---
title: Basic Declarations & Definitions
layout: default
chapter: 4
---

# Basic Declarations and Definitions

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

A _declaration_ introduces names and assigns them types. It can
form part of a [class definition](05-classes-and-objects.html#templates) or of a
refinement in a [compound type](03-types.html#compound-types).

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

The scope of a name introduced by a declaration or definition is the
whole statement sequence containing the binding.  However, there is a
restriction on forward references in blocks: In a statement sequence
$s_1 \ldots s_n$ making up a block, if a simple name in $s_i$ refers
to an entity defined by $s_j$ where $j \geq i$, then for all $s_k$
between and including $s_i$ and $s_j$,

- $s_k$ cannot be a variable definition.
- If $s_k$ is a value definition, it must be lazy.

<!--
Every basic definition may introduce several defined names, separated
by commas. These are expanded according to the following scheme:
\bda{lcl}
\VAL;x, y: T = e && \VAL; x: T = e \\
                 && \VAL; y: T = x \\[0.5em]

\LET;x, y: T = e && \LET; x: T = e \\
                 && \VAL; y: T = x \\[0.5em]

\DEF;x, y (ps): T = e &\tab\mbox{expands to}\tab& \DEF; x(ps): T = e \\
                      && \DEF; y(ps): T = x(ps)\\[0.5em]

\VAR;x, y: T := e && \VAR;x: T := e\\
                  && \VAR;y: T := x\\[0.5em]

\TYPE;t,u = T && \TYPE; t = T\\
              && \TYPE; u = t\\[0.5em]
\eda

All definitions have a ``repeated form`` where the initial
definition keyword is followed by several constituent definitions
which are separated by commas.  A repeated definition is
always interpreted as a sequence formed from the
constituent definitions. E.g. the function definition
`def f(x) = x, g(y) = y` expands to
`def f(x) = x; def g(y) = y` and
the type definition
`type T, U <: B` expands to
`type T; type U <: B`.
}
\comment{
If an element in such a sequence introduces only the defined name,
possibly with some type or value parameters, but leaves out any
additional parts in the definition, then those parts are implicitly
copied from the next subsequent sequence element which consists of
more than just a defined name and parameters. Examples:

- []
The variable declaration `var x, y: Int`
expands to `var x: Int; var y: Int`.
- []
The value definition `val x, y: Int = 1`
expands to `val x: Int = 1; val y: Int = 1`.
- []
The class definition `case class X(), Y(n: Int) extends Z` expands to
`case class X extends Z; case class Y(n: Int) extends Z`.
- The object definition `case object Red, Green, Blue extends Color`~
expands to
```
case object Red extends Color
case object Green extends Color
case object Blue extends Color .
```
-->

## Value Declarations and Definitions

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

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

A value definition `val $x$: $T$ = $e$` defines $x$ as a
name of the value that results from the evaluation of $e$.
If the value definition is not recursive, the type
$T$ may be omitted, in which case the [packed type](06-expressions.html#expression-typing) of
expression $e$ is assumed.  If a type $T$ is given, then $e$ is expected to
conform to it.

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

A _constant value definition_ is of the form

```scala
final val x = e
```

where `e` is a [constant expression](06-expressions.html#constant-expressions).
The `final` modifier must be
present and no type annotation may be given. References to the
constant value `x` are themselves treated as constant expressions; in the
generated code they are replaced by the definition's right-hand side `e`.

Value definitions can alternatively have a [pattern](08-pattern-matching.html#patterns)
as left-hand side.  If $p$ is some pattern other
than a simple name or a name followed by a colon and a type, then the
value definition `val $p$ = $e$` is expanded as follows:

1. If the pattern $p$ has bound variables $x_1 , \ldots , x_n$, where $n > 1$:

```scala
val $\$ x$ = $e$ match {case $p$ => ($x_1 , \ldots , x_n$)}
val $x_1$ = $\$ x$._1
$\ldots$
val $x_n$ = $\$ x$._n  .
```

Here, $\$ x$ is a fresh name.

2. If $p$ has a unique bound variable $x$:

```scala
val $x$ = $e$ match { case $p$ => $x$ }
```

3. If $p$ has no bound variables:

```scala
$e$ match { case $p$ => ()}
```

###### Example

The following are examples of value definitions

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

The last two definitions have the following expansions.

```scala
val x = f() match { case Some(x) => x }

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

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

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

## Variable Declarations and Definitions

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

A variable declaration `var $x$: $T$` is equivalent to the declarations
of both a _getter function_ $x$ *and* a _setter function_ `$x$_=`:

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

An implementation of a class may _define_ a declared variable
using a variable definition, or by defining the corresponding setter and getter methods.

A variable definition `var $x$: $T$ = $e$` introduces a
mutable variable with type $T$ and initial value as given by the
expression $e$. The type $T$ can be omitted, in which case the type of
$e$ is assumed. If $T$ is given, then $e$ is expected to
[conform to it](06-expressions.html#expression-typing).

Variable definitions can alternatively have a [pattern](08-pattern-matching.html#patterns)
as left-hand side.  A variable definition
 `var $p$ = $e$` where $p$ is a pattern other
than a simple name or a name followed by a colon and a type is expanded in the same way
as a [value definition](#value-declarations-and-definitions)
`val $p$ = $e$`, except that
the free names in $p$ are introduced as mutable variables, not values.

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

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

| default  | type $T$                           |
|----------|------------------------------------|
|`0`       | `Int` or one of its subrange types |
|`0L`      | `Long`                             |
|`0.0f`    | `Float`                            |
|`0.0d`    | `Double`                           |
|`false`   | `Boolean`                          |
|`()`      | `Unit`                             |
|`null`    | all other types                    |

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

###### Example

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

```scala
class TimeOfDayVar {
  private var h: Int = 0
  private var m: Int = 0
  private var s: Int = 0

  def hours              =  h
  def hours_= (h: Int)   =  if (0 <= h && h < 24) this.h = h
                            else throw new DateError()

  def minutes            =  m
  def minutes_= (m: Int) =  if (0 <= m && m < 60) this.m = m
                            else throw new DateError()

  def seconds            =  s
  def seconds_= (s: Int) =  if (0 <= s && s < 60) this.s = s
                            else throw new DateError()
}
val d = new TimeOfDayVar
d.hours = 8; d.minutes = 30; d.seconds = 0
d.hours = 25                  // throws a DateError exception
```

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

## Type Declarations and Type Aliases

<!-- TODO: Higher-kinded tdecls should have a separate section -->

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

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

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

A type constructor declaration imposes additional restrictions on the
concrete types for which $t$ may stand. Besides the bounds $L$ and
$U$, the type parameter clause may impose higher-order bounds and
variances, as governed by the [conformance of type constructors](03-types.html#conformance).

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

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

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

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

###### Example

The following are legal type declarations and definitions:

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

The following are illegal:

```scala
type Abs = Comparable[Abs]      // recursive type alias

type S <: T                     // S, T are bounded by themselves.
type T <: S

type T >: Comparable[T.That]    // Cannot select from T.
                                // T is a type, not a value
type MyCollection <: Iterable   // Type constructor members must explicitly
                                // state their type parameters.
```

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

###### Example

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

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

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

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

## Type Parameters

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

Type parameters appear in type definitions, class definitions, and
function definitions.  In this section we consider only type parameter
definitions with lower bounds `>: $L$` and upper bounds
`<: $U$` whereas a discussion of context bounds
`: $U$` and view bounds `<% $U$`
is deferred to [here](07-implicit-parameters-and-views.html#context-bounds-and-view-bounds).

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

<!--
The upper bound $U$ in a type parameter clauses may not be a final
class. The lower bound may not denote a value type.

TODO: Why
-->

<!--
TODO: this is a pretty awkward description of scoping and distinctness of binders
-->

The names of all type parameters must be pairwise different in their enclosing type parameter clause.  The scope of a type parameter includes in each case the whole type parameter clause. Therefore it is possible that a type parameter appears as part of its own bounds or the bounds of other type parameters in the same clause.  However, a type parameter may not be bounded directly or indirectly by itself.

A type constructor parameter adds a nested type parameter clause to the type parameter. The most general form of a type constructor parameter is `$@a_1\ldots@a_n$ $\pm$ $t[\mathit{tps}\,]$ >: $L$ <: $U$`.

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

###### Example
Here are some well-formed type parameter clauses:

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

The following type parameter clauses are illegal:

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

## Variance Annotations

Variance annotations indicate how instances of parameterized types
vary with respect to [subtyping](03-types.html#conformance).  A
‘+’ variance indicates a covariant dependency, a
‘-’ variance indicates a contravariant dependency, and a
missing variance indication indicates an invariant dependency.

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

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

- The variance position of a method parameter is the opposite of the
  variance position of the enclosing parameter clause.
- The variance position of a type parameter is the opposite of the
  variance position of the enclosing type parameter clause.
- The variance position of the lower bound of a type declaration or type parameter
  is the opposite of the variance position of the type declaration or parameter.
- The type of a mutable variable is always in invariant position.
- The right-hand side of a type alias is always in invariant position.
- The prefix $S$ of a type selection `$S$#$T$` is always in invariant position.
- For a type argument $T$ of a type `$S$[$\ldots T \ldots$ ]`: If the
  corresponding type parameter is invariant, then $T$ is in
  invariant position.  If the corresponding type parameter is
  contravariant, the variance position of $T$ is the opposite of
  the variance position of the enclosing type `$S$[$\ldots T \ldots$ ]`.

<!-- TODO: handle type aliases -->

References to the type parameters in
[object-private or object-protected values, types, variables, or methods](05-classes-and-objects.html#modifiers) of the class are not
checked for their variance position. In these members the type parameter may
appear anywhere without restricting its legal variance annotations.

###### Example
The following variance annotation is legal.

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

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

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

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

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

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

```scala
abstract class R[+A, +B](x: A, y: B) {
  private[this] var fst: A = x        // OK
  private[this] var snd: B = y        // OK
}
```

###### Example

The following variance annotation is illegal, since $a$ appears
in contravariant position in the parameter of `append`:

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

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

```scala
abstract class Sequence[+A] {
  def append[B >: A](x: Sequence[B]): Sequence[B]
}
```

###### Example

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

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

## Function Declarations and Definitions

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

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

The type of the function body is expected to [conform](06-expressions.html#expression-typing)
to the function's declared
result type, if one is given. If the function definition is not
recursive, the result type may be omitted, in which case it is
determined from the packed type of the function body.

A type parameter clause $\mathit{tps}$ consists of one or more
[type declarations](#type-declarations-and-type-aliases), which introduce type
parameters, possibly with bounds.  The scope of a type parameter includes
the whole signature, including any of the type parameter bounds as
well as the function body, if it is present.

A value parameter clause $\mathit{ps}$ consists of zero or more formal
parameter bindings such as `$x$: $T$` or `$x: T = e$`, which bind value
parameters and associate them with their types.

### Default Arguments

Each value parameter
declaration may optionally define a default argument. The default argument
expression $e$ is type-checked with an expected type $T'$ obtained
by replacing all occurrences of the function's type parameters in $T$ by
the undefined type.

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

###### Example
In the method

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

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

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

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

A default value which depends on earlier parameters uses the actual arguments
if they are provided, not the default arguments.

```scala
def f(a: Int = 0)(b: Int = a + 1) = b // OK
// def f(a: Int = 0, b: Int = a + 1)  // "error: not found: value a"
f(10)()                               // returns 11 (not 1)
```

### By-Name Parameters

```ebnf
ParamType          ::=  ‘=>’ Type
```

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

The by-name modifier is disallowed for parameters of classes that
carry a `val` or `var` prefix, including parameters of case
classes for which a `val` prefix is implicitly generated. The
by-name modifier is also disallowed for
[implicit parameters](07-implicit-parameters-and-views.html#implicit-parameters).

###### Example
The declaration

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

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

### Repeated Parameters

```ebnf
ParamType          ::=  Type ‘*’
```

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

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

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

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

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

```scala
sum()
sum(1)
sum(1, 2, 3)
```

Furthermore, assume the definition:

```scala
val xs = List(1, 2, 3)
```

The following application of method `sum` is ill-formed:

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

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

```scala
sum(xs: _*)
```

### Procedures

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

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

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

###### Example
Here is a declaration and a definition of a procedure named `write`:

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

The code above is implicitly completed to the following code:

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

### Method Return Type Inference

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

###### Example
Assume the following definitions:

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

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

<!-- ## Overloaded Definitions
\label{sec:overloaded-defs}
\todo{change}

An overloaded definition is a set of $n > 1$ value or function
definitions in the same statement sequence that define the same name,
binding it to types `$T_1 \commadots T_n$`, respectively.
The individual definitions are called _alternatives_.  Overloaded
definitions may only appear in the statement sequence of a template.
Alternatives always need to specify the type of the defined entity
completely.  It is an error if the types of two alternatives $T_i$ and
$T_j$ have the same erasure (\sref{sec:erasure}).

\todo{Say something about bridge methods.}
%This must be a well-formed
%overloaded type -->

## Import Clauses

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

An import clause has the form `import $p$.$I$` where $p$ is a
[stable identifier](03-types.html#paths) and $I$ is an import expression.
The import expression determines a set of names of importable members of $p$
which are made available without qualification.  A member $m$ of $p$ is
_importable_ if it is not [object-private](05-classes-and-objects.html#modifiers).
The most general form of an import expression is a list of _import selectors_

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

for $n \geq 0$, where the final wildcard `‘_’` may be absent.  It
makes available each importable member `$p$.$x_i$` under the unqualified name
$y_i$. I.e. every import selector `$x_i$ => $y_i$` renames
`$p$.$x_i$` to
$y_i$.  If a final wildcard is present, all importable members $z$ of
$p$ other than `$x_1 , \ldots , x_n,y_1 , \ldots , y_n$` are also made available
under their own unqualified names.

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

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

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

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

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

###### Example
Consider the object definition:

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

Then the block

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

is equivalent to the block

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