# Expressions

Expr         ::=  (Bindings | id | _') =>' Expr
|  Expr1
Expr1        ::=  if' (' Expr )' {nl} Expr [[semi] else' Expr]
|  while' (' Expr )' {nl} Expr
|  try' ({' Block }' | Expr) [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 BlockStat} [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.

## 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 $t_1[\mathit{tps}_1] >: L_1 <: U_1 , \ldots , t_n[\mathit{tps}_n] >: L_n <: U_n$ 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 $t_n[\mathit{tps}\_n] >: L_n <: U_n$ }.


## Literals

SimpleExpr    ::=  Literal


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

## 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:

• eq($x\,$) and ==($x\,$) return true iff the argument $x$ is also the "null" object.
• ne($x\,$) and !=($x\,$) return true iff the argument x is not also the "null" object.
• isInstanceOf[$T\,$] always returns false.
• asInstanceOf[$T\,$] returns the default value of type $T$.
• ## returns 0.

A reference to any other member of the "null" object causes a NullPointerException to be thrown.

## 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 $\mathit{pt}$ is a stable type, or
3. The expected type $\mathit{pt}$ 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 $\mathit{pt}$, 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 $m$.

## 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 $m'$ 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. <!-- explanation: so that we need not create several fields for overriding vals -->

If it is a method, it must be concrete, or the template containing the reference must have a member $m'$ 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 $m'$ 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 $m'$ 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.

###### Example

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.

## 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 $e_1 , \ldots , e_m$. If $f$ has a method type ($p_1$:$T_1 , \ldots , p_n$:$T_n$)$U$, the type of each argument expression $e_i$ is typed with the corresponding parameter type $T_i$ as expected type. Let $S_i$ be type type of argument $e_i$ $(i = 1 , \ldots , m)$. 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 $e_1 , \ldots , e_n$ of types $S_1 , \ldots , S_n$.

If $f$ has a method type $(p_1:T_1 , \ldots , p_n:T_n)U$ we say that an argument expression $e_i$ is a named argument if it has the form $x_i=e'_i$ and $x_i$ is one of the parameter names $p_1 , \ldots , p_n$. The function $f$ is applicable if all of the following conditions hold:

• For every named argument $x_i=e_i'$ the type $S_i$ is compatible with the parameter type $T_j$ whose name $p_j$ matches $x_i$.
• For every positional argument $e_i$ the type $S_i$ is compatible with $T_i$.
• If the expected type is defined, the result type $U$ is compatible to it.

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 $e_1 , \ldots , e_n$ 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.

###### Example

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.

### Named and Default Arguments

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

• For every named argument $p_i = e_i$ which appears left of a positional argument in the argument list $e_1 \ldots e_m$, the argument position $i$ coincides with the position of parameter $p_i$ in the parameter list of the applied function.
• The names $x_i$ of all named arguments are pairwise distinct and no named argument defines a parameter which is already specified by a positional argument.
• Every formal parameter $p_j:T_j$ which is not specified by either a positional or a named argument has a default argument.

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 $(\mathit{args}_1) , \ldots , (\mathit{args}_l)$ is a reference to one of the values $x_1 , \ldots , x_k$. To integrate the current application into the block, first a value definition using a fresh name $y_i$ is created for every argument in $e_1 , \ldots , e_m$, which is initialised to $e_i$ for positional arguments and to $e'_i$ 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 $z_i$ is created, which is initialized using the method computing the default argument of this parameter.

Let $\mathit{args}$ be a permutation of the generated names $y_i$ and $z_i$ 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.$m$[$\mathit{targs}$]($\mathit{args}_1$)$, \ldots ,$($\mathit{args}_l$)($\mathit{args}$)
}


### Signature Polymorphic Methods

For invocations of signature polymorphic methods of the target platform $f$($e_1 , \ldots , e_m$), the invoked function has a different method type ($p_1$:$T_1 , \ldots , p_n$:$T_n$)$U$ at each call site. The parameter types $T_ , \ldots , T_n$ are the types of the argument expressions $e_1 , \ldots , e_m$ and $U$ is the expected type at the call site. If the expected type is undefined then $U$ is scala.AnyRef. The parameter names $p_1 , \ldots , p_n$ are fresh.

###### Note

On the Java platform version 7 and later, the methods invoke and invokeExact in class java.lang.invoke.MethodHandle are signature polymorphic.

## 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 ().

###### Example

The method values in the left column are each equivalent to the eta-expanded expressions on the right.

placeholder syntax eta-expansion
math.sin _ x => math.sin(x)
math.pow _ (x1, x2) => math.pow(x1, x2)
val vs = 1 to 9; vs.fold _ (z) => (op) => vs.fold(z)(op)
(1 to 9).fold(z)_ { val eta1 = z; val eta2 = 1 to 9; op => eta2.fold(eta1)(op) }
Some(1).fold(??? : Int)_ { val eta1 = () => ???; val eta2 = Some(1); op => eta2.fold(eta1())(op) }

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.

## 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 $T_i$ must obey the corresponding bounds $L_i$ and $U_i$. That is, for each $i = 1 , \ldots , n$, we must have $\sigma L_i <: T_i <: \sigma U_i$, where $\sigma$ is the substitution $[a_1 := T_1 , \ldots , a_n := T_n]$. The type of the application is $\sigma S$.

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.

## 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 $n \geq 2$. The empty tuple () is the unique value of type scala.Unit.

## 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 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{$D$}.

###### Example

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. ## Blocks BlockExpr ::= ‘{’ CaseClauses ‘}’ | ‘{’ Block ‘}’ Block ::= BlockStat {semi BlockStat} [ResultExpr]  A block expression {$s_1$;$\ldots$;$s_n$;$e\,$} is constructed from a sequence of block statements$s_1 , \ldots , s_n$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$s_1 , \ldots , s_n$. We say the existential clause binds the occurrence of the value or type name. Specifically, • A locally defined type definition type$\;t = T$ is bound by the existential clause type$\;t >: T <: T$. It is an error if$t$carries type parameters. • A locally defined value definition val$\;x: T = e$ is bound by the existential clause val$\;x: T$. • A locally defined class definition class$\;c$extends$\;t$ is bound by the existential clause type$\;c <: T$ where$T$is the least class type or refinement type which is a proper supertype of the type$c$. It is an error if$c$carries type parameters. • A locally defined object definition object$\;x\;$extends$\;t$ is bound by the existential clause val$\;x: T$ where$T$is the least class type or refinement type which is a proper supertype of the type $x$.type. 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. ###### Example 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. ## 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. ### Prefix Operations A prefix operation$\mathit{op};e$consists of a prefix operator$\mathit{op}$, which must be one of the identifiers ‘+’, ‘-’, ‘!’ or ‘~’. The expression$\mathit{op};e$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). ### Postfix Operations A postfix operator can be an arbitrary identifier. The postfix operation$e;\mathit{op}$is interpreted as$e.\mathit{op}$. ### 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. (all letters) | ^ & = ! < > : + - * / % (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 assignment 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. • If there are several infix operations in an expression, then operators with higher precedence bind more closely than operators with lower precedence. • If there are consecutive infix operations$e_0; \mathit{op}_1; e_1; \mathit{op}_2 \ldots \mathit{op}_n; e_n$with operators$\mathit{op}_1 , \ldots , \mathit{op}_n$of the same precedence, then all these operators must have the same associativity. If all operators are left-associative, the sequence is interpreted as$(\ldots(e_0;\mathit{op}_1;e_1);\mathit{op}_2\ldots);\mathit{op}_n;e_n$. Otherwise, if all operators are right-associative, the sequence is interpreted as$e_0;\mathit{op}_1;(e_1;\mathit{op}_2;(\ldots \mathit{op}_n;e_n)\ldots)$. • Postfix operators always have lower precedence than infix operators. E.g.$e_1;\mathit{op}_1;e_2;\mathit{op}_2$is always equivalent to$(e_1;\mathit{op}_1;e_2);\mathit{op}_2$. The right-hand operand of a left-associative operator may consist of several arguments enclosed in parentheses, e.g.$e;\mathit{op};(e_1,\ldots,e_n)$. This expression is then interpreted as$e.\mathit{op}(e_1,\ldots,e_n)$. A left-associative binary operation$e_1;\mathit{op};e_2$is interpreted as$e_1.\mathit{op}(e_2)$. If$\mathit{op}$is right-associative, the same operation is interpreted as { val$x$=$e_1$;$e_2$.$\mathit{op}$($x\,$) }, where$x$is a fresh name. ### 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 +. ## 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$T$. ###### Example Here are examples of well-typed and ill-typed expressions. 1: Int // legal, of type Int 1: Long // legal, of type Long // 1: string // ***** illegal  ## Annotated Expressions Expr1 ::= PostfixExpr :' Annotation {Annotation}  An annotated expression $e$: @$a_1\ldots$@$a_n$ attaches annotations$a_1 , \ldots , a_n$to the expression$e$. ## 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$f$. ###### Example Here are some assignment expressions and their equivalent expansions. assignment expansion 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) ###### Example Imperative Matrix Multiplication 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 }  ## 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$e_2$and$e_3$, depending on the value of$e_1$. The condition$e_1$is expected to conform to type Boolean. The then-part$e_2$and the else-part$e_3$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$e_2$and$e_3$. A semicolon preceding the else symbol of a conditional expression is ignored. The conditional expression is evaluated by evaluating first$e_1$. If this evaluates to true, the result of evaluating$e_2$is returned, otherwise the result of evaluating$e_3$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 (). ## 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 {}  ## 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. ## For Comprehensions and For Loops Expr1 ::= for' ((' Enumerators )' | {' Enumerators }') {nl} [yield'] Expr Enumerators ::= Generator {semi Generator} Generator ::= Pattern1 <-' Expr {[semi] Guard | semi Pattern1 =' Expr} Guard ::= if' PostfixExpr  A for loop for ($\mathit{enums}\,$)$e$ executes expression$e$for each binding generated by the enumerators$\mathit{enums}$. A for comprehension for ($\mathit{enums}\,$) yield$e$ evaluates expression$e$for each binding generated by the enumerators$\mathit{enums}$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. • A for comprehension for ($p$<-$e\,$) yield$e'$ is translated to $e$.map { case$p$=>$e'$}. • A for loop for ($p$<-$e\,$)$e'$ is translated to $e$.foreach { case$p$=>$e'$}. • A for comprehension for ($p$<-$e$;$p'$<-$e'; \ldots$) yield$e''$ where $\ldots$ is a (possibly empty) sequence of generators, definitions, or guards, is translated to $e$.flatMap { case$p$=> for ($p'$<-$e'; \ldots$) yield$e''$}  • A for loop for ($p$<-$e$;$p'$<-$e'; \ldots$)$e''$ where $\ldots$ is a (possibly empty) sequence of generators, definitions, or guards, is translated to $e$.foreach { case$p$=> for ($p'$<-$e'; \ldots$)$e''$}  • A generator $p$<-$e$ followed by a guard if$g$ is translated to a single generator $p$<-$e$.withFilter(($x_1 , \ldots , x_n$) =>$g\,$) where$x_1 , \ldots , x_n$are the free variables of$p$. • A generator $p$<-$e$ followed by a value definition $p'$=$e'$ is translated to the following generator of pairs of values, where$x$and$x'$are fresh names: ($p$,$p'$) <- for ($x @ p$<-$e$) yield { val$x' @ p'$=$e'$; ($x$,$x'$) }  ###### Example The following code produces all pairs of numbers between$1$and$n-1$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) } }  ###### Example 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. 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. ## 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. ## 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. ## Try Expressions Expr1 ::= try' ({' Block }' | Expr) [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$\mathit{pt}$be the expected type of the try expression. The block$b$is expected to conform to$\mathit{pt}$. 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$e_2$. ## 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$x_i$of types$T_i$to a result given by expression$e$. The scope of each formal parameter$x_i$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$T_i$of any of the parameters$x_i$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$x_i$. 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. ###### Example 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.  ### 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$u_1 , \ldots , u_n$, in this order, it is equivalent to the anonymous function ($u'_1$, ...$u'_n$) =>$e'$ where each$u_i'$results from$u_i$by replacing the underscore with a fresh identifier and$e'$results from$e$by replacing each underscore section$u_i$by$u_i'$. ###### Example 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) ## 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: • A literal of a value class, such as an integer • A string literal • A class constructed with Predef.classOf • An element of an enumeration from the underlying platform • A literal array, of the form Array$(c_1 , \ldots , c_n)$, where all of the$c_i$'s are themselves constant expressions • An identifier defined by a constant value definition. ## Statements BlockStat ::= Import | {Annotation} [‘implicit’ | ‘lazy’] 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. ## 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$T$weakly conforms to$U$after applying eta-expansion and view applications. ### Value Conversions The following seven implicit conversions can be applied to an expression$e$which has some value type$T$and which is type-checked with some expected type$\mathit{pt}$. ###### Static 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$\mathit{pt}$, 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. ### 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$\mathit{pt}$is a function type$(\mathit{Ts}') \Rightarrow T'$, 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$e()$. ### 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$\mathscr{A}$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$\mathit{shape}(e)$, is a type that is defined as follows: • For a function expression ($p_1$:$T_1 , \ldots , p_n$:$T_n$) =>$b$: (Any$, \ldots ,$Any) =>$\mathit{shape}(b)$, where Any occurs$n$times in the argument type. • For a named argument $n$=$e$:$\mathit{shape}(e)$. • For all other expressions: Nothing. Let$\mathscr{B}$be the set of alternatives in$\mathscr{A}$that are applicable to expressions$(e_1 , \ldots , e_n)$of types$(\mathit{shape}(e_1) , \ldots , \mathit{shape}(e_n))$. If there is precisely one alternative in$\mathscr{B}$, that alternative is chosen. Otherwise, let$S_1 , \ldots , S_m$be the vector of types obtained by typing each argument with an undefined expected type. For every member$m$in$\mathscr{B}$one determines whether it is applicable to expressions ($e_1 , \ldots , e_m$) of types$S_1 , \ldots , S_m$. It is an error if none of the members in$\mathscr{B}$is applicable. If there is one single applicable alternative, that alternative is chosen. Otherwise, let$\mathscr{CC}$be the set of applicable alternatives which don't employ any default argument in the application to$e_1 , \ldots , e_m$. It is again an error if$\mathscr{CC}$is empty. Otherwise, one chooses the most specific alternative among the alternatives in$\mathscr{CC}$, according to the following definition of being "as specific as", and "more specific than": • A parameterized method$m$of type ($p_1:T_1, \ldots , p_n:T_n$)$U$ is as specific as some other member$m'$of type$S$if$m'$is applicable to arguments ($p_1 , \ldots , p_n\,$) of types$T_1 , \ldots , T_n$. • A polymorphic method of type [$a_1$>:$L_1$<:$U_1 , \ldots , a_n$>:$L_n$<:$U_n$]$T$ is as specific as some other member of type$S$if$T$is as specific as$S$under the assumption that for$i = 1 , \ldots , n$each$a_i$is an abstract type name bounded from below by$L_i$and from above by$U_i$. • A member of any other type is always as specific as a parameterized method or a polymorphic method. • Given two members of types$T$and$U$which are neither parameterized nor polymorphic method types, the member of type$T$is as specific as the member of type$U$if the existential dual of$T$conforms to the existential dual of$U$. Here, the existential dual of a polymorphic type [$a_1$>:$L_1$<:$U_1 , \ldots , a_n$>:$L_n$<:$U_n$]$T$ is $T$forSome { type$a_1$>:$L_1$<:$U_1, \ldots ,$type$a_n$>:$L_n$<:$U_n$}. The existential dual of every other type is the type itself. The relative weight of an alternative$A$over an alternative$B$is a number from 0 to 2, defined as the sum of • 1 if$A$is as specific as$B$, 0 otherwise, and • 1 if$A$is defined in a class or object which is derived from the class or object defining$B$, 0 otherwise. A class or object$C$is derived from a class or object$D$if one of the following holds: •$C$is a subclass of$D$, or •$C$is a companion object of a class derived from$D$, or •$D$is a companion object of a class from which$C$is derived. 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$\mathscr{CC}$which is more specific than all other alternatives in$\mathscr{CC}$. Assume next that$e$appears as a function in a type application, as in $e$[$\mathit{targs}\,$]. Then all alternatives in$\mathscr{A}$which take the same number of type parameters as there are type arguments in$\mathit{targs}$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$\mathscr{B}$be the set of those alternatives in$\mathscr{A}$which are compatible to it. Otherwise, let$\mathscr{B}$be the same as$\mathscr{A}$. We choose in this case the most specific alternative among all alternatives in$\mathscr{B}$. It is an error if there is no alternative in$\mathscr{B}$which is more specific than all other alternatives in$\mathscr{B}$. ###### Example 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. ### Local Type Inference Local type inference infers type arguments to be passed to expressions of polymorphic type. Say$e$is of type [$a_1$>:$L_1$<:$U_1 , \ldots , a_n$>:$L_n$<:$U_n$]$T$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$T_1 , \ldots , T_n$depends on the context in which the expression appears and on the expected type$\mathit{pt}$. 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 [$a_1$>:$L_1$<:$U_1 , \ldots , a_n$>:$L_n$<:$U_n$]$S$, and local type inference is applied in turn to infer type arguments for$a_1 , \ldots , a_n$, 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$\mathit{pt}$. 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$\sigma$of types$T_i$for the type parameters$a_i$such that • None of the inferred types$T_i$is a singleton type • All type parameter bounds are respected, i.e.$\sigma L_i <: \sigma a_i$and$\sigma a_i <: \sigma U_i$for$i = 1 , \ldots , n$. • The expression's type conforms to the expected type, i.e.$\sigma T <: \sigma \mathit{pt}$. It is a compile time error if no such substitution exists. If several substitutions exist, local-type inference will choose for each type variable$a_i$a minimal or maximal type$T_i$of the solution space. A maximal type$T_i$will be chosen if the type parameter$a_i$appears contravariantly in the type$T$of the expression. A minimal type$T_i$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$e(d_1 , \ldots , d_m)$. In that case$T$is a method type$(p_1:R_1 , \ldots , p_m:R_m)T'$. Without loss of generality we can assume that the result type$T'$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$S_j$of the argument expressions$d_j$, using two alternative schemes. Each argument expression$d_j$is typed first with the expected type$R_j$, in which the type parameters$a_1 , \ldots , a_n$are taken as type constants. If this fails, the argument$d_j$is typed instead with an expected type$R_j'$which results from$R_j$by replacing every type parameter in$a_1 , \ldots , a_n$with undefined. In a second step, type arguments are inferred by solving a constraint system which relates the method's type with the expected type$\mathit{pt}$and the argument types$S_1 , \ldots , S_m$. Solving the constraint system means finding a substitution$\sigma$of types$T_i$for the type parameters$a_i$such that • None of the inferred types$T_i$is a singleton type • All type parameter bounds are respected, i.e.$\sigma L_i <: \sigma a_i$and$\sigma a_i <: \sigma U_i$for$i = 1 , \ldots , n$. • The method's result type$T'$conforms to the expected type, i.e.$\sigma T' <: \sigma \mathit{pt}$. • Each argument type weakly conforms to the corresponding formal parameter type, i.e.$\sigma S_j <:_w \sigma R_j$for$j = 1 , \ldots , m$. It is a compile time error if no such substitution exists. If several solutions exist, an optimal one for the type$T'$is chosen. All or parts of an expected type$\mathit{pt}$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:$\mathit{undefined} <: T$and$T <: \mathit{undefined}$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. ###### Example 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?] <:$\mathit{undefined}$ The optimal solution of this constraint system is a = Int  so Int is the type inferred for a. ###### Example 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[$\mathit{undefined}$]. 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?] <:$\mathit{undefined}$ The optimal solution of this constraint system is a = scala.Any  so scala.Any is the type inferred for a. ### Eta Expansion Eta-expansion converts an expression of method type to an equivalent expression of function type. It proceeds in two steps. First, one identifies the maximal sub-expressions of$e$; let's say these are$e_1 , \ldots , e_m$. For each of these, one creates a fresh name$x_i$. Let$e'$be the expression resulting from replacing every maximal subexpression$e_i$in$e$by the corresponding fresh name$x_i$. Second, one creates a fresh name$y_i$for every argument type$T_i$of the method ($i = 1 , \ldots , n$). The result of eta-conversion is then: { val$x_1$=$e_1$;$\ldots$val$x_m$=$e_m$; ($y_1: T_1 , \ldots , y_n: T_n$) =>$e'$($y_1 , \ldots , y_n$) }  The behavior of call-by-name parameters is preserved under eta-expansion: the corresponding actual argument expression, a sub-expression of parameterless method type, is not evaluated in the expanded block. ### Dynamic Member Selection The standard Scala library defines a trait scala.Dynamic which defines a member applyDynamic 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 rewritten under the conditions given here to: $e$.applyDynamic("$x$")  If the selection is followed by some arguments, e.g.$e.x(\mathit{args})$, then that expression is rewritten to $e$.applyDynamic("$x$",$\mathit{args}\$)