The map function changes each element of a list while preserving its order and length. List concatenation removes one level of nesting. Currying changes a function on a pair into a function taking its two arguments separately; uncurrying reverses this conversion:
map :: (a -> b) -> [a] -> [b]
map f []     = []
map f (x:xs) = f x : map f xs

concat :: [[a]] -> [a]
concat []       = []
concat (xs:xss) = xs ++ concat xss

curry :: ((a, b) -> c) -> a -> b -> c
curry f x y = f (x, y)

uncurry :: (a -> b -> c) -> (a, b) -> c
uncurry f (x, y) = f x y
These polymorphic type signatures impose no numerical, equality or ordering constraints: the definitions only inspect list or pair structure and apply a supplied function. In particular,
(1)
The recursive equations describe the two possible list constructors, so they also explain how the empty case terminates each finite computation.

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