src/Symantic/Dityped/Composable.hs

   1 module Symantic.Dityped.Composable where
   2
   3 import Symantic.Dityped.Transformable
   4
   5 -- * Class 'Composable'
   6 class Composable repr where
   7   (<.>) :: repr a b -> repr b c -> repr a c
   8   (<.>) = lift2 (<.>)
   9   default (<.>) ::
  10     Liftable2 repr => Composable (Unlifted repr) =>
  11     repr a b -> repr b c -> repr a c
  12 infixr 4 <.>
  13
  14 -- * Class 'Voidable'
  15 class Voidable repr where
  16   default void :: Liftable1 repr => Voidable (Unlifted repr) =>
  17           a -> repr (a -> b) k -> repr b k
  18   void :: a -> repr (a -> b) k -> repr b k
  19   void a = lift1 (void a)
  20
  21 -- ** Type 'IdentityTrans'
  22 -- | A 'Transformable' that does nothing.
  23 newtype IdentityTrans repr a k
  24  =      IdentityTrans
  25  {    unIdentityTrans :: repr a k }
  26 type instance Unlifted (IdentityTrans repr) = repr
  27 instance Transformable (IdentityTrans repr) repr where
  28   trans = unIdentityTrans
  29 instance Transformable repr (IdentityTrans repr) where
  30   trans = IdentityTrans
  31
  32 -- * Class 'Dimapable'
  33 class Dimapable repr where
  34   dimap :: (a->b) -> (b->a) -> repr (a->k) k -> repr (b->k) k
  35   dimap a2b b2a = lift1 (dimap a2b b2a)
  36   default dimap :: Liftable1 repr => Dimapable (Unlifted repr) =>
  37            (a->b) -> (b->a) -> repr (a->k) k -> repr (b->k) k