src/Symantic/Base/Univariant.hs

   1 {-# LANGUAGE DefaultSignatures #-}
   2 module Symantic.Base.Univariant where
   3
   4 -- TODO: move to symantic-base
   5
   6 import Data.Function ((.))
   7
   8 -- * Type family 'Unlift'
   9 type family Unlift (repr :: * -> *) :: * -> *
  10
  11 -- * Class 'Unliftable'
  12 class Unliftable repr where
  13   unlift :: repr a -> Unlift repr a
  14
  15 -- * Class 'Liftable'
  16 class Liftable repr where
  17   lift :: Unlift repr a -> repr a
  18   lift1 :: (Unlift repr a -> Unlift repr b) ->
  19            repr a -> repr b
  20   lift2 :: (Unlift repr a -> Unlift repr b -> Unlift repr c) ->
  21            repr a -> repr b -> repr c
  22   lift3 :: (Unlift repr a -> Unlift repr b -> Unlift repr c -> Unlift repr d) ->
  23            repr a -> repr b -> repr c -> repr d
  24   default lift1 ::
  25            Unliftable repr =>
  26            (Unlift repr a -> Unlift repr b) ->
  27            repr a -> repr b
  28   default lift2 ::
  29            Unliftable repr =>
  30            (Unlift repr a -> Unlift repr b -> Unlift repr c) ->
  31            repr a -> repr b -> repr c
  32   default lift3 ::
  33            Unliftable repr =>
  34            (Unlift repr a -> Unlift repr b -> Unlift repr c -> Unlift repr d) ->
  35            repr a -> repr b -> repr c -> repr d
  36   lift1 f = lift . f . unlift
  37   lift2 f a b = lift (f (unlift a) (unlift b))
  38   lift3 f a b c = lift (f (unlift a) (unlift b) (unlift c))
  39   {-# INLINE lift1 #-}
  40   {-# INLINE lift2 #-}
  41   {-# INLINE lift3 #-}
  42
  43 -- * Class 'Symantic'
  44 class Symantic from to where
  45   sym :: from a -> to a