-{-# OPTIONS_GHC -XModalTypes -XScopedTypeVariables -XFlexibleContexts -XMultiParamTypeClasses -ddump-types -XNoMonoPatBinds -XFlexibleInstances -XGADTs #-}
+{-# OPTIONS_GHC -XModalTypes -XScopedTypeVariables -XFlexibleContexts -XMultiParamTypeClasses -ddump-types -XNoMonoPatBinds -XFlexibleInstances -XGADTs -XUndecidableInstances #-}
module GArrowsTutorial
where
import Data.Bits
--------------------------------------------------------------------------------
-- BiGArrows
-class GArrow g (**) => BiGArrow g (**) where
+class GArrow g (**) u => BiGArrow g (**) u where
-- Note that we trust the user's pair of functions actually are
-- mutually inverse; confirming this in the type system would
-- require very powerful dependent types (such as Coq's). However,
biga_inv :: g x y -> g y x
-- For any GArrow instance, its mutually inverse pairs form a BiGArrow
-data GArrow g (**) => GArrowInversePair g (**) x y =
+data GArrow g (**) u => GArrowInversePair g (**) u x y =
GArrowInversePair { forward :: g x y , backward :: g y x }
-instance GArrow g (**) => Category (GArrowInversePair g (**)) where
+instance GArrow g (**) u => Category (GArrowInversePair g (**) u) where
id = GArrowInversePair { forward = id , backward = id }
f . g = GArrowInversePair { forward = (forward f) . (forward g) , backward = (backward g) . (backward f) }
-instance GArrow g (**) => GArrow (GArrowInversePair g (**)) (**) where
+instance GArrow g (**) u => GArrow (GArrowInversePair g (**) u) (**) u where
ga_first f = GArrowInversePair { forward = ga_first (forward f), backward = ga_first (backward f) }
ga_second f = GArrowInversePair { forward = ga_second (forward f), backward = ga_second (backward f) }
ga_cancell = GArrowInversePair { forward = ga_cancell , backward = ga_uncancell }
ga_uncancelr = GArrowInversePair { forward = ga_uncancelr , backward = ga_cancelr }
ga_assoc = GArrowInversePair { forward = ga_assoc , backward = ga_unassoc }
ga_unassoc = GArrowInversePair { forward = ga_unassoc , backward = ga_assoc }
-instance GArrowSwap g (**) => GArrowSwap (GArrowInversePair g (**)) (**) where
+instance GArrowSwap g (**) u => GArrowSwap (GArrowInversePair g (**) u) (**) u where
ga_swap = GArrowInversePair { forward = ga_swap , backward = ga_swap }
-instance (GArrowDrop g (**), GArrowCopy g (**)) => GArrowCopy (GArrowInversePair g (**)) (**) where
+{-
+instance (GArrowDrop g (**) u, GArrowCopy g (**) u) => GArrowCopy (GArrowInversePair g (**) u) (**) u where
ga_copy = GArrowInversePair { forward = ga_copy , backward = ga_second ga_drop >>> ga_cancelr }
+-}
-- but notice that we can't (in general) get
-- instance GArrowDrop g => GArrowDrop (GArrowInversePair g) where ...