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Hint: if you're just looking for an introduction to partible types, see Plainly partible.

The Partible class

Partible types have an common (and austere) programming interface, this being captured by the Partible class:

module Partible where

class Partible a where
    part :: a -> (a, a)
    parts :: a -> [a]

     -- Minimal complete definition: part or parts --
    part u = case parts u of u1:u2:_ -> (u1, u2)
    parts u = case part u of (u1, u2) -> u1 : parts u2

In addition to implementing the methods of the class, partible types should satisfy certain equations; for an explanation of them along with why they should be satisfied, see Partible laws.