category-theory-presentation/categories/30_How/040_Haskell_Types.md

Haskell Types

Sometimes, the type determine a lot about the function^★:

fst :: (a,b) -> a -- Only one choice
snd :: (a,b) -> b -- Only one choice
f :: a -> [a]     -- Many choices
-- Possibilities: f x=[], or [x], or [x,x] or [x,...,x]

? :: [a] -> [a] -- Many choices
-- can only rearrange: duplicate/remove/reorder elements
-- for example: the type of addOne isn't [a] -> [a]
addOne l = map (+1) l
-- The (+1) force 'a' to be a Num.

★:Theorems for free!, Philip Wadler, 1989