# Implicits

## The Implicit Modifier

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


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

###### Example Monoid

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

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


## Implicit Parameters

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

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

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

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

The parts of a type $T$ are:

• if $T$ is a compound type $T_1$ with $\ldots$ with $T_n$, the union of the parts of $T_1 , \ldots , T_n$, as well as $T$ itself;
• if $T$ is a parameterized type $S$[$T_1 , \ldots , T_n$], the union of the parts of $S$ and $T_1 , \ldots , T_n$;
• if $T$ is a singleton type $p$.type, the parts of the type of $p$;
• if $T$ is a type projection $S$#$U$, the parts of $S$ as well as $T$ itself;
• if $T$ is a type alias, the parts of its expansion;
• if $T$ is an abstract type, the parts of its upper bound;
• if $T$ denotes an implicit conversion to a type with a method with argument types $T_1 , \ldots , T_n$ and result type $U$, the union of the parts of $T_1 , \ldots , T_n$ and $U$;
• the parts of quantified (existential or universal) and annotated types are defined as the parts of the underlying types (e.g., the parts of T forSome { ... } are the parts of T);
• in all other cases, just $T$ itself.

Note that packages are internally represented as classes with companion modules to hold the package members. Thus, implicits defined in a package object are part of the implicit scope of a type prefixed by that package.

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

###### Example

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

def sum[A](xs: List[A])(implicit m: Monoid[A]): A =
if (xs.isEmpty) m.unit


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

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

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

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


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


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

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


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

sort(yss)


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

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


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

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


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

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


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

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

The set of top-level type constructors $\mathit{ttcs}(T)$ of a type $T$ depends on the form of the type:

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

The complexity $\operatorname{complexity}(T)$ of a core type is an integer which also depends on the form of the type:

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

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

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


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

###### Example

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

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


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

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


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

## Views

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

Views are applied in three situations:

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

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

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

###### Example Ordered

Class scala.Ordered[A] contains a method

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


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

  xs <= ys


is legal, and is expanded to:

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


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

## Context Bounds and View Bounds

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


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

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

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

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


Then the method definition above is expanded to

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


where the $v_i$ and $w_j$ are fresh names for the newly introduced implicit parameters. These parameters are called evidence parameters.

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

Evidence parameters are prepended to the existing implicit parameter section, if one exists.

For example:

def foo[A: M](implicit b: B): C
// expands to: