6.11.1. Explicit universal quantification (forall)
- ExplicitForAll
- Since:
- 6.12.1 
 - Allow use of the - forallkeyword 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 - forallin 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-forallsflag is enabled, a warning will be emitted when you write a type variable in an explicit- forallstatement 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- forallis 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- forallis 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:
- Type signature declarations for functions, values, and class methods 
- Expression type annotations 
- Instance declarations 
- Type signatures in a SPECIALIZE pragma or SPECIALIZE instance pragma 
- Type signatures for Generalised Algebraic Data Types (GADTs) constructors 
- Type signatures for Pattern synonyms 
- Data instance declarations, Type instance declarations, Closed type families, and Associated instances 
- Rewrite rules in which the type variables are explicitly quantified 
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 - forallin the type of- MkT, the- bwould 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.