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:
 the expected type of $e$ is $T$, and
 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==($x\,$)
returntrue
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 returnsfalse
.asInstanceOf[$T\,$]
returns the default value of type $T$.##
returns0
.
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:
 The path $p$ occurs as the prefix of a selection and it does not designate a constant, or
 The expected type $\mathit{pt}$ is a stable type, or
 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
 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 righthand 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
righthand side of the rewrite rule entails a reevaluation of $e$.
In other words, the evaluation order for
=>
parameters is callbyname whereas the evaluation
order for normal parameters is callbyvalue.
Furthermore, it is required that $e$'s packed type
conforms to the parameter type $T$.
The behavior of byname 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 runtime stack. However, if a local function or a final method calls itself as its last action, the call is executed using the stackframe 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 wellformed if $e$ is of method
type or if $e$ is a callbyname 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 callbyname 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 etaexpanded expressions on the right.
placeholder syntax  etaexpansion 

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 nonabstract 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 clausetype$\;t >: T <: T$
. It is an error if $t$ carries type parameters.  A locally defined value definition
val$\;x: T = e$
is bound by the existential clauseval$\;x: T$
.  A locally defined class definition
class$\;c$ extends$\;t$
is bound by the existential clausetype$\;c <: T$
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 clauseval$\;x: T$
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
rightassociative. All other operators are leftassociative.
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 leftassociative, 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 rightassociative, 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 righthand operand of a leftassociative 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 leftassociative binary
operation $e_1;\mathit{op};e_2$ is interpreted as $e_1.\mathit{op}(e_2)$. If $\mathit{op}$ is
rightassociative, 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:
 the operator also starts with an equals character, or
 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 reinterpreted as an operation which corresponds
to the assignment
$l$ = $l$ + $r$
except that the operation's lefthandside $l$ is evaluated only once.
The reinterpretation occurs if the following two conditions are fulfilled.
 The lefthandside $l$ does not have a member named
+=
, and also cannot be converted by an implicit conversion to a value with a member named+=
.  The assignment
$l$ = $l$ + $r$
is typecorrect. 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 welltyped and illtyped 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 thenpart $e_2$ and the
elsepart $e_3$ 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
elsepart. 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 guardif $g$
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 $n1$ 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) } }
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 typechecked 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 rethrown.
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
rethrown 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 nonlocal 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 blocklocal 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 subsections.
We say, a type $T$ is compatible to a type $U$ if $T$ weakly conforms to $U$ after applying etaexpansion 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 typechecked 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 $(\mathit{Ts}') \Rightarrow T'$, etaexpansion 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) => $\mathit{shape}(b)$
, whereAny
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 etaexpansion 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, localtype 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, nonvariantly 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 etaexpansion 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 compiletime error results. Because $<:$ is a preorder, 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 typecheck 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
Etaexpansion converts an expression of method type to an equivalent expression of function type. It proceeds in two steps.
First, one identifies the maximal subexpressions 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 etaconversion 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 callbyname parameters is preserved under etaexpansion: the corresponding actual argument expression, a subexpression 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("$x$", $\mathit{args}$)