map :: (a -> b) -> [a] -> [b]
map takes a function and transforms a list of a's to b's.
map succ [1,2,3]
==> [succ 1, succ 2, succ 3]
==> [2, 3, 4]
In general,
map f :: [a] -> [b]
where a is domain-type of f and b is image-type of f (f :: a -> b).
map map [x, y, z]
==> [map x, map y, map z]
so, x,y,z should functions of type (a -> b).
and the result list, [map x, map y, map z], should have type [([a] -> [b])]
because
map x :: [a] -> [b] where x :: a -> b
On 3/6/09, R J
Given the following (usual) definition of "map":
map :: (a -> b) -> [a] -> [b] map f [] = [] map f (x : xs) = f x : map f xs
What's the type of "map map"?
GHCi's :t command reveals:
*Main> :t map map map map :: [a -> b] -> [[a] -> [b]]
I'd be grateful if anyone could provide a systematic type calculation so that I can reason through more complicated examples myself.
Thanks.
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