Expressions
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
Literals
Typing of literals is described along with their lexical syntax; their evaluation is immediate.
The Null Value
The null
value is of type scala.Null
, and thus conforms to 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
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
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.
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
The linearization of class C
is {C, B, Root}
and
the linearization of class D
is {D, B, A, Root}
.
Then we have:
Note that the superB
method returns different results
depending on whether B
is mixed in with class Root
or A
.
Function Applications
An application ´f(e_1 , \ldots , e_m)´
applies the function ´f´
to the argument expressions ´e_1, \ldots , e_m´
. For this expression to be welltyped, the function must be applicable to its arguments, which is defined next by case analysis on ´f´'s type.
If ´f´ has a method type (´p_1´:´T_1 , \ldots , p_n´:´T_n´)´U´
, each argument expression ´e_i´ is typed with the corresponding parameter type ´T_i´ as expected type. Let ´S_i´ be the type of argument ´e_i´ ´(i = 1 , \ldots , m)´. The method ´f´ must be applicable to its arguments ´e_1, \ldots , e_n´ of types ´S_1 , \ldots , S_n´. 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´
.
Once the types ´S_i´ have been determined, the method ´f´ of the above method type is said to be applicable if all of the following conditions hold:
 for every named argument ´p_j=e_i'´ the type ´S_i´ is compatible with the parameter type ´T_j´;
 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, local type inference is used to instantiate ´f´'s type parameters. The polymorphic method is applicable if type inference can determine type arguments so that the instantiated method is applicable.
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 value ´f´
is applicable to the given arguments if ´f´.apply
is applicable.
The application ´f´(´e_1 , \ldots , e_n´)
evaluates ´f´ and then each argument
´e_1 , \ldots , e_n´ from left to right, except for arguments that correspond to
a byname parameter (see below). 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.
If only a single argument is supplied, it may be supplied as a block expression
and parentheses can be omitted, in the form ´f´ { block }
. This is valid when
f
has a single formal parameter or when all other formal parameters have
default values.
A function application usually allocates a new frame on the program's runtime stack. However, if a local method or a final method calls itself as its last action, the call is executed using the stackframe of the caller.
Example
Assume the following method which computes the sum of a variable number of arguments:
Then
both yield 10
as result. On the other hand,
would not typecheck.
An argument list may begin with the soft keyword using
to facilitate crosscompilation with Scala 3.
The keyword is ignored.
Named and Default Arguments
If an application is to use 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 method.
 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 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 method ´f´
has the form ´p.m´[´\mathit{targs}´]
it is transformed into the
block
If the method ´f´ is itself an application expression the transformation is applied recursively on ´f´. The result of transforming ´f´ is a block of the form
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
Signature Polymorphic Methods
For invocations of signature polymorphic methods of the target platform ´f´(´e_1 , \ldots , e_m´)
,
the invoked method 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´
. If the declared return type ´R´
of the signature polymorphic method is
any type other than scala.AnyRef
, then the return type ´U´
is ´R´
.
Otherwise, ´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 11 and later, a method is signature polymorphic if it is native,
a member of java.lang.invoke.MethodHandle
or java.lang.invoke.VarHandle
, and has a single
repeated parameter of type java.lang.Object*
. (These requirements also work for Java 8,
which had fewer such methods.)
Method Values
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
parameter list ()
.
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 = 1 to 9; val eta2 = z; op => eta1.fold(eta2)(op) } 
Some(1).fold(??? : Int)_ 
{ val eta1 = Some(1); val eta2 = () => ???; op => eta1.fold(eta2())(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
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 method from the types of the actual method arguments and the expected result type.
Tuples
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
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
(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
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:
This is a shorthand for the general instance creation expression
The latter is in turn a shorthand for the block
where anon$X
is some freshly created name.
Blocks
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.
A block expression {´c_1´; ´\ldots´; ´c_n´}
where ´s_1 , \ldots , s_n´ are
case clauses forms a pattern matching anonymous function.
Example
Assuming a class Ref[T](x: T)
, the block
has the type Ref[_1] forSome { type _1 <: B }
.
The block
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
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 ‘~
’,
which must not be enclosed in backquotes.
The expression ´\mathit{op};e´ is
equivalent to the postfix method application
e.unary_´\mathit{op}´
.
Prefix operators are different from normal method applications in
that their operand expression need not be atomic. For instance, the
input sequence sin(x)
is read as (sin(x))
, whereas the
method 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.
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 and its parameter is passed by name, the same operation is interpreted as
´e_2.\mathit{op}(e_1)´. If ´\mathit{op}´ is rightassociative and its parameter is passed by value,
it 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 following exceptions:
 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
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
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.
Annotated Expressions
An annotated expression ´e´: @´a_1´ ´\ldots´ @´a_n´
attaches annotations ´a_1 , \ldots , a_n´ to the
expression ´e´.
Assignments
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
method defined in some template, and the same template contains a
setter method ´x´_=
as member, then the assignment
´x´ = ´e´
is interpreted as the invocation
´x´_=(´e\,´)
of that setter method. Analogously, an
assignment ´f.x´ = ´e´
to a parameterless method ´x´
is interpreted as the invocation ´f.x´_=(´e\,´)
.
If ´x´ is an application of a unary operator, then the expression
is interpreted as though it were written as the explicit application
´x´.unary_´\mathit{op}´
, namely, as ´x´.unary_´\mathit{op}´_=(´e\,´)
.
An assignment ´f´(´\mathit{args}\,´) = ´e´
with a method application to the
left of the ‘=
’ operator is interpreted as
´f.´update(´\mathit{args}´, ´e\,´)
, i.e.
the invocation of an update
method 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.
Desugaring the array accesses and assignments yields the following expanded version:
Conditional Expressions
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
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 method whileLoop
is defined as follows.
Do Loop Expressions
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
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´. Optionally, case
can appear in front
of a generator pattern, this has no meaning in Scala 2 but will be required in
Scala 3 if p
is not
irrefutable.
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
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
where
´\ldots´
is a (possibly empty) sequence of generators, definitions, or guards, is translated toA for loop
where
´\ldots´
is a (possibly empty) sequence of generators, definitions, or guards, is translated toA 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:
Example
The following code produces all pairs of numbers between ´1´ and ´n1´ whose sums are prime.
The for comprehension is translated to:
Example
For comprehensions can be used to express vector and matrix algorithms concisely. For instance, here is a method to compute the transpose of a given matrix:
Here is a method to compute the scalar product of two vectors:
Finally, here is a method to compute the product of two matrices. Compare with the imperative version.
The code above makes use of the fact that map
, flatMap
,
withFilter
, and foreach
are defined for instances of class
scala.Array
.
Return Expressions
A return expression return ´e´
must occur inside the body of some
enclosing user defined method. The innermost enclosing method in a
source program, ´m´, 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 ´m´. 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 were return ()
.
Returning from the method from within a nested function may be
implemented by throwing and catching a
scala.runtime.NonLocalReturnControl
. Any exception catches
between the point of return and the enclosing methods might see
and catch that exception. A key comparison makes sure that this
exception is 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 method ´m´ has already returned
before the return expression is executed. In that case, the thrown
scala.runtime.NonLocalReturnControl
will not be caught, and will
propagate up the call stack.
Throw Expressions
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
A try expression is of the form try { ´b´ } catch ´h´
where the handler ´h´ is usually a
pattern matching anonymous function
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. More generally, if the handler is a PartialFunction
,
it is applied only if it is defined at the given exception.
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.Function[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
The anonymous function of arity ´n´, (´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.
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. Hence, arguments to anonymous functions always have to be given explicitly.
Translation
If the expected type of the anonymous function is of the shape scala.Function´n´[´S_1 , \ldots , S_n´, ´R\,´]
, or can be SAMconverted to such a function type, the type ´T_i´
of a parameter ´x_i´
can be omitted, as far as ´S_i´
is defined in the expected type, and ´T_i´ = ´S_i´
is assumed. Furthermore, the expected type when type checking ´e´ is ´R´.
If there is no expected type for the function literal, all formal parameter types ´T_i´
must be specified explicitly, and the expected type of ´e´ is undefined. The type of the anonymous function is scala.Function´n´[´T_1 , \ldots , T_n´, ´R\,´]
, where ´R´ is the packed type of ´e´. ´R´ must be equivalent to a type which does not refer to any of the formal parameters ´x_i´.
The eventual runtime value of an anonymous function is determined by the expected type:
 a subclass of one of the builtin function types,
scala.Function´n´[´S_1 , \ldots , S_n´, ´R\,´]
(with ´S_i´ and ´R´ fully defined),  a singleabstractmethod (SAM) type;
PartialFunction[´T´, ´U´]
 some other type.
The standard anonymous function evaluates in the same way as the following instance creation expression:
The same evaluation holds for a SAM type, except that the instantiated type is given by the SAM type, and the implemented method is the single abstract method member of this type.
The underlying platform may provide more efficient ways of constructing these instances, such as Java 8's invokedynamic
bytecode and LambdaMetaFactory
class.
When a PartialFunction
is required, an additional member isDefinedAt
is synthesized, which simply returns true
.
However, if the function literal has the shape x => x match { $\ldots$ }
,
then isDefinedAt
is derived from the pattern match in the following way:
each case from the match expression evaluates to true
,
and if there is no default case,
a default case is added that evaluates to false
.
For more details on how that is implemented see
"Pattern Matching Anonymous Functions".
Example
Examples of anonymous functions:
Placeholder Syntax for Anonymous Functions
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
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.
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
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 in the standard library.
Since conversions from Int
to Float
and from Long
to Float
or Double
may incur a loss of precision, those implicit conversions are deprecated.
The conversion is permitted for literals if the original value can be recovered,
that is, if conversion back to the original type produces the original value.
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´; () }
.
SAM conversion
An expression (p1, ..., pN) => body
of function type (T1, ..., TN) => T
is samconvertible to the expected type S
if the following holds:
 the class
C
ofS
declares an abstract methodm
with signature(p1: A1, ..., pN: AN): R
;  besides
m
,C
must not declare or inherit any other deferred value members;  the method
m
must have a single argument list;  there must be a type
U
that is a subtype ofS
, so that the expressionnew U { final def m(p1: A1, ..., pN: AN): R = body }
is welltyped (conforming to the expected typeS
);  for the purpose of scoping,
m
should be considered a static member (U
's members are not in scope inbody
); (A1, ..., AN) => R
is a subtype of(T1, ..., TN) => T
(satisfying this condition drives type inference of unknown type parameters inS
);
Note that a function literal that targets a SAM is not necessarily compiled to the above instance creation expression. This is platformdependent.
It follows that:
 if class
C
defines a constructor, it must be accessible and must define exactly one, empty, argument list;  class
C
cannot befinal
orsealed
(for simplicity we ignore the possibility of SAM conversion in the same compilation unit as the sealed class); m
cannot be polymorphic; it must be possible to derive a fullydefined type
U
fromS
by inferring any unknown type parameters ofC
.
Finally, we impose some implementation restrictions (these may be lifted in future releases):
C
must not be nested or local (it must not capture its environment, as that results in a nonzeroargument constructor)C
's constructor must not have an implicit argument list (this simplifies type inference);C
must not declare a self type (this simplifies type inference);C
must not be@specialized
.
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.
Selection on Dynamic
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, or, for methods of nonzero arity, a type samconvertible to a function type, ´(\mathit{Ts}') \Rightarrow T'´, etaexpansion is performed on the expression ´e´.
(The exception for zeroarity methods is to avoid surprises due to unexpected sam conversion.)
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 patternmatching anonymous function definition
{ case ... }
:PartialFunction[Any, Nothing]
.  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 list of types obtained by typing each argument as follows.
Normally, an argument is typed without an expected type, except when
all alternatives explicitly specify the same parameter type for this argument (a missing parameter type,
due to e.g. arity differences, is taken as NoType
, thus resorting to no expected type),
or when trying to propagate more type information to aid inference of higherorder function parameter types, as explained next.
The intuition for higherorder function parameter type inference is that all arguments must be of a functionlike type
(PartialFunction
, FunctionN
or some equivalent SAM type),
which in turn must define the same set of higherorder argument types, so that they can safely be used as
the expected type of a given argument of the overloaded method, without unduly ruling out any alternatives.
The intent is not to steer overloading resolution, but to preserve enough type information to steer type
inference of the arguments (a function literal or etaexpanded method) to this overloaded method.
Note that the expected type drives etaexpansion (not performed unless a functionlike type is expected), as well as inference of omitted parameter types of function literals.
More precisely, an argument ´e_i´
is typed with an expected type that is derived from the ´i´
th argument
type found in each alternative (call these ´T_{ij}´
for alternative ´j´
and argument position ´i´
) when
all ´T_{ij}´
are function types ´(A_{1j},..., A_{nj}) => ?´
(or the equivalent PartialFunction
, or SAM)
of some arity ´n´
, and their argument types ´A_{kj}´
are identical across all overloads ´j´
for a
given ´k´
. Then, the expected type for ´e_i´
is derived as follows:
 we use
´PartialFunction[A_{1j},..., A_{nj}, ?]´
if for some overload´j´
,´T_{ij}´
's type symbol isPartialFunction
;  else, if for some
´j´
,´T_{ij}´
isFunctionN
, the expected type is´FunctionN[A_{1j},..., A_{nj}, ?]´
;  else, if for all
´j´
,´T_{ij}´
is a SAM type of the same class, defining argument types´A_{1j},..., A_{nj}´
(and a potentially varying result type), the expected type encodes these argument types and the SAM class.
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_last´; if ´T_n´ denotes a repeated parameter (it has shape ´T*´), and so does ´m'´'s last parameter, ´T_last´ is taken as ´T´, otherwise ´T_n´ is used directly.  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}´. In this last case we choose 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:
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
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
unless it is a singleton type corresponding to an object or a constant value
definition or the corresponding bound ´U_i´ is a subtype of
scala.Singleton
.  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
unless it is a singleton type corresponding to an object or a constant value
definition or the corresponding bound ´U_i´ is a subtype of
scala.Singleton
.  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:
and the definition
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
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
In a second step, one solves the following constraint system for
the type parameter a
of cons
:
The optimal solution of this constraint system is
so Int
is the type inferred for a
.
Example
Consider now the definition
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
:
The optimal solution of this constraint system is
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:
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 marker trait scala.Dynamic
. Subclasses of this trait are able to intercept selections and applications on their instances by defining methods of the names applyDynamic
, applyDynamicNamed
, selectDynamic
, and updateDynamic
.
The following rewrites are performed, assuming ´e´'s type conforms to scala.Dynamic
, and the original expression does not type check under the normal rules, as specified fully in the relevant subsection of implicit conversion:

e.m[Ti](xi)
becomese.applyDynamic[Ti]("m")(xi)

e.m[Ti]
becomese.selectDynamic[Ti]("m")

e.m = x
becomese.updateDynamic("m")(x)
If any arguments are named in the application (one of the xi
is of the shape arg = x
), their name is preserved as the first component of the pair passed to applyDynamicNamed
(for missing names, ""
is used):

e.m[Ti](argi = xi)
becomese.applyDynamicNamed[Ti]("m")(("argi", xi))
Finally:

e.m(x) = y
becomese.selectDynamic("m").update(x, y)
None of these methods are actually defined in the scala.Dynamic
, so that users are free to define them with or without type parameters, or implicit arguments.