6.11.1. Explicit universal quantification (forall)

ExplicitForAll
Implied by:

ScopedTypeVariables, LiberalTypeSynonyms, RankNTypes, ExistentialQuantification

Since:

6.12.1

Status:

Included in GHC2021

Allow use of the forall keyword in places where universal quantification is implicit.

Haskell type signatures are implicitly quantified. When the language option ExplicitForAll is used, the keyword forall allows us to say exactly what this means. For example:

g :: b -> b

means this:

g :: forall b. (b -> b)

The two are treated identically, except that the latter may bring type variables into scope (see Lexically scoped type variables).

This extension also enables explicit quantification of type and kind variables in Data instance declarations, Type instance declarations, Closed type families, Associated instances, and Rewrite rules.

Notes:

  • As well as in type signatures, you can also use an explicit forall in an instance declaration:

    instance forall a. Eq a => Eq [a] where ...

    Note that the use of foralls in instance declarations is somewhat restricted in comparison to other types. For example, instance declarations are not allowed to contain nested foralls. See Formal syntax for instance declaration types for more information.

  • If the -Wunused-foralls flag is enabled, a warning will be emitted when you write a type variable in an explicit forall statement that is otherwise unused. For instance:

    g :: forall a b. (b -> b)

    would warn about the unused type variable a.

6.11.1.1. The forall-or-nothing rule

In certain forms of types, type variables obey what is known as the “forall-or-nothing” rule: if a type has an outermost, explicit, invisible forall, then all of the type variables in the type must be explicitly quantified. These two examples illustrate how the rule works:

f  :: forall a b. a -> b -> b         -- OK, `a` and `b` are explicitly bound
g  :: forall a. a -> forall b. b -> b -- OK, `a` and `b` are explicitly bound
h  :: forall a. a -> b -> b           -- Rejected, `b` is not in scope

The type signatures for f, g, and h all begin with an outermost invisible forall, so every type variable in these signatures must be explicitly bound by a forall. Both f and g obey the forall-or-nothing rule, since they explicitly quantify a and b. On the other hand, h does not explicitly quantify b, so GHC will reject its type signature for being improperly scoped.

In places where the forall-or-nothing rule takes effect, if a type does not have an outermost invisible forall, then any type variables that are not explicitly bound by a forall become implicitly quantified. For example:

i :: a -> b -> b             -- `a` and `b` are implicitly quantified
j :: a -> forall b. b -> b   -- `a` is implicitly quantified
k :: (forall a. a -> b -> b) -- `b` is implicitly quantified
type L :: forall a -> b -> b -- `b` is implicitly quantified

GHC will accept i, j, and k’s type signatures, as well as L’s kind signature. Note that:

  • j’s signature is accepted despite its mixture of implicit and explicit quantification. As long as a forall is not an outermost one, it is fine to use it among implicitly bound type variables.

  • k’s signature is accepted because the outermost parentheses imply that the forall is not an outermost forall. The forall-or-nothing rule is one of the few places in GHC where the presence or absence of parentheses can be semantically significant!

  • L’s signature begins with an outermost forall, but it is a visible forall, not an invisible forall, and therefore does not trigger the forall-or-nothing rule.

The forall-or-nothing rule takes effect in the following places:

Notes:

  • Pattern type signatures are a notable example of a place where types do not obey the forall-or-nothing rule. For example, GHC will accept the following:

    f (g :: forall a. a -> b) x = g x :: b

    Furthermore, Rewrite rules do not obey the forall-or-nothing rule when their type variables are not explicitly quantified:

    {-# RULES "f" forall (g :: forall a. a -> b) x. f g x = g x :: b #-}

  • GADT constructors are extra particular about their foralls. In addition to adhering to the forall-or-nothing rule, GADT constructors also forbid nested foralls. For example, GHC would reject the following GADT:

    data T where
  MkT :: (forall a. a -> b -> T)

    Because of the lack of an outermost forall in the type of MkT, the b would be implicitly quantified. In effect, it would be as if one had written MkT :: forall b. (forall a. a -> b -> T), which contains nested foralls. See Formal syntax for GADTs.