inj

A class for injective (one-to-one) functions.

An injection is a function that never maps distinct elements of the domain to the same element of the codomain. For example, \x -> x + 1 is an injection, but \x -> min x 0 is not.

class Inj p a where
  inj :: p -> a

The instances compose, so inj can construct nested structures from singleton elements, wrapping and converting as needed:

ghci> inj 'a' :: Maybe [Char]
Just "a"

ghci> inj True :: Maybe [Bool]
Just [True]

ghci> inj (5 :: Int) :: Maybe Double
Just 5.0

ghci> inj [1, 2, 3 :: Int] :: [Double]
[1.0,2.0,3.0]

ghci> inj (True, 2 :: Int) :: (Maybe Bool, [Double])
(Just True,[2.0])

By convention, the instances of Inj never match on p and always match on a. This guarantees that users will not encounter overlapping instances.

Instances for base types are provided by this package. Before version 2.0 they lived in a separate inj-base package; see the changelog for migration notes.