A *pattern type signature* can introduce a *scoped type
variable*. For example

f (xs::[a]) = ys ++ ys where ys :: [a] ys = reverse xs |

The pattern `(xs::[a])` includes a type signature for `xs`.
This brings the type variable `a` into scope; it scopes over
all the patterns and right hand sides for this equation for `f`.
In particular, it is in scope at the type signature for `y`.

At ordinary type signatures, such as that for `ys`, any type variables
mentioned in the type signature *that are not in scope* are
implicitly universally quantified. (If there are no type variables in
scope, all type variables mentioned in the signature are universally
quantified, which is just as in Haskell 98.) In this case, since `a`
is in scope, it is not universally quantified, so the type of `ys` is
the same as that of `xs`. In Haskell 98 it is not possible to declare
a type for `ys`; a major benefit of scoped type variables is that
it becomes possible to do so.

Scoped type variables are implemented in both GHC and Hugs. Where the implementations differ from the specification below, those differences are noted.

So much for the basic idea. Here are the details.

All the type variables mentioned in the patterns for a single function definition equation, that are not already in scope, are brought into scope by the patterns. We describe this set as the

*type variables bound by the equation*.The type variables thus brought into scope may be mentioned in ordinary type signatures or pattern type signatures anywhere within their scope.

In ordinary type signatures, any type variable mentioned in the signature that is in scope is

*not*universally quantified.Ordinary type signatures do not bring any new type variables into scope (except in the type signature itself!). So this is illegal:

It's illegal becausef :: a -> a f x = x::a

`a`is not in scope in the body of`f`, so the ordinary signature`x::a`is equivalent to`x::forall a.a`; and that is an incorrect typing.There is no implicit universal quantification on pattern type signatures, nor may one write an explicit

`forall`type in a pattern type signature. The pattern type signature is a monotype.The type variables in the head of a

`class`or`instance`declaration scope over the methods defined in the`where`part. For example:

(Not implemented in Hugs yet, Dec 98).class C a where op :: [a] -> a op xs = let ys::[a] ys = reverse xs in head ys

Pattern type signatures are completely orthogonal to ordinary, separate type signatures. The two can be used independently or together. There is no scoping associated with the names of the type variables in a separate type signature.

f :: [a] -> [a] f (xs::[b]) = reverse xs

The function must be polymorphic in the type variables bound by all its equations. Operationally, the type variables bound by one equation must not:

Be unified with a type (such as

`Int`, or`[a]`).Be unified with a type variable free in the environment.

Be unified with each other. (They may unify with the type variables bound by another equation for the same function, of course.)

f (x::a) (y::b) = [x,y] -- a unifies with b g (x::a) = x + 1::Int -- a unifies with Int h x = let k (y::a) = [x,y] -- a is free in the in k x -- environment k (x::a) True = ... -- a unifies with Int k (x::Int) False = ... w :: [b] -> [b] w (x::a) = x -- a unifies with [b]

The pattern-bound type variable may, however, be constrained by the context of the principal type, thus:

gets the inferred type:f (x::a) (y::a) = x+y*2

`forall a. Num a => a -> a -> a`.

The result type of a function can be given a signature, thus:

The finalf (x::a) :: [a] = [x,x,x]

`:: [a]`after all the patterns gives a signature to the result type. Sometimes this is the only way of naming the type variable you want:f :: Int -> [a] -> [a] f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x) in \xs -> map g (reverse xs `zip` xs)

Result type signatures are not yet implemented in Hugs.

A pattern type signature can be on an arbitrary sub-pattern, not just on a variable:

f ((x,y)::(a,b)) = (y,x) :: (b,a)

Pattern type signatures, including the result part, can be used in lambda abstractions:

Type variables bound by these patterns must be polymorphic in the sense defined above. For example:(\ (x::a, y) :: a -> x)

Here,f1 (x::c) = f1 x -- ok f2 = \(x::c) -> f2 x -- not ok

`f1`is OK, but`f2`is not, because`c`gets unified with a type variable free in the environment, in this case, the type of`f2`, which is in the environment when the lambda abstraction is checked.Pattern type signatures, including the result part, can be used in

`case`expressions:

The pattern-bound type variables must, as usual, be polymorphic in the following sense: each case alternative, considered as a lambda abstraction, must be polymorphic. Thus this is OK:case e of { (x::a, y) :: a -> x }

Even though the context is that of a pair of booleans, the alternative itself is polymorphic. Of course, it is also OK to say:case (True,False) of { (x::a, y) -> x }

case (True,False) of { (x::Bool, y) -> x }

To avoid ambiguity, the type after the “

`::`” in a result pattern signature on a lambda or`case`must be atomic (i.e. a single token or a parenthesised type of some sort). To see why, consider how one would parse this:\ x :: a -> b -> x

Pattern type signatures that bind new type variables may not be used in pattern bindings at all. So this is illegal:

But these are OK, because they do not bind fresh type variables:f x = let (y, z::a) = x in ...

However a single variable is considered a degenerate function binding, rather than a degerate pattern binding, so this is permitted, even though it binds a type variable:f1 x = let (y, z::Int) = x in ... f2 (x::(Int,a)) = let (y, z::a) = x in ...

f :: (b->b) = \(x::b) -> x

g :: a -> a -> Bool = \x y. x==y |

Here `g` has type `forall a. Eq a => a -> a -> Bool`, just as if
`g` had a separate type signature. Lacking a type signature, `g`
would get a monomorphic type.

Pattern type signatures can bind existential type variables. For example:

data T = forall a. MkT [a] f :: T -> T f (MkT [t::a]) = MkT t3 where t3::[a] = [t,t,t]