Haskell 98 allows expressions to be annotated with type signatures.
With the -98 option,
these annotations are also allowed on patterns:
f (x::Int) = fromIntegral x :: Double |
Moreover type variables in pattern annotations are treated specially:
unless the type variable is already bound (by another pattern annotation),
it is universally quantified over the pattern and its scope, e.g.
snoc (xs::[a]) (x::a) = xs++[x] :: [a] |
Occurrences of the type variable in type signatures within this scope
are bound to this type variable.
In the above example the second and third occurrences of
a
are bound by the first.
This permits locally defined variables to be given signatures in situations
where it would be impossible in Haskell 98:
sortImage :: Ord b => (a -> b) -> [a] -> [a]
sortImage (f::a->b) = sortBy cmp
where
cmp :: a -> a -> Ordering
cmp x y = compare (f x) (f y) |
Note that the relationship between signature declarations and pattern
annotations is asymmetrical: pattern annotations may capture type variables
in signature declarations, but not vice versa.
There is no connection between the type variables in the type signature
of
sortImage and those in its definition,
but the occurrence of
a in the signature of
cmp is bound by the pattern
(f::a->b).
In GHC, type variables bound by pattern annotations are existentially
quantified, and so may be instantiated.
Thus the following is accepted by GHC but not Hugs:
GHC also allows
result type signatures,
where a type signature is attached to the left side of a function definition,
but Hugs does not.