered[A]): Ordered[A] = 
  a2ordered(x)

Now, if one tried to apply sort to an argument arg of a type that did not have another injection into the Ordered class, one would obtain an infinite expansion:

sort(arg)(x => magic(x)(x => magic(x)(x => ... )))

To prevent such infinite expansions, the compiler keeps track of a stack of “open implicit types” for which implicit arguments are currently being searched. Whenever an implicit argument for type T is searched, the “core type” of T is added to the stack. Here, the core type of T is T with aliases expanded, top-level type annotations and refinements removed, and occurrences of top-level existentially bound variables replaced by their upper bounds. The core type is removed from the stack once the search for the implicit argument either definitely fails or succeeds. Everytime a core type is added to the stack, it is checked that this type does not dominate any of the other types in the set.

Here, a core type T dominates a type U if T is equivalent to U, or if the top-level type constructors of T and U have a common element and T is more complex than U.

The set of top-level type constructors ttcs(T) of a type T depends on the form of the type:

For a type designator,
ttcs(p.c)={c};
For a parameterized type,
ttcs(p.c[targs])={c};
For a singleton type,
ttcs(p.type)=ttcs(T), provided p has type T;
For a compound type,
$\mathit{ttcs}(T_1$ with $\ldots$ with $T_n)$ =ttcs(T1)ttcs(Tn).

The complexity complexity(T) of a core type is an integer which also depends on the form of the type:

For a type designator,
complexity(p.c)=1+complexity(p)
For a parameterized type,
complexity(p.c[targs])=1+Σcomplexity(targs)
For a singleton type denoting a package p,
complexity(p.type)=0
For any other singleton type,
complexity(p.type)=1+complexity(T), provided p has type T;
For a compound type,
$\mathit{complexity}(T_1$ with $\ldots$ with $T_n)$ =Σcomplexity(Ti)

  1. When typing sort(xs) for some list xs of type List[List[List[Int]]], the sequence of types for which implicit arguments are searched is

    List[List[Int]] => Ordered[List[List[Int]]], 
    List[Int] => Ordered[List[Int]]
    Int => Ordered[Int]

    All types share the common type constructor scala.Function1, but the complexity of the each new type is lower than the complexity of the previous types. Hence, the code typechecks.

  2. Let ys be a list of some type which cannot be converted to Ordered. For instance:

    val ys = List(new IllegalArgumentException, new ClassCastException, new Error)

    Assume that the definition of magic above is in scope. Then the sequence of types for which implicit arguments are searched is

    Throwable => Ordered[Throwable],
    Throwable => Ordered[Throwable],
    ...

    Since the second type in the sequence is equal to the first, the compiler will issue an error signalling a divergent implicit expansion.

7.3 Views

Implicit parameters and methods can also define implicit conversions called views. A view from type S to type T is defined by an implicit value which has function type $S$=>$T$ or (=>$S$)=>$T$ or by a method convertible to a value of that type.

Views are applied in three situations.

  1. If an expression e is of type T, and T does not conform to the expression's expected type pt. In this case an implicit v is searched which is applicable to e and whose result type conforms to pt. The search proceeds as in the case of implicit parameters, where the implicit scope is the one of $T$ => $\mathit{pt}$. If such a view is found, the expression e is converted to $v$($e$).
  2. In a selection e.m with e of type T, if the selector m does not denote a member of T. In this case, a view v is searched which is applicable to e and whose result contains a member named m. The search proceeds as in the case of implicit parameters, where the implicit scope is the one of T. If such a view is found, the selection e.m is converted to $v$($e$).$m$.
  3. In a selection e.m(args) with e of type T, if the selector m denotes some member(s) of T, but none of these members is applicable to the arguments args. In this case a view v is searched which is applicable to e and whose result contains a method m which is applicable to args. The search proceeds as in the case of implicit parameters, where the implicit scope is the one of T. If such a view is found, the selection e.m is converted to $v$($e$).$m(\mathit{args})$.

The implicit view, if it is found, can accept is argument e as a call-by-value or as a call-by-name parameter. However, call-by-value implicits take precedence over call-by-name implicits.

As for implicit parameters, overloading resolution is applied if there are several possible candidates (of either the call-by-value or the call-by-name category).

  1. Class scala.Ordered[A] contains a method

      def <= [B >: A](that: B)(implicit b2ordered: B => Ordered[B]): Boolean .

    Assume two lists xs and ys of type List[Int] and assume that the list2ordered and int2ordered methods defined here are in scope. Then the operation

      xs <= ys

    is legal, and is expanded to:

      list2ordered(xs)(int2ordered).<=
        (ys)
        (xs => list2ordered(xs)(int2ordered))

    The first application of list2ordered converts the list xs to an instance of class Ordered, whereas the second occurrence is part of an implicit parameter passed to the <= method.

7.4 Context Bounds and View Bounds

  TypeParam ::= (id | ‘_’) [TypeParamClause] [‘>:’ Type] [‘<:’ Type] 
                {‘<%’ Type} {‘:’ Type}

A type parameter A of a method or non-trait class may have one or more view bounds $A$ <% $T$. In this case the type parameter may be instantiated to any type S which is convertible by application of a view to the bound T.

A type parameter A of a method or non-trait class may also have one or more context bounds $A$ : $T$. In this case the type parameter may be instantiated to any type S for which evidence exists at the instantiation point that S satisfies the bound T. Such evidence consists of an implicit value with type T[S].

A method or class containing type parameters with view or context bounds is treated as being equivalent to a method with implicit parameters. Consider first the case of a single parameter with view and/or context bounds such as:

def $f$[$A$ <% $T_1$ ... <% $T_m$ : $U_1$ : $U_n$]($\mathit{ps}$): $R$ = ...

Then the method definition above is expanded to

def $f$[$A$]($\mathit{ps}$)(implicit $v_1$: $A$ => $T_1$, ..., $v_m$: $A$ => $T_m$,
                       $w_1$: $U_1$[$A$], ..., $w_n$: $U_n$[$A$]): $R$ = ...

where the vi and wj are fresh names for the newly introduced implicit parameters. These parameters are called evidence parameters.

If a class or method has several view- or context-bounded type parameters, each such type parameter is expanded into evidence parameters in the order they appear and all the resulting evidence parameters are concatenated in one implicit parameter section. Since traits do not take constructor parameters, this translation does not work for them. Consequently, type-parameters in traits may not be view- or context-bounded. Also, a method or class with view- or context bounds may not define any additional implicit parameters.

  1. The <= method mentioned in can be declared more concisely as follows:

      def <= [B >: A <% Ordered[B]](that: B): Boolean

7.5 Manifests

Manifests are type descriptors that can be automatically generated by the Scala compiler as arguments to implicit parameters. The Scala standard library contains a hierarchy of four manifest classes, with OptManifest at the top. Their signatures follow the outline below.

trait OptManifest[+T]
object NoManifest extends OptManifest[Nothing]
trait ClassManifest[T] extends OptManifest[T]
trait Manifest[T] extends ClassManifest[T]

If an implicit parameter of a method or constructor is of a subtype M[T] of class OptManifest[T], a manifest is determined for M[S], according to the following rules.

First if there is already an implicit argument that matches M[T], this argument is selected.

Otherwise, let Mobj be the companion object scala.reflect.Manifest if M is trait Manifest, or be the companion object scala.reflect.ClassManifest otherwise. Let Mʹ be the trait Manifest if M is trait Manifest, or be the trait OptManifest otherwise.
Then the following rules apply.

  1. If T is a value class or one of the classes Any, AnyVal, Object, Null, or Nothing, a manifest for it is generated by selecting the corresponding manifest value Manifest.$T$, which exists in the Manifest module.
  2. If T is an instance of Array[$S$], a manifest is generated with the invocation $\mathit{Mobj}$.arrayType[S](m), where m is the manifest determined for M[S].
  3. If T is some other class type S#C[U1,,Un] where the prefix type S cannot be statically determined from the class C, a manifest is generated with the invocation $\mathit{Mobj}$.classType[T]($m_0$, classOf[T], $ms$) where m0 is the manifest determined for Mʹ[S] and ms are the manifests determined for Mʹ[U1],,Mʹ[Un].
  4. If T is some other class type with type arguments U1,,Un, a manifest is generated with the invocation $\mathit{Mobj}$.classType[T](classOf[T], $ms$) where ms are the manifests determined for Mʹ[U1],,Mʹ[Un].
  5. If T is a singleton type $p$.type, a manifest is generated with the invocation $\mathit{Mobj}$.singleType[T]($p$)
  6. If T is a refined type Tʹ{R}, a manifest is generated for Tʹ. (That is, refinements are never reflected in manifests).
  7. If T is an intersection type $T_1$ with $, \ldots ,$ with $T_n$ where n>1, the result depends on whether a full manifest is to be determined or not. If M is trait Manifest, then a manifest is generated with the invocation Manifest.intersectionType[T]($ms$) where ms are the manifests determined for M[T1],,M[Tn]. Otherwise, if M is trait ClassManifest, then a manifest is generated for the intersection dominator of the types T1,,Tn.
  8. If T is some other type, then if M is trait OptManifest, a manifest is generated from the designator scala.reflect.NoManifest. If M is a type different from OptManifest, a static error results.

8 Pattern Matching

8.1 Patterns

  Pattern         ::=  Pattern1 { ‘|’ Pattern1 }
  Pattern1        ::=  varid ‘:’ TypePat
                    |  ‘_’ ‘:’ TypePat
                    |  Pattern2
  Pattern2        ::=  varid [‘@’ Pattern3]
                    |  Pattern3
  Pattern3        ::=  SimplePattern 
                    |  SimplePattern {id [nl] SimplePattern}
  SimplePattern   ::=  ‘_’
                    |  varid
                    |  Literal
                    |  StableId
                    |  StableId ‘(’ [Patterns] ‘)’
                    |  StableId ‘(’ [Patterns ‘,’] [varid ‘@’] ‘_’ ‘*’ ‘)’
                    |  ‘(’ [Patterns] ‘)’
                    |  XmlPattern
  Patterns        ::=  Pattern {‘,’ Patterns}

A pattern is built from constants, constructors, variables and type tests. Pattern matching tests whether a given value (or sequence of values) has the shape defined by a pattern, and, if it does, binds the variables in the pattern to the corresponding components of the value (or sequence of values). The same variable name may not be bound more than once in a pattern.

  1. Some examples of patterns are:

    1. The pattern ex: IOException matches all instances of class IOException, binding variable to the instance.
    2. The pattern Some(x) matches values of the form Some($v$), binding x to the argument value v of the Some constructor.
    3. The pattern (x, _) matches pairs of values, binding x to the first component of the pair. The second component is matched with a wildcard pattern.
    4. The pattern x :: y :: xs matches lists of length 2, binding x to the list's first element, y to the list's second element, and xs to the remainder.
    5. The pattern 1 | 2 | 3 matches the integers between 1 and 3.

    Pattern matching is always done in a context which supplies an expected type of the pattern. We distinguish the following kinds of patterns.

8.1.1 Variable Patterns

  SimplePattern   ::=  `_'
                    |  varid

A variable pattern x is a simple identifier which starts with a lower case letter. It matches any value, and binds the variable name to that value. The type of x is the expected type of the pattern as given from outside. A special case is the wild-card pattern _ which is treated as if it was a fresh variable on each occurrence.

8.1.2 Typed Patterns

  Pattern1        ::=  varid `:' TypePat
                    |  `_' `:' TypePat

A typed pattern x:T consists of a pattern variable x and a type pattern T. The type of x is the type pattern T, where each type variable and wildcard is replaced by a fresh, unknown type. This pattern matches any value matched by the type pattern T; it binds the variable name to that value.

8.1.3 Pattern Binders

  Pattern2        ::=  varid `@' Pattern3

A pattern binder $x$@$p$ consists of a pattern variable x and a pattern p. The type of the variable x is the static type T of the pattern p. This pattern matches any value v matched by the pattern p, provided the run-time type of v is also an instance of T, and it binds the variable name to that value.

8.1.4 Literal Patterns

  SimplePattern   ::=  Literal

A literal pattern L matches any value that is equal (in terms of ==) to the literal L. The type of L must conform to the expected type of the pattern.

8.1.5 Stable Identifier Patterns

  SimplePattern   ::=  StableId

A stable identifier pattern is a stable identifier r. The type of r must conform to the expected type of the pattern. The pattern matches any value v such that $r$ == $v$ (see here).

To resolve the syntactic overlap with a variable pattern, a stable identifier pattern may not be a simple name starting with a lower-case letter. However, it is possible to enclose a such a variable name in backquotes; then it is treated as a stable identifier pattern.

  1. Consider the following function definition:

    def f(x: Int, y: Int) = x match {
      case y => ...
    }

    Here, y is a variable pattern, which matches any value. If we wanted to turn the pattern into a stable identifier pattern, this can be achieved as follows:

    def f(x: Int, y: Int) = x match {
      case `y` => ...
    }

    Now, the pattern matches the y parameter of the enclosing function f. That is, the match succeeds only if the x argument and the y argument of f are equal.

8.1.6 Constructor Patterns

  SimplePattern   ::=  StableId `(' [Patterns] `)

A constructor pattern is of the form c(p1,,pn) where n0. It consists of a stable identifier c, followed by element patterns p1,,pn. The constructor c is a simple or qualified name which denotes a case class. If the case class is monomorphic, then it must conform to the expected type of the pattern, and the formal parameter types of x's primary constructor are taken as the expected types of the element patterns p1,,pn. If the case class is polymorphic, then its type parameters are instantiated so that the instantiation of c conforms to the expected type of the pattern. The instantiated formal parameter types of c's primary constructor are then taken as the expected types of the component patterns p1,,pn. The pattern matches all objects created from constructor invocations c(v1,,vn) where each element pattern pi matches the corresponding value vi.

A special case arises when c's formal parameter types end in a repeated parameter. This is further discussed here.

8.1.7 Tuple Patterns

  SimplePattern   ::=  `(' [Patterns] `)'

A tuple pattern ($p_1 , \ldots , p_n$) is an alias for the constructor pattern scala.Tuple$n$($p_1 , \ldots , p_n$), where n2. The empty tuple () is the unique value of type scala.Unit.

8.1.8 Extractor Patterns

  SimplePattern   ::=  StableId `(' [Patterns] `)'

An extractor pattern x(p1,,pn) where n0 is of the same syntactic form as a constructor pattern. However, instead of a case class, the stable identifier x denotes an object which has a member method named unapply or unapplySeq that matches the pattern.

An unapply method in an object x matches the pattern x(p1,,pn) if it takes exactly one argument and one of the following applies:

An unapplySeq method in an object x matches the pattern x(p1,,pn) if it takes exactly one argument and its result type is of the form Option[$S$], where S is a subtype of Seq[$T$] for some element type T. This case is further discussed here.

  1. The Predef object contains a definition of an extractor object Pair:

    object Pair {
      def apply[A, B](x: A, y: B) = Tuple2(x, y)
      def unapply[A, B](x: Tuple2[A, B]): Option[Tuple2[A, B]] = Some(x)
    }

    This means that the name Pair can be used in place of Tuple2 for tuple formation as well as for deconstruction of tuples in patterns. Hence, the following is possible:

    val x = (1, 2)
    val y = x match {
      case Pair(i, s) => Pair(s + i, i * i)
    }

8.1.9 Pattern Sequences

  SimplePattern ::= StableId `(' [Patterns `,'] [varid `@'] `_' `*' `)'

A pattern sequence p1,,pn appears in two contexts. First, in a constructor pattern c(q1,,qm,p1,,pn), where c is a case class which has m+1 primary constructor parameters, ending in a repeated parameter of type S*. Second, in an extractor pattern x(p1,,pn) if the extractor object x has an unapplySeq method with a result type conforming to Seq[$S$], but does not have an unapply method that matches p1,,pn. The expected type for the pattern sequence is in each case the type S.

The last pattern in a pattern sequence may be a sequence wildcard _*. Each element pattern pi is type-checked with S as expected type, unless it is a sequence wildcard. If a final sequence wildcard is present, the pattern matches all values v that are sequences which start with elements matching patterns p1,,pn1. If no final sequence wildcard is given, the pattern matches all values v that are sequences of length n which consist of elements matching patterns p1,,pn.

8.1.10 Infix Operation Patterns

  Pattern3  ::=  SimplePattern {id [nl] SimplePattern}

An infix operation pattern p;op;q is a shorthand for the constructor or extractor pattern op(p,q). The precedence and associativity of operators in patterns is the same as in expressions.

An infix operation pattern p;op;(q1,,qn) is a shorthand for the constructor or extractor pattern op(p,q1,,qn).

8.1.11 Pattern Alternatives

  Pattern   ::=  Pattern1 { `|' Pattern1 }

A pattern alternative $p_1$ | $\ldots$ | $p_n$ consists of a number of alternative patterns pi. All alternative patterns are type checked with the expected type of the pattern. They may no bind variables other than wildcards. The alternative pattern matches a value v if at least one its alternatives matches v.

8.1.12 XML Patterns

XML patterns are treated here.

8.1.13 Regular Expression Patterns

Regular expression patterns have been discontinued in Scala from version 2.0.

Later version of Scala provide a much simplified version of regular expression patterns that cover most scenarios of non-text sequence processing. A sequence pattern is a pattern that stands in a position where either (1) a pattern of a type T which is conforming to Seq[A] for some A is expected, or (2) a case class constructor that has an iterated formal parameter A*. A wildcard star pattern _* in the rightmost position stands for arbitrary long sequences. It can be bound to variables using @, as usual, in which case the variable will have the type Seq[A].

8.1.14 Irrefutable Patterns

A pattern p is irrefutable for a type T, if one of the following applies:

  1. p is a variable pattern,
  2. p is a typed pattern x:Tʹ, and T<:Tʹ,
  3. p is a constructor pattern c(p1,,pn), the type T is an instance of class c, the primary constructor of type T has argument types T1,,Tn, and each pi is irrefutable for Ti.

8.2 Type Patterns

  TypePat           ::=  Type

Type patterns consist of types, type variables, and wildcards. A type pattern T is of one of the following forms:

The bottom types scala.Nothing and scala.Null cannot be used as type patterns, because they would match nothing in any case.

Types which are not of one of the forms described above are also accepted as type patterns. However, such type patterns will be translated to their erasure. The Scala compiler will issue an ``unchecked'' warning for these patterns to flag the possible loss of type-safety.

A type variable pattern is a simple identifier which starts with a lower case letter. However, the predefined primitive type aliases unit, boolean, byte, short, char, int, long, float, and double are not classified as type variable patterns.

8.3 Type Parameter Inference in Patterns

Type parameter inference is the process of finding bounds for the bound type variables in a typed pattern or constructor pattern. Inference takes into account the expected type of the pattern.

Type parameter inference for typed patterns.
Assume a typed pattern p:Tʹ. Let T result from Tʹ where all wildcards in Tʹ are renamed to fresh variable names. Let a1,,an be the type variables in T. These type variables are considered bound in the pattern. Let the expected type of the pattern be pt.

Type parameter inference constructs first a set of subtype constraints over the type variables ai. The initial constraints set 𝒞0 reflects just the bounds of these type variables. That is, assuming T has bound type variables a1,,an which correspond to class type parameters aʹ1,,aʹn with lower bounds L1,,Ln and upper bounds U1,,Un, 𝒞0 contains the constraints

ai <: σUi (i=1,,n)
σLi <: ai (i=1,,n)

where σ is the substitution [aʹ1:=a1,,aʹn:=an].

The set 𝒞0 is then augmented by further subtype constraints. There are two cases.

Case 1:
If there exists a substitution σ over the type variables ai,,an such that σT conforms to pt, one determines the weakest subtype constraints 𝒞1 over the type variables a1,,an such that 𝒞0𝒞1 implies that T conforms to pt.

Case 2:
Otherwise, if T can not be made to conform to pt by instantiating its type variables, one determines all type variables in pt which are defined as type parameters of a method enclosing the pattern. Let the set of such type parameters be b1,,bm. Let 𝒞ʹ0 be the subtype constraints reflecting the bounds of the type variables bi. If T denotes an instance type of a final class, let 𝒞2 be the weakest set of subtype constraints over the type variables a1,,an and b1,,bm such that 𝒞0𝒞ʹ0𝒞2 implies that T conforms to pt. If T does not denote an instance type of a final class, let 𝒞2 be the weakest set of subtype constraints over the type variables a1,,an and b1,,bm such that 𝒞0𝒞ʹ0𝒞2 implies that it is possible to construct a type Tʹ which conforms to both T and pt. It is a static error if there is no satisfiable set of constraints 𝒞2 with this property.

The final step consists in choosing type bounds for the type variables which imply the established constraint system. The process is different for the two cases above.

Case 1:
We take ai>:Li<:Ui where each Li is minimal and each Ui is maximal wrt <: such that ai>:Li<:Ui for i=1,,n implies 𝒞0𝒞1.

Case 2:
We take ai>:Li<:Ui and bi>:Lʹi<:Uʹi where each Li and Lʹj is minimal and each Ui and Uʹj is maximal such that ai>:Li<:Ui for i=1,,n and bj>:Lʹj<:Uʹj for j=1,,m implies 𝒞0𝒞ʹ0𝒞2.

In both cases, local type inference is permitted to limit the complexity of inferred bounds. Minimality and maximality of types have to be understood relative to the set of types of acceptable complexity.

Type parameter inference for constructor patterns.
Assume a constructor pattern C(p1,,pn) where class C has type type parameters a1,,an. These type parameters are inferred in the same way as for the typed pattern (_: $C[a_1 , \ldots , a_n]$).

  1. Consider the program fragment:

    val x: Any
    x match {
      case y: List[a] => ...
    }

    Here, the type pattern List[a] is matched against the expected type Any. The pattern binds the type variable a. Since List[a] conforms to Any for every type argument, there are no constraints on a. Hence, a is introduced as an abstract type with no bounds. The scope of a is right-hand side of its case clause.

    On the other hand, if x is declared as

    val x: List[List[String]],

    this generates the constraint List[a] <: List[List[String]], which simplifies to a <: List[String], because List is covariant. Hence, a is introduced with upper bound List[String].

  2. Consider the program fragment:

    val x: Any
    x match {
      case y: List[String] => ...
    }

    Scala does not maintain information about type arguments at run-time, so there is no way to check that x is a list of strings. Instead, the Scala compiler will erase the pattern to List[_]; that is, it will only test whether the top-level runtime-class of the value x conforms to List, and the pattern match will succeed if it does. This might lead to a class cast exception later on, in the case where the list x contains elements other than strings. The Scala compiler will flag this potential loss of type-safety with an ``unchecked'' warning message.

  3. Consider the program fragment

    class Term[A]
    class Number(val n: Int) extends Term[Int]
    def f[B](t: Term[B]): B = t match {
      case y: Number => y.n
    }

    The expected type of the pattern y: Number is Term[B]. The type Number does not conform to Term[B]; hence Case 2 of the rules above applies. This means that b is treated as another type variable for which subtype constraints are inferred. In our case the applicable constraint is Number <: Term[B], which entails B = Int. Hence, B is treated in the case clause as an abstract type with lower and upper bound Int. Therefore, the right hand side of the case clause, y.n, of type Int, is found to conform to the function's declared result type, Number.

8.4 Pattern Matching Expressions

  Expr            ::=  PostfixExpr `match' `{' CaseClauses `}'
  CaseClauses     ::=  CaseClause {CaseClause}
  CaseClause      ::=  `case' Pattern [Guard] `=>' Block

A pattern matching expression

e match { case $p_1$ => $b_1$ $\ldots$ case $p_n$ => $b_n$ }

consists of a selector expression e and a number n>0 of cases. Each case consists of a (possibly guarded) pattern pi and a block bi. Each pi might be complemented by a guard if $e$ where e is a boolean expression. The scope of the pattern variables in pi comprises the pattern's guard and the corresponding block bi.

Let T be the type of the selector expression e and let a1,,am be the type parameters of all methods enclosing the pattern matching expression. For every ai, let Li be its lower bound and Ui be its higher bound. Every pattern p{p1,,,pn} can be typed in two ways. First, it is attempted to type p with T as its expected type. If this fails, p is instead typed with a modified expected type Tʹ which results from T by replacing every occurrence of a type parameter ai by . If this second step fails also, a compile-time error results. If the second step succeeds, let Tp be the type of pattern p seen as an expression. One then determines minimal bounds Lʹ1,,Lʹm and maximal bounds Uʹ1,,Uʹm such that for all i, Li<:Lʹi and Uʹi<:Ui and the following constraint system is satisfied:

L1<:a1<:U1Lm<:am<:Um Tp<:T

If no such bounds can be found, a compile time error results. If such bounds are found, the pattern matching clause starting with p is then typed under the assumption that each ai has lower bound Lʹi instead of Li and has upper bound Uʹi instead of Ui.

The expected type of every block bi is the expected type of the whole pattern matching expression. The type of the pattern matching expression is then the weak least upper bound of the types of all blocks bi.

When applying a pattern matching expression to a selector value, patterns are tried in sequence until one is found which matches the selector value. Say this case is casepibi. The result of the whole expression is then the result of evaluating bi, where all pattern variables of pi are bound to the corresponding parts of the selector value. If no matching pattern is found, a scala.MatchError exception is thrown.

The pattern in a case may also be followed by a guard suffix
if e with a boolean expression e. The guard expression is evaluated if the preceding pattern in the case matches. If the guard expression evaluates to true, the pattern match succeeds as normal. If the guard expression evaluates to false, the pattern in the case is considered not to match and the search for a matching pattern continues.

In the interest of efficiency the evaluation of a pattern matching expression may try patterns in some other order than textual sequence. This might affect evaluation through side effects in guards. However, it is guaranteed that a guard expression is evaluated only if the pattern it guards matches.

If the selector of a pattern match is an instance of a sealed class, the compilation of pattern matching can emit warnings which diagnose that a given set of patterns is not exhaustive, i.e. that there is a possibility of a MatchError being raised at run-time.

  1. Consider the following definitions of arithmetic terms:

    abstract class Term[T]
    case class Lit(x: Int) extends Term[Int]
    case class Succ(t: Term[Int]) extends Term[Int]
    case class IsZero(t: Term[Int]) extends Term[Boolean]
    case class If[T](c: Term[Boolean],
                     t1: Term[T],
                     t2: Term[T]) extends Term[T]

    There are terms to represent numeric literals, incrementation, a zero test, and a conditional. Every term carries as a type parameter the type of the expression it representes (either Int or Boolean).

    A type-safe evaluator for such terms can be written as follows.

    def eval[T](t: Term[T]): T = t match {
      case Lit(n)        => n
      case Succ(u)       => eval(u) + 1
      case IsZero(u)     => eval(u) == 0
      case If(c, u1, u2) => eval(if (eval(c)) u1 else u2)
    }

    Note that the evaluator makes crucial use of the fact that type parameters of enclosing methods can acquire new bounds through pattern matching.

    For instance, the type of the pattern in the second case, Succ(u), is Int. It conforms to the selector type T only if we assume an upper and lower bound of Int for T. Under the assumption Int <: T <: Int we can also verify that the type right hand side of the second case, Int conforms to its expected type, T.

8.5 Pattern Matching Anonymous Functions

  BlockExpr ::= `{' CaseClauses `}'

An anonymous function can be defined by a sequence of cases

{ case $p_1$ => $b_1$ $\ldots$ case $p_n$ => $b_n$ }

which appear as an expression without a prior match. The expected type of such an expression must in part be defined. It must be either scala.Function$k$[$S_1 , \ldots , S_k$, $R$] for some k>0, or scala.PartialFunction[$S_1$, $R$], where the argument type(s) S1,,Sk must be fully determined, but the result type R may be undetermined.

If the expected type is scala.Function$k$[$S_1 , \ldots , S_k$, $R$], the expression is taken to be equivalent to the anonymous function:

($x_1: S_1 , \ldots , x_k: S_k$) => ($x_1 , \ldots , x_k$) match { 
  case $p_1$ => $b_1$ $\ldots$ case $p_n$ => $b_n$ 
}

Here, each xi is a fresh name. As was shown here, this anonymous function is in turn equivalent to the following instance creation expression, where T is the weak least upper bound of the types of all bi.

new scala.Function$k$[$S_1 , \ldots , S_k$, $T$] {
  def apply($x_1: S_1 , \ldots , x_k: S_k$): $T$ = ($x_1 , \ldots , x_k$) match {
    case $p_1$ => $b_1$ $\ldots$ case $p_n$ => $b_n$
  }
}

If the expected type is scala.PartialFunction[$S$, $R$], the expression is taken to be equivalent to the following instance creation expression:

new scala.PartialFunction[$S$, $T$] {
  def apply($x$: $S$): $T$ = x match {
    case $p_1$ => $b_1$ $\ldots$ case $p_n$ => $b_n$
  }
  def isDefinedAt($x$: $S$): Boolean = {
    case $p_1$ => true $\ldots$ case $p_n$ => true
    case _ => false
  }
}

Here, x is a fresh name and T is the weak least upper bound of the types of all bi. The final default case in the isDefinedAt method is omitted if one of the patterns p1,,pn is already a variable or wildcard pattern.

  1. Here is a method which uses a fold-left operation /: to compute the scalar product of two vectors:

    def scalarProduct(xs: Array[Double], ys: Array[Double]) = 
      (0.0 /: (xs zip ys)) {
        case (a, (b, c)) => a + b * c
      }

    The case clauses in this code are equivalent to the following anonymous function:

      (x, y) => (x, y) match {
        case (a, (b, c)) => a + b * c
      }

9 Top-Level Definitions

9.1 Compilation Units

CompilationUnit  ::=  {‘package’ QualId semi} TopStatSeq
TopStatSeq       ::=  TopStat {semi TopStat}
TopStat          ::=  {Annotation} {Modifier} TmplDef
                   |  Import
                   |  Packaging
                   |  PackageObject
                   |
QualId           ::=  id {‘.’ id}

A compilation unit consists of a sequence of packagings, import clauses, and class and object definitions, which may be preceded by a package clause.

A compilation unit

package $p_1$;
$\ldots$
package $p_n$;
$\mathit{stats}$

starting with one or more package clauses is equivalent to a compilation unit consisting of the packaging

package $p_1$ { $\ldots$
  package $p_n$ {
    $\mathit{stats}$
  } $\ldots$
}

Implicitly imported into every compilation unit are, in that order : the package java.lang, the package scala, and the object scala.Predef. Members of a later import in that order hide members of an earlier import.

9.2 Packagings

Packaging       ::=  ‘package’ QualId [nl] ‘{’ TopStatSeq ‘}’

A package is a special object which defines a set of member classes, objects and packages. Unlike other objects, packages are not introduced by a definition. Instead, the set of members of a package is determined by packagings.

A packaging package $p$ { $\mathit{ds}$ } injects all definitions in ds as members into the package whose qualified name is p. Members of a package are called top-level definitions. If a definition in ds is labeled private, it is visible only for other members in the package.

Inside the packaging, all members of package p are visible under their simple names. However this rule does not extend to members of enclosing packages of p that are designated by a prefix of the path p.

package org.net.prj {
  ...
}

all members of package org.net.prj are visible under their simple names, but members of packages org or org.net require explicit qualification or imports.

Selections p.m from p as well as imports from p work as for objects. However, unlike other objects, packages may not be used as values. It is illegal to have a package with the same fully qualified name as a module or a class.

Top-level definitions outside a packaging are assumed to be injected into a special empty package. That package cannot be named and therefore cannot be imported. However, members of the empty package are visible to each other without qualification.

9.3 Package Objects

PackageObject   ::=  ‘package’ ‘object’ ObjectDef

A package object package object $p$ extends $t$ adds the members of template t to the package p. There can be only one package object per package. The standard naming convention is to place the definition above in a file named package.scala that's located in the directory corresponding to package p.

The package object should not define a member with the same name as one of the top-level objects or classes defined in package p. If there is a name conflict, the behavior of the program is currently undefined. It is expected that this restriction will be lifted in a future version of Scala.

9.4 Package References

QualId           ::=  id {‘.’ id}

A reference to a package takes the form of a qualified identifier. Like all other references, package references are relative. That is, a package reference starting in a name p will be looked up in the closest enclosing scope that defines a member named p.

The special predefined name _root_ refers to the outermost root package which contains all top-level packages.

  1. Consider the following program:

    package b {
      class B 
    }
    
    package a.b {
      class A {
        val x = new _root_.b.B
      }
    }

    Here, the reference _root_.b.B refers to class B in the toplevel package b. If the _root_ prefix had been omitted, the name b would instead resolve to the package a.b, and, provided that package does not also contain a class B, a compiler-time error would result.

9.5 Programs

A program is a top-level object that has a member method main of type (Array[String])Unit. Programs can be executed from a command shell. The program's command arguments are are passed to the main method as a parameter of type Array[String].

The main method of a program can be directly defined in the object, or it can be inherited. The scala library defines a special class scala.App whose body acts as a main method. An objects m inheriting from this class is thus a program, which executes the initializaton code of the object m.

  1. The following example will create a hello world program by defining a method main in module test.HelloWorld.

    package test
    object HelloWorld {
      def main(args: Array[String]) { println("Hello World") }
    }

    This program can be started by the command

    scala test.HelloWorld

    In a Java environment, the command

    java test.HelloWorld

    would work as well.

    HelloWorld can also be defined without a main method by inheriting from App instead:

    package test 
    object HelloWorld extends App {
      println("Hello World")
    }

10 XML Expressions and Patterns

By Burak Emir
This chapter describes the syntactic structure of XML expressions and patterns. It follows as closely as possible the XML 1.0 specification , changes being mandated by the possibility of embedding Scala code fragments.

10.1 XML expressions

XML expressions are expressions generated by the following production, where the opening bracket `<' of the first element must be in a position to start the lexical XML mode.

XmlExpr ::= XmlContent {Element}

Well-formedness constraints of the XML specification apply, which means for instance that start tags and end tags must match, and attributes may only be defined once, with the exception of constraints related to entity resolution.

The following productions describe Scala's extensible markup language, designed as close as possible to the W3C extensible markup language standard. Only the productions for attribute values and character data are changed. Scala does not support declarations, CDATA sections or processing instructions. Entity references are not resolved at runtime.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ {.grammar} Element ::= EmptyElemTag | STag Content ETag

EmptyElemTag ::= ‘<’ Name {S Attribute} [S] ‘/>’

STag ::= ‘<’ Name {S Attribute} [S] ‘>’
ETag ::= ‘'{CharNoRef} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

XML expressions may contain Scala expressions as attribute values or within nodes. In the latter case, these are embedded using a single opening brace ‘{’ and ended by a closing brace ‘}’. To express a single opening braces within XML text as generated by CharData, it must be doubled. Thus, ‘{{’ represents the XML text ‘{’ and does not introduce an embedded Scala expression.

BaseChar, Char, Comment, CombiningChar, Ideographic, NameChar, S, Reference
              ::=  $\mbox{\rm\em “as in W3C XML”}$

Char1         ::=  Char $\mbox{\rm\em without}$ ‘<’ | ‘&’
CharQ         ::=  Char1 $\mbox{\rm\em without}$ ‘"’
CharA         ::=  Char1 $\mbox{\rm\em without}$ ‘'’
CharB         ::=  Char1 $\mbox{\rm\em without}$ ‘{’

Name          ::=  XNameStart {NameChar}

XNameStart    ::= ‘_’ | BaseChar | Ideographic 
                 $\mbox{\rm\em (as in W3C XML, but without }$ ‘:’

10.2 XML patterns

XML patterns are patterns generated by the following production, where the opening bracket ‘<’ of the element patterns must be in a position to start the lexical XML mode.

XmlPattern  ::= ElementPattern 

Well-formedness constraints of the XML specification apply.

An XML pattern has to be a single element pattern. It matches exactly those runtime representations of an XML tree that have the same structure as described by the pattern. XML patterns may contain Scala patterns.

Whitespace is treated the same way as in XML expressions. Patterns that are entity references, CDATA sections, processing instructions and comments match runtime representations which are the the same.

By default, beginning and trailing whitespace in element content is removed, and consecutive occurrences of whitespace are replaced by a single space character \u0020. This behavior can be changed to preserve all whitespace with a compiler option.

ElemPattern   ::=    EmptyElemTagP
                |    STagP ContentP ETagP                                    

EmptyElemTagP ::=    ‘<’  Name [S] ‘/>’
STagP         ::=    ‘<’  Name [S] ‘>’                          
ETagP         ::=    ‘</’ Name [S] ‘>’                                        
ContentP      ::=    [CharData] {(ElemPattern|ScalaPatterns) [CharData]}
ContentP1     ::=    ElemPattern
                |    Reference
                |    CDSect
                |    PI
                |    Comment
                |    ScalaPatterns
ScalaPatterns ::=    ‘{’ Patterns ‘}’

11 User-Defined Annotations

  Annotation       ::=  ‘@’ SimpleType {ArgumentExprs}
  ConstrAnnotation ::=  ‘@’ SimpleType ArgumentExprs

User-defined annotations associate meta-information with definitions. A simple annotation has the form @$c$ or @$c(a_1 , \ldots , a_n)$. Here, c is a constructor of a class C, which must conform to the class scala.Annotation.

Annotations may apply to definitions or declarations, types, or expressions. An annotation of a definition or declaration appears in front of that definition. An annotation of a type appears after that type. An annotation of an expression e appears after the expression e, separated by a colon. More than one annotation clause may apply to an entity. The order in which these annotations are given does not matter.

Examples:

@serializable class C { ... }         // A class annotation.
@transient @volatile var m: Int       // A variable annotation
String @local                         // A type annotation
(e: @unchecked) match { ... }         // An expression annotation

The meaning of annotation clauses is implementation-dependent. On the Java platform, the following annotations have a standard meaning.

Other annotations may be interpreted by platform- or application-dependent tools. Class scala.Annotation has two sub-traits which are used to indicate how these annotations are retained. Instances of an annotation class inheriting from trait scala.ClassfileAnnotation will be stored in the generated class files. Instances of an annotation class inheriting from trait scala.StaticAnnotation will be visible to the Scala type-checker in every compilation unit where the annotated symbol is accessed. An annotation class can inherit from both scala.ClassfileAnnotation and scala.StaticAnnotation. If an annotation class inherits from neither scala.ClassfileAnnotation nor scala.StaticAnnotation, its instances are visible only locally during the compilation run that analyzes them.

Classes inheriting from scala.ClassfileAnnotation may be subject to further restrictions in order to assure that they can be mapped to the host environment. In particular, on both the Java and the .NET platforms, such classes must be toplevel; i.e. they may not be contained in another class or object. Additionally, on both Java and .NET, all constructor arguments must be constant expressions.

12 The Scala Standard Library

The Scala standard library consists of the package scala with a number of classes and modules. Some of these classes are described in the following.

Class hierarchy of Scala

12.1 Root Classes

Figure~ illustrates Scala's class hierarchy. The root of this hierarchy is formed by class Any. Every class in a Scala execution environment inherits directly or indirectly from this class. Class Any has two direct subclasses: AnyRef and AnyVal`.

The subclass AnyRef represents all values which are represented as objects in the underlying host system. Every user-defined Scala class inherits directly or indirectly from this class. Furthermore, every user-defined Scala class also inherits the trait scala.ScalaObject. Classes written in other languages still inherit from scala.AnyRef, but not from scala.ScalaObject.

The class AnyVal has a fixed number of subclasses, which describe values which are not implemented as objects in the underlying host system.

Classes AnyRef and AnyVal are required to provide only the members declared in class Any, but implementations may add host-specific methods to these classes (for instance, an implementation may identify class AnyRef with its own root class for objects).

The signatures of these root classes are described by the following definitions.

package scala 
/** The universal root class */
abstract class Any {

  /** Defined equality; abstract here */
  def equals(that: Any): Boolean 

  /** Semantic equality between values */
  final def == (that: Any): Boolean  =  
    if (null eq this) null eq that else this equals that

  /** Semantic inequality between values */
  final def != (that: Any): Boolean  =  !(this == that)

  /** Hash code; abstract here */
  def hashCode: Int = $\ldots$

  /** Textual representation; abstract here */
  def toString: String = $\ldots$

  /** Type test; needs to be inlined to work as given */
  def isInstanceOf[a]: Boolean

  /** Type cast; needs to be inlined to work as given */ */
  def asInstanceOf[A]: A = this match {
    case x: A => x
    case _ => if (this eq null) this
              else throw new ClassCastException()
  }
}

/** The root class of all value types */
final class AnyVal extends Any 

/** The root class of all reference types */
class AnyRef extends Any {
  def equals(that: Any): Boolean      = this eq that 
  final def eq(that: AnyRef): Boolean = $\ldots$ // reference equality
  final def ne(that: AnyRef): Boolean = !(this eq that)

  def hashCode: Int = $\ldots$     // hashCode computed from allocation address
  def toString: String  = $\ldots$ // toString computed from hashCode and class name

  def synchronized[T](body: => T): T // execute `body` in while locking `this`.
}                           

/** A mixin class for every user-defined Scala class */
trait ScalaObject extends AnyRef 

The type test $x$.isInstanceOf[$T$] is equivalent to a typed pattern match

$x$ match {
  case _: $T'$ => true
  case _ => false
}

where the type Tʹ is the same as T except if T is of the form D or D[tps] where D is a type member of some outer class C. In this case Tʹ is $C$#$D$ (or $C$#$D[tps]$, respectively), whereas T itself would expand to $C$.this.$D[tps]$. In other words, an isInstanceOf test does not check for the

The test $x$.asInstanceOf[$T$] is treated specially if T is a numeric value type. In this case the cast will be translated to an application of a conversion method x.to$T$. For non-numeric values x the operation will raise a ClassCastException.

12.2 Value Classes

Value classes are classes whose instances are not represented as objects by the underlying host system. All value classes inherit from class AnyVal. Scala implementations need to provide the value classes Unit, Boolean, Double, Float, Long, Int, Char, Short, and Byte (but are free to provide others as well). The signatures of these classes are defined in the following.

12.2.1 Numeric Value Types

Classes Double, Float, Long, Int, Char, Short, and Byte are together called numeric value types. Classes Byte, Short, or Char are called subrange types. Subrange types, as well as Int and Long are called integer types, whereas Float and Double are called floating point types.

Numeric value types are ranked in the following partial order:

Byte - Short 
             \
               Int - Long - Float - Double
             / 
        Char 

Byte and Short are the lowest-ranked types in this order, whereas Double is the highest-ranked. Ranking does not imply a conformance relationship; for instance Int is not a subtype of Long. However, object Predef defines views from every numeric value type to all higher-ranked numeric value types. Therefore, lower-ranked types are implicitly converted to higher-ranked types when required by the context.

Given two numeric value types S and T, the operation type of S and T is defined as follows: If both S and T are subrange types then the operation type of S and T is Int. Otherwise the operation type of S and T is the larger of the two types wrt ranking. Given two numeric values v and w the operation type of v and w is the operation type of their run-time types.

Any numeric value type T supports the following methods.

Integer numeric value types support in addition the following operations:

Numeric value types also implement operations equals, hashCode, and toString from class Any.

The equals method tests whether the argument is a numeric value type. If this is true, it will perform the == operation which is appropriate for that type. That is, the equals method of a numeric value type can be thought of being defined as follows:

def equals(other: Any): Boolean = other match {
  case that: Byte   => this == that
  case that: Short  => this == that
  case that: Char   => this == that
  case that: Int    => this == that
  case that: Long   => this == that
  case that: Float  => this == that
  case that: Double => this == that
  case _ => false
}

The hashCode method returns an integer hashcode that maps equal numeric values to equal results. It is guaranteed to be the identity for for type Int and for all subrange types.

The toString method displays its receiver as an integer or floating point number.

  1. As an example, here is the signature of the numeric value type Int:

    package scala 
    abstract sealed class Int extends AnyVal {
      def == (that: Double): Boolean  // double equality
      def == (that: Float): Boolean   // float equality
      def == (that: Long): Boolean    // long equality
      def == (that: Int): Boolean     // int equality
      def == (that: Short): Boolean   // int equality
      def == (that: Byte): Boolean    // int equality
      def == (that: Char): Boolean    // int equality
      /* analogous for !=, <, >, <=, >= */
    
      def + (that: Double): Double    // double addition
      def + (that: Float): Double     // float addition
      def + (that: Long): Long        // long addition
      def + (that: Int): Int          // int addition
      def + (that: Short): Int        // int addition
      def + (that: Byte): Int         // int addition
      def + (that: Char): Int         // int addition
      /* analogous for -, *, /, % */
    
      def & (that: Long): Long        // long bitwise and
      def & (that: Int): Int          // int bitwise and
      def & (that: Short): Int        // int bitwise and
      def & (that: Byte): Int         // int bitwise and
      def & (that: Char): Int         // int bitwise and
      /* analogous for |, ^ */
    
      def << (cnt: Int): Int          // int left shift
      def << (cnt: Long): Int         // long left shift
      /* analogous for >>, >>> */
    
      def unary_+ : Int               // int identity
      def unary_- : Int               // int negation
      def unary_~ : Int               // int bitwise negation
    
      def toByte: Byte                // convert to Byte
      def toShort: Short              // convert to Short
      def toChar: Char                // convert to Char
      def toInt: Int                  // convert to Int
      def toLong: Long                // convert to Long
      def toFloat: Float              // convert to Float
      def toDouble: Double            // convert to Double
    }

12.2.2 Class Boolean

Class Boolean has only two values: true and false. It implements operations as given in the following class definition.

package scala 
abstract sealed class Boolean extends AnyVal {
  def && (p: => Boolean): Boolean = // boolean and
    if (this) p else false
  def || (p: => Boolean): Boolean = // boolean or
    if (this) true else p
  def &  (x: Boolean): Boolean =    // boolean strict and
    if (this) x else false
  def |  (x: Boolean): Boolean =    // boolean strict or
    if (this) true else x
  def == (x: Boolean): Boolean =    // boolean equality
    if (this) x else x.unary_!
  def != (x: Boolean): Boolean =    // boolean inequality
    if (this) x.unary_! else x
  def unary_!: Boolean =            // boolean negation
    if (this) false else true
}

The class also implements operations equals, hashCode, and toString from class Any.

The equals method returns true if the argument is the same boolean value as the receiver, false otherwise. The hashCode method returns a fixed, implementation-specific hash-code when invoked on true, and a different, fixed, implementation-specific hash-code when invoked on false. The toString method returns the receiver converted to a string, i.e. either "true" or "false".

12.2.3 Class Unit

Class Unit has only one value: (). It implements only the three methods equals, hashCode, and toString from class Any.

The equals method returns true if the argument is the unit value (), false otherwise. The hashCode method returns a fixed, implementation-specific hash-code, The toString method returns "()".

12.3 Standard Reference Classes

This section presents some standard Scala reference classes which are treated in a special way in Scala compiler -- either Scala provides syntactic sugar for them, or the Scala compiler generates special code for their operations. Other classes in the standard Scala library are documented in the Scala library documentation by HTML pages.

12.3.1 Class String

Scala's String class is usually derived from the standard String class of the underlying host system (and may be identified with it). For Scala clients the class is taken to support in each case a method

def + (that: Any): String 

which concatenates its left operand with the textual representation of its right operand.

12.3.2 The Tuple classes

Scala defines tuple classes Tuple$n$ for n=2,,9. These are defined as follows.

package scala 
case class Tuple$n$[+A_1, ..., +A_n](_1: A_1, ..., _$n$: A_$n$) {
  def toString = "(" ++ _1 ++ "," ++ $\ldots$ ++ "," ++ _$n$ ++ ")"
}

The implicitly imported Predef object defines the names Pair as an alias of Tuple2 and Triple as an alias for Tuple3.

12.3.3 The Function Classes

Scala defines function classes Function$n$ for n=1,,9. These are defined as follows.

package scala 
trait Function$n$[-A_1, ..., -A_$n$, +B] {
  def apply(x_1: A_1, ..., x_$n$: A_$n$): B 
  def toString = "<function>" 
}

A subclass of Function1 represents partial functions, which are undefined on some points in their domain. In addition to the apply method of functions, partial functions also have a isDefined method, which tells whether the function is defined at the given argument:

class PartialFunction[-A, +B] extends Function1[A, B] {
  def isDefinedAt(x: A): Boolean
}

The implicitly imported Predef object defines the name Function as an alias of Function1.

12.3.4 Class Array

The class of generic arrays is given as follows.

final class Array[A](len: Int) extends Seq[A] {
  def length: Int = len
  def apply(i: Int): A = $\ldots$
  def update(i: Int, x: A): Unit = $\ldots$
  def elements: Iterator[A] = $\ldots$
  def subArray(from: Int, end: Int): Array[A] = $\ldots$
  def filter(p: A => Boolean): Array[A] = $\ldots$
  def map[B](f: A => B): Array[B] = $\ldots$
  def flatMap[B](f: A => Array[B]): Array[B] = $\ldots$
}

If T is not a type parameter or abstract type, the type Array[T] is represented as the native array type []$T$ in the underlying host system. In that case length returns the length of the array, apply means subscripting, and update means element update. Because of the syntactic sugar for apply and update operations, we have the following correspondences between Scala and Java/C# code for operations on an array xs:

Scala Java/C#
xs.length xs.length
xs(i) xs[i]
xs(i) = e xs[i] = e

Arrays also implement the sequence trait scala.Seq by defining an elements method which returns all elements of the array in an Iterator.

Because of the tension between parametrized types in Scala and the ad-hoc implementation of arrays in the host-languages, some subtle points need to be taken into account when dealing with arrays. These are explained in the following.

First, unlike arrays in Java or C#, arrays in Scala are not co-variant; That is, S<:T does not imply Array[$S$] $<:$ Array[$T$] in Scala.
However, it is possible to cast an array of S to an array of T if such a cast is permitted in the host environment.

For instance Array[String] does not conform to Array[Object], even though String conforms to Object. However, it is possible to cast an expression of type Array[String] to Array[Object], and this cast will succeed without raising a ClassCastException. Example:

val xs = new Array[String](2)
// val ys: Array[Object] = xs   // **** error: incompatible types
val ys: Array[Object] = xs.asInstanceOf[Array[Object]] // OK

Second, for polymorphic arrays, that have a type parameter or abstract type T as their element type, a representation different from []T might be used. However, it is guaranteed that isInstanceOf and asInstanceOf still work as if the array used the standard representation of monomorphic arrays:

val ss = new Array[String](2)

def f[T](xs: Array[T]): Array[String] = 
  if (xs.isInstanceOf[Array[String]]) xs.asInstanceOf[Array[String])
  else throw new Error("not an instance")

f(ss)                                     // returns ss

The representation chosen for polymorphic arrays also guarantees that polymorphic array creations work as expected. An example is the following implementation of method mkArray, which creates an array of an arbitrary type T, given a sequence of T's which defines its elements.

def mkArray[T](elems: Seq[T]): Array[T] = {
  val result = new Array[T](elems.length)
  var i = 0
  for (elem <- elems) {
    result(i) = elem
    i += 1
  }
}

Note that under Java's erasure model of arrays the method above would not work as expected -- in fact it would always return an array of Object.

Third, in a Java environment there is a method System.arraycopy which takes two objects as parameters together with start indices and a length argument, and copies elements from one object to the other, provided the objects are arrays of compatible element types. System.arraycopy will not work for Scala's polymorphic arrays because of their different representation. One should instead use method Array.copy which is defined in the companion object of class Array. This companion object also defines various constructor methods for arrays, as well as the extractor method unapplySeq which enables pattern matching over arrays.

package scala
object Array { 
  /** copies array elements from `src' to `dest'. */
  def copy(src: AnyRef, srcPos: Int, 
           dest: AnyRef, destPos: Int, length: Int): Unit = $\ldots$

  /** Concatenate all argument arrays into a single array. */
  def concat[T](xs: Array[T]*): Array[T] = $\ldots$

  /** Create a an array of successive integers. */
  def range(start: Int, end: Int): Array[Int] = $\ldots$

  /** Create an array with given elements. */
  def apply[A <: AnyRef](xs: A*): Array[A] = $\ldots$

  /** Analogous to above. */
  def apply(xs: Boolean*): Array[Boolean] = $\ldots$
  def apply(xs: Byte*)   : Array[Byte]    = $\ldots$
  def apply(xs: Short*)  : Array[Short]   = $\ldots$
  def apply(xs: Char*)   : Array[Char]    = $\ldots$
  def apply(xs: Int*)    : Array[Int]     = $\ldots$
  def apply(xs: Long*)   : Array[Long]    = $\ldots$
  def apply(xs: Float*)  : Array[Float]   = $\ldots$
  def apply(xs: Double*) : Array[Double]  = $\ldots$
  def apply(xs: Unit*)   : Array[Unit]    = $\ldots$

  /** Create an array containing several copies of an element. */
  def make[A](n: Int, elem: A): Array[A] = {

  /** Enables pattern matching over arrays */
  def unapplySeq[A](x: Array[A]): Option[Seq[A]] = Some(x)
}
  1. The following method duplicates a given argument array and returns a pair consisting of the original and the duplicate:

    def duplicate[T](xs: Array[T]) = {
      val ys = new Array[T](xs.length)
      Array.copy(xs, 0, ys, 0, xs.length)
      (xs, ys)
    }

12.4 Class Node

package scala.xml 

trait Node {

  /** the label of this node */
  def label: String               

  /** attribute axis */
  def attribute: Map[String, String] 

  /** child axis (all children of this node) */
  def child: Seq[Node]          

  /** descendant axis (all descendants of this node) */
  def descendant: Seq[Node] = child.toList.flatMap { 
    x => x::x.descendant.asInstanceOf[List[Node]] 
  } 

  /** descendant axis (all descendants of this node) */
  def descendant_or_self: Seq[Node] = this::child.toList.flatMap { 
    x => x::x.descendant.asInstanceOf[List[Node]] 
  } 

  override def equals(x: Any): Boolean = x match {
    case that:Node => 
      that.label == this.label && 
        that.attribute.sameElements(this.attribute) && 
          that.child.sameElements(this.child)
    case _ => false
  } 

 /** XPath style projection function. Returns all children of this node
  *  that are labeled with 'that'. The document order is preserved.
  */
    def \(that: Symbol): NodeSeq = {
      new NodeSeq({
        that.name match {
          case "_" => child.toList  
          case _ =>
            var res:List[Node] = Nil 
            for (x <- child.elements if x.label == that.name) {
              res = x::res 
            }
            res.reverse
        }
      }) 
    }

 /** XPath style projection function. Returns all nodes labeled with the 
  *  name 'that' from the 'descendant_or_self' axis. Document order is preserved.
  */
  def \\(that: Symbol): NodeSeq = {
    new NodeSeq(
      that.name match {
        case "_" => this.descendant_or_self 
        case _ => this.descendant_or_self.asInstanceOf[List[Node]].
        filter(x => x.label == that.name) 
      })
  }

  /** hashcode for this XML node */
  override def hashCode = 
    Utility.hashCode(label, attribute.toList.hashCode, child) 

  /** string representation of this node */
  override def toString = Utility.toXML(this) 

}

12.5 The Predef Object

The Predef object defines standard functions and type aliases for Scala programs. It is always implicitly imported, so that all its defined members are available without qualification. Its definition for the JVM environment conforms to the following signature:

package scala
object Predef {

  // classOf ---------------------------------------------------------

  /** Returns the runtime representation of a class type. */
  def classOf[T]: Class[T] = null  
   // this is a dummy, classOf is handled by compiler.

  // Standard type aliases ---------------------------------------------

  type String    = java.lang.String
  type Class[T]  = java.lang.Class[T]

  // Miscellaneous -----------------------------------------------------
  
  type Function[-A, +B] = Function1[A, B]

  type Map[A, +B] = collection.immutable.Map[A, B]
  type Set[A] = collection.immutable.Set[A]

  val Map = collection.immutable.Map
  val Set = collection.immutable.Set

  // Manifest types, companions, and incantations for summoning ---------

  type ClassManifest[T] = scala.reflect.ClassManifest[T]
  type Manifest[T]      = scala.reflect.Manifest[T]
  type OptManifest[T]   = scala.reflect.OptManifest[T]
  val ClassManifest     = scala.reflect.ClassManifest
  val Manifest          = scala.reflect.Manifest
  val NoManifest        = scala.reflect.NoManifest
  
  def manifest[T](implicit m: Manifest[T])           = m
  def classManifest[T](implicit m: ClassManifest[T]) = m
  def optManifest[T](implicit m: OptManifest[T])     = m

  // Minor variations on identity functions -----------------------------
  def identity[A](x: A): A         = x    // @see `conforms` for the implicit version
  def implicitly[T](implicit e: T) = e    // for summoning implicit values from the nether world
  @inline def locally[T](x: T): T  = x    // to communicate intent and avoid unmoored statements

  // Asserts, Preconditions, Postconditions -----------------------------

  def assert(assertion: Boolean) {
    if (!assertion)
      throw new java.lang.AssertionError("assertion failed")
  }

  def assert(assertion: Boolean, message: => Any) {
    if (!assertion)
      throw new java.lang.AssertionError("assertion failed: " + message)
  }

  def assume(assumption: Boolean) {
    if (!assumption)
      throw new IllegalArgumentException("assumption failed")
  }

  def assume(assumption: Boolean, message: => Any) {
    if (!assumption)
      throw new IllegalArgumentException(message.toString)
  }

  def require(requirement: Boolean) {
    if (!requirement)
      throw new IllegalArgumentException("requirement failed")
  }

  def require(requirement: Boolean, message: => Any) {
    if (!requirement)
      throw new IllegalArgumentException("requirement failed: "+ message)
  }

  // tupling ---------------------------------------------------------

  type Pair[+A, +B] = Tuple2[A, B]
  object Pair {
    def apply[A, B](x: A, y: B) = Tuple2(x, y)
    def unapply[A, B](x: Tuple2[A, B]): Option[Tuple2[A, B]] = Some(x)
  }

  type Triple[+A, +B, +C] = Tuple3[A, B, C]
  object Triple {
    def apply[A, B, C](x: A, y: B, z: C) = Tuple3(x, y, z)
    def unapply[A, B, C](x: Tuple3[A, B, C]): Option[Tuple3[A, B, C]] = Some(x)
  }

  // Printing and reading -----------------------------------------------

  def print(x: Any) = Console.print(x)
  def println() = Console.println()
  def println(x: Any) = Console.println(x)
  def printf(text: String, xs: Any*) = Console.printf(text.format(xs: _*))

  def readLine(): String = Console.readLine()
  def readLine(text: String, args: Any*) = Console.readLine(text, args)
  def readBoolean() = Console.readBoolean()
  def readByte() = Console.readByte()
  def readShort() = Console.readShort()
  def readChar() = Console.readChar()
  def readInt() = Console.readInt()
  def readLong() = Console.readLong()
  def readFloat() = Console.readFloat()
  def readDouble() = Console.readDouble()
  def readf(format: String) = Console.readf(format)
  def readf1(format: String) = Console.readf1(format)
  def readf2(format: String) = Console.readf2(format)
  def readf3(format: String) = Console.readf3(format)

  // Implict conversions ------------------------------------------------

  ...
}

12.5.1 Predefined Implicit Definitions

The Predef object also contains a number of implicit definitions, which are available by default (because Predef is implicitly imported). Implicit definitions come in two priorities. High-priority implicits are defined in the Predef class itself whereas low priority implicits are defined in a class inherited by Predef. The rules of static overloading resolution stipulate that, all other things being equal, implicit resolution prefers high-priority implicits over low-priority ones.

The available low-priority implicits include definitions falling into the following categories.

  1. For every primitive type, a wrapper that takes values of that type to instances of a runtime.Rich* class. For instance, values of type Int can be implicitly converted to instances of class runtime.RichInt.

  2. For every array type with elements of primitive type, a wrapper that takes the arrays of that type to instances of a runtime.WrappedArray class. For instance, values of type Array[Float] can be implicitly converted to instances of class runtime.WrappedArray[Float]. There are also generic array wrappers that take elements of type Array[T] for arbitrary T to WrappedArrays.

  3. An implicit conversion from String to WrappedString.

The available high-priority implicits include definitions falling into the following categories.

13 Scala Syntax Summary

The lexical syntax of Scala is given by the following grammar in EBNF form.

upper            ::=  ‘A’ | … | ‘Z’ | ‘\$’ | ‘_’  // and Unicode category Lu
lower            ::=  ‘a’ | … | ‘z’ // and Unicode category Ll
letter           ::=  upper | lower // and Unicode categories Lo, Lt, Nl
digit            ::=  ‘0’ | … | ‘9’
opchar           ::= // “all other characters in \u0020-\u007F and Unicode
                     // categories Sm, So except parentheses ([{}]) and periods”

op               ::=  opchar {opchar} 
varid            ::=  lower idrest
plainid          ::=  upper idrest
                 |  varid
                 |  op
id               ::=  plainid
                 |  ‘\`’ stringLit ‘\`’
idrest           ::=  {letter | digit} [‘_’ op]

integerLiteral   ::=  (decimalNumeral | hexNumeral | octalNumeral) [‘L’ | ‘l’]
decimalNumeral   ::=  ‘0’ | nonZeroDigit {digit}
hexNumeral       ::=  ‘0’ ‘x’ hexDigit {hexDigit}
octalNumeral     ::=  ‘0’ octalDigit {octalDigit}
digit            ::=  ‘0’ | nonZeroDigit
nonZeroDigit     ::=  ‘1’ | … | ‘9’
octalDigit       ::=  ‘0’ | … | ‘7’

floatingPointLiteral 
               ::=  digit {digit} ‘.’ {digit} [exponentPart] [floatType]
                 |  ‘.’ digit {digit} [exponentPart] [floatType]
                 |  digit {digit} exponentPart [floatType]
                 |  digit {digit} [exponentPart] floatType
exponentPart     ::=  (‘E’ | ‘e’) [‘+’ | ‘-’] digit {digit}
floatType        ::=  ‘F’ | ‘f’ | ‘D’ | ‘d’

booleanLiteral   ::=  ‘true’ | ‘false’

characterLiteral ::=  ‘\'‘ printableChar ‘\'’
                 |  ‘\’ charEscapeSeq ‘\'’

stringLiteral    ::=  ‘"’ {stringElement} ‘"’
                 |  ‘"""’ multiLineChars ‘"""’
stringElement    ::=  printableCharNoDoubleQuote 
                 |  charEscapeSeq
multiLineChars   ::=  {[‘"’] [‘"’] charNoDoubleQuote} {‘"’}

symbolLiteral    ::=  ‘'’ plainid

comment          ::=  ‘/*’ “any sequence of characters” ‘*/’
                 |  ‘//’ “any sequence of characters up to end of line”

nl               ::=  $\mathit{“new line character”}$
semi             ::=  ‘;’ |  nl {nl}

The context-free syntax of Scala is given by the following EBNF grammar.

  Literal           ::=  [‘-’] integerLiteral
                      |  [‘-’] floatingPointLiteral
                      |  booleanLiteral
                      |  characterLiteral
                      |  stringLiteral
                      |  symbolLiteral
                      |  ‘null’

  QualId            ::=  id {‘.’ id}
  ids               ::=  id {‘,’ id}

  Path              ::=  StableId
                      |  [id ‘.’] ‘this’
  StableId          ::=  id
                      |  Path ‘.’ id
                      |  [id ‘.’] ‘super’ [ClassQualifier] ‘.’ id
  ClassQualifier    ::=  ‘[’ id ‘]’

  Type              ::=  FunctionArgTypes ‘=>’ Type
                      |  InfixType [ExistentialClause]
  FunctionArgTypes  ::= InfixType
                      | ‘(’ [ ParamType {‘,’ ParamType } ] ‘)’
  ExistentialClause ::=  ‘forSome’ ‘{’ ExistentialDcl {semi ExistentialDcl} ‘}’
  ExistentialDcl    ::=  ‘type’ TypeDcl 
                      |  ‘val’ ValDcl
  InfixType         ::=  CompoundType {id [nl] CompoundType}
  CompoundType      ::=  AnnotType {‘with’ AnnotType} [Refinement]
                      |  Refinement
  AnnotType         ::=  SimpleType {Annotation}
  SimpleType        ::=  SimpleType TypeArgs
                      |  SimpleType ‘#’ id
                      |  StableId
                      |  Path ‘.’ ‘type’
                      |  ‘(’ Types ‘)’
  TypeArgs          ::=  ‘[’ Types ‘]’
  Types             ::=  Type {‘,’ Type}
  Refinement        ::=  [nl] ‘{’ RefineStat {semi RefineStat} ‘}’
  RefineStat        ::=  Dcl
                      |  ‘type’ TypeDef
                      |
  TypePat           ::=  Type

  Ascription        ::=  ‘:’ InfixType
                      |  ‘:’ Annotation {Annotation} 
                      |  ‘:’ ‘_’ ‘*’

  Expr              ::=  (Bindings | [‘implicit’] id | ‘_’) ‘=>’ Expr
                      |  Expr1
  Expr1             ::=  ‘if’ ‘(’ Expr ‘)’ {nl} Expr [[semi] else Expr]
                      |  ‘while’ ‘(’ Expr ‘)’ {nl} Expr
                      |  ‘try’ ‘{’ Block ‘}’ [‘catch’  ‘{’ CaseClauses ‘}’] 
                         [‘finally’ Expr]
                      |  ‘do’ Expr [semi] ‘while’ ‘(’ Expr ‘)’
                      |  ‘for’ (‘(’ Enumerators ‘)’ | ‘{’ Enumerators ‘}’) 
                         {nl} [‘yield’] Expr
                      |  ‘throw’ Expr
                      |  ‘return’ [Expr]
                      |  [SimpleExpr ‘.’] id ‘=’ Expr
                      |  SimpleExpr1 ArgumentExprs ‘=’ Expr
                      |  PostfixExpr
                      |  PostfixExpr Ascription
                      |  PostfixExpr ‘match’ ‘{’ CaseClauses ‘}’
  PostfixExpr       ::=  InfixExpr [id [nl]]
  InfixExpr         ::=  PrefixExpr
                      |  InfixExpr id [nl] InfixExpr
  PrefixExpr        ::=  [‘-’ | ‘+’ | ‘~’ | ‘!’] SimpleExpr 
  SimpleExpr        ::=  ‘new’ (ClassTemplate | TemplateBody)
                      |  BlockExpr
                      |  SimpleExpr1 [‘_’]
  SimpleExpr1       ::=  Literal
                      |  Path
                      |  ‘_’
                      |  ‘(’ [Exprs] ‘)’
                      |  SimpleExpr ‘.’ id 
                      |  SimpleExpr TypeArgs
                      |  SimpleExpr1 ArgumentExprs
                      |  XmlExpr
  Exprs             ::=  Expr {‘,’ Expr}
  ArgumentExprs     ::=  ‘(’ [Exprs] ‘)’
                      |  ‘(’ [Exprs ‘,’] PostfixExpr ‘:’ ‘_’ ‘*’ ‘)’
                      |  [nl] BlockExpr
  BlockExpr         ::=  ‘{’ CaseClauses ‘}’
                      |  ‘{’ Block ‘}’
  Block             ::=  {BlockStat semi} [ResultExpr]
  BlockStat         ::=  Import
                      |  {Annotation} [‘implicit’ | ‘lazy’] Def
                      |  {Annotation} {LocalModifier} TmplDef
                      |  Expr1
                      |
  ResultExpr        ::=  Expr1
                      |  (Bindings | ([‘implicit’] id | ‘_’) ‘:’ CompoundType) ‘=>’ Block

  Enumerators       ::=  Generator {semi Enumerator}
  Enumerator        ::=  Generator
                      |  Guard
                      |  ‘val’ Pattern1 ‘=’ Expr
  Generator         ::=  Pattern1 ‘<-’ Expr [Guard]

  CaseClauses       ::=  CaseClause { CaseClause }
  CaseClause        ::=  ‘case’ Pattern [Guard] ‘=>’ Block 
  Guard             ::=  ‘if’ PostfixExpr

  Pattern           ::=  Pattern1 { ‘|’ Pattern1 }
  Pattern1          ::=  varid ‘:’ TypePat
                      |  ‘_’ ‘:’ TypePat
                      |  Pattern2
  Pattern2          ::=  varid [‘@’ Pattern3]
                      |  Pattern3
  Pattern3          ::=  SimplePattern
                      |  SimplePattern { id [nl] SimplePattern }
  SimplePattern     ::=  ‘_’
                      |  varid
                      |  Literal
                      |  StableId
                      |  StableId ‘(’ [Patterns ‘)’
                      |  StableId ‘(’ [Patterns ‘,’] [varid ‘@’] ‘_’ ‘*’ ‘)’
                      |  ‘(’ [Patterns] ‘)’
                      |  XmlPattern
  Patterns          ::=  Pattern [‘,’ Patterns]
                      |  ‘_’ *

  TypeParamClause   ::=  ‘[’ VariantTypeParam {‘,’ VariantTypeParam} ‘]’
  FunTypeParamClause::=  ‘[’ TypeParam {‘,’ TypeParam} ‘]’
  VariantTypeParam  ::=  {Annotation} [‘+’ | ‘-’] TypeParam
  TypeParam         ::=  (id | ‘_’) [TypeParamClause] [‘>:’ Type] [‘<:’ Type] 
                         {‘<%’ Type} {‘:’ Type}
  ParamClauses      ::=  {ParamClause} [[nl] ‘(’ ‘implicit’ Params ‘)’]
  ParamClause       ::=  [nl] ‘(’ [Params] ‘)’
  Params            ::=  Param {‘,’ Param}
  Param             ::=  {Annotation} id [‘:’ ParamType] [‘=’ Expr]
  ParamType         ::=  Type 
                      |  ‘=>’ Type 
                      |  Type ‘*’
  ClassParamClauses ::=  {ClassParamClause} 
                         [[nl] ‘(’ ‘implicit’ ClassParams ‘)’]
  ClassParamClause  ::=  [nl] ‘(’ [ClassParams] ‘)’
  ClassParams       ::=  ClassParam {‘’ ClassParam}
  ClassParam        ::=  {Annotation} [{Modifier} (‘val’ | ‘var’)] 
                         id ‘:’ ParamType [‘=’ Expr]
  Bindings          ::=  ‘(’ Binding {‘,’ Binding ‘)’
  Binding           ::=  (id | ‘_’) [‘:’ Type]

  Modifier          ::=  LocalModifier 
                      |  AccessModifier
                      |  ‘override’
  LocalModifier     ::=  ‘abstract’
                      |  ‘final’
                      |  ‘sealed’
                      |  ‘implicit’
                      |  ‘lazy’
  AccessModifier    ::=  (‘private’ | ‘protected’) [AccessQualifier]
  AccessQualifier   ::=  ‘[’ (id | ‘this’) ‘]’

  Annotation        ::=  ‘@’ SimpleType {ArgumentExprs}
  ConstrAnnotation  ::=  ‘@’ SimpleType ArgumentExprs
  NameValuePair     ::=  ‘val’ id ‘=’ PrefixExpr

  TemplateBody      ::=  [nl] ‘{’ [SelfType] TemplateStat {semi TemplateStat} ‘}’
  TemplateStat      ::=  Import
                      |  {Annotation [nl]} {Modifier} Def
                      |  {Annotation [nl]} {Modifier} Dcl
                      |  Expr
                      |
  SelfType          ::=  id [‘:’ Type] ‘=>’
                      |  ‘this’ ‘:’ Type ‘=>’ 

  Import            ::=  ‘import’ ImportExpr {‘,’ ImportExpr}
  ImportExpr        ::=  StableId ‘.’ (id | ‘_’ | ImportSelectors)
  ImportSelectors   ::=  ‘{’ {ImportSelector ‘,’} (ImportSelector | ‘_’) ‘}’
  ImportSelector    ::=  id [‘=>’ id | ‘=>’ ‘_’]

  Dcl               ::=  ‘val’ ValDcl
                      |  ‘var’ VarDcl
                      |  ‘def’ FunDcl
                      |  ‘type’ {nl} TypeDcl

  ValDcl            ::=  ids ‘:’ Type
  VarDcl            ::=  ids ‘:’ Type
  FunDcl            ::=  FunSig [‘:’ Type]
  FunSig            ::=  id [FunTypeParamClause] ParamClauses
  TypeDcl           ::=  id [TypeParamClause] [‘>:’ Type] [‘<:’ Type]

  PatVarDef         ::=  ‘val’ PatDef
                      |  ‘var’ VarDef
  Def               ::=  PatVarDef
                      |  ‘def’ FunDef
                      |  ‘type’ {nl} TypeDef
                      |  TmplDef
  PatDef            ::=  Pattern2 {‘,’ Pattern2} [‘:’ Type] ‘=’ Expr
  VarDef            ::=  PatDef
                      |  ids ‘:’ Type ‘=’ ‘_’
  FunDef            ::=  FunSig [‘:’ Type] ‘=’ Expr
                      |  FunSig [nl] ‘{’ Block ‘}’
                      |  ‘this’ ParamClause ParamClauses 
                         (‘=’ ConstrExpr | [nl] ConstrBlock)
  TypeDef           ::=  id [TypeParamClause] ‘=’ Type

  TmplDef           ::=  [‘case’] ‘class’ ClassDef
                      |  [‘case’] ‘object’ ObjectDef
                      |  ‘trait’ TraitDef
  ClassDef          ::=  id [TypeParamClause] {ConstrAnnotation} [AccessModifier] 
                         ClassParamClauses ClassTemplateOpt 
  TraitDef          ::=  id [TypeParamClause] TraitTemplateOpt
  ObjectDef         ::=  id ClassTemplateOpt
  ClassTemplateOpt  ::=  ‘extends’ ClassTemplate | [[‘extends’] TemplateBody]
  TraitTemplateOpt  ::=  ‘extends’ TraitTemplate | [[‘extends’] TemplateBody]
  ClassTemplate     ::=  [EarlyDefs] ClassParents [TemplateBody]
  TraitTemplate     ::=  [EarlyDefs] TraitParents [TemplateBody]
  ClassParents      ::=  Constr {‘with’ AnnotType}
  TraitParents      ::=  AnnotType {‘with’ AnnotType}
  Constr            ::=  AnnotType {ArgumentExprs}
  EarlyDefs         ::= ‘{’ [EarlyDef {semi EarlyDef}] ‘}’ ‘with’
  EarlyDef          ::=  {Annotation [nl]} {Modifier} PatVarDef

  ConstrExpr        ::=  SelfInvocation 
                      |  ConstrBlock
  ConstrBlock       ::=  ‘{’ SelfInvocation {semi BlockStat} ‘}’
  SelfInvocation    ::=  ‘this’ ArgumentExprs {ArgumentExprs}

  TopStatSeq        ::=  TopStat {semi TopStat}
  TopStat           ::=  {Annotation [nl]} {Modifier} TmplDef
                      |  Import
                      |  Packaging
                      |  PackageObject
                      |  
  Packaging         ::=  ‘package’ QualId [nl] ‘{’ TopStatSeq ‘}’
  PackageObject     ::=  ‘package’ ‘object’ ObjectDef

  CompilationUnit   ::=  {‘package’ QualId semi} TopStatSeq

14 References

Kennedy, Andrew J., and Benjamin C. Pierce. 2007. “On Decidability of Nominal Subtyping with Variance.”

Odersky, Martin. 2006. “The Scala Experiment – Can We Provide Better Language Support for Component Systems?” In Proc. ACM Symposium on Principles of Programming Languages.

Odersky, Martin, Vincent Cremet, Christine Röckl, and Matthias Zenger. 2003. “A Nominal Theory of Objects with Dependent Types.” In Proc. ECOOP’03.

Odersky, Martin, and Matthias Zenger. 2005a. “Scalable Component Abstractions.” In Proc. OOPSLA.

———. 2005b. “Independently Extensible Solutions to the Expression Problem.” In Proc. FOOL 12.

Odersky, Martin, and al. 2004. An Overview of the Scala Programming Language.


  1. We assume that objects and packages also implicitly define a class (of the same name as the object or package, but inaccessible to user programs).

  2. A reference to a structurally defined member (method call or access to a value or variable) may generate binary code that is significantly slower than an equivalent code to a non-structural member.

  3. A congruence is an equivalence relation which is closed under formation of contexts.

  4. The current Scala compiler limits the nesting level of parameterization in such bounds to be at most two deeper than the maximum nesting level of the operand types.

  5. However, at present singleton types of method parameters may only appear in the method body; so dependent method types are not supported.