-{-# OPTIONS -XRankNTypes -XMultiParamTypeClasses -XNoMonomorphismRestriction -XTypeOperators -XFlexibleInstances #-}
+{-# OPTIONS -XRankNTypes -XMultiParamTypeClasses -XNoMonomorphismRestriction -XTypeOperators -XFlexibleInstances -XFunctionalDependencies #-}
-----------------------------------------------------------------------------
-- |
-- Module : GHC.HetMet.GArrow
GArrowDrop(..),
GArrowCopy(..),
GArrowSwap(..),
+
GArrowLoop(..),
+
+ GArrowEval(..),
+ GArrowConstant(..),
+ GArrowLiteral(..), -- should be implemented, but never invoked, by user code
+
+ GArrowSum(..),
+ GArrowProd(..),
+
GArrowReify(..),
- GArrowReflect(..)
+ GArrowReflect(..),
+
+ GArrowCurry(..),
+ GArrowApply(..)
) where
-import Control.Arrow
+import Control.Category
+
+------------------------------------------------------------------------
+-- The main GArrow class
-class GArrow g (**) where
- ga_id :: g x x
- ga_comp :: g x y -> g y z -> g x z
+class Category g => GArrow g (**) u | (**) -> u where
+--id :: g x x
+--comp :: g x y -> g y z -> g x z
ga_first :: g x y -> g (x ** z) (y ** z)
ga_second :: g x y -> g (z ** x) (z ** y)
- ga_cancell :: g (()**x) x
- ga_cancelr :: g (x**()) x
- ga_uncancell :: g x (()**x)
- ga_uncancelr :: g x (x**())
- ga_assoc :: g ((x**y)**z) (x**(y**z))
- ga_unassoc :: g (x**(y**z)) ((x**y)**z)
+ ga_cancell :: g (u**x) x
+ ga_cancelr :: g (x**u) x
+ ga_uncancell :: g x (u**x)
+ ga_uncancelr :: g x (x**u)
+ ga_assoc :: g ((x** y)**z ) ( x**(y **z))
+ ga_unassoc :: g ( x**(y **z)) ((x** y)**z )
-class GArrow g (**) => GArrowDrop g (**) where
- ga_drop :: g x ()
-class GArrow g (**) => GArrowCopy g (**) where
+------------------------------------------------------------------------
+-- The three context-manipulation classes
+
+class GArrow g (**) u => GArrowCopy g (**) u where
ga_copy :: g x (x**x)
-class GArrow g (**) => GArrowSwap g (**) where
- ga_swap :: g (x**y) (y**x)
+class GArrow g (**) u => GArrowDrop g (**) u where
+ ga_drop :: g x u
+
+class GArrow g (**) u => GArrowSwap g (**) u where
+ ga_swap :: g (x**y) (y**x)
+
+ga_swap_second f =
+ ga_swap >>> ga_first f >>> ga_swap
+ -- implementation of ga_second for GArrowSwap
+ -- See also
+ -- http://haskell.org/haskellwiki/Class_system_extension_proposal
+ -- "Allowing superclass methods to be overridden in derived classes";
+ -- if we had this we could do a better job here
+
+
+
+------------------------------------------------------------------------
+-- Products, Coproducts, etc
+
+
+class (GArrow g (**) u,
+ GArrow g (<*>) u) =>
+ GArrowProd g (**) u (<*>) where
+ ga_prod_copy :: g x (x<*>x)
+ ga_prod_drop :: g x u
+
+class (GArrow g (**) u,
+ GArrow g (<+>) v) =>
+ GArrowSum g (**) u v (<+>) where
+ ga_merge :: g (x<+>x) x
+ ga_never :: g v x
+
+
+
+
+
+------------------------------------------------------------------------
+-- Loop
+
+class GArrow g (**) u => GArrowLoop g (**) u where
+ ga_loopl :: g (x**z) (y**z) -> g x y
+ ga_loopr :: g (z**x) (z**y) -> g x y
+
+
+------------------------------------------------------------------------
+-- Literal. Note that ga_literal should never appear in (unflattened)
+-- Haskell programs, though the user may wish to write implementations
+-- of this function (I haven't yet found a way to enforce this
+-- restriction using exports)
+
+class GArrow g (**) u => GArrowLiteral g (**) u t r where
+ ga_literal :: t -> g u r
+
+
+
+
+------------------------------------------------------------------------
+-- Constant and Run, which are dual to each other
+
+class GArrow g (**) u => GArrowEval g (**) u r t where
+ ga_eval :: g u r -> t
+
+class GArrow g (**) u => GArrowConstant g (**) u t r where
+ ga_constant :: t -> g u r
+
+
+
+------------------------------------------------------------------------
+-- Reify and Reflect, which are "curried" versions
--- implementation of ga_second for GArrowSwap instances
-ga_swap_second f = ga_comp (ga_comp ga_swap (ga_first f)) ga_swap
+-- If you have this for R the identity map on types, you're basically
+-- a Control.Arrow; you can also define essentially all the other
+-- methods of GArrow, GArrowDrop, GArrowCopy, etc in terms of this.
+class GArrow g (**) u => GArrowReify g (**) u x y r q where
+ ga_reify :: (x -> y) -> g r q
-class GArrow g (**) => GArrowLoop g (**) where
- ga_loop :: g (x**z) (y**z) -> g x y
+class GArrow g (**) u => GArrowReflect g (**) u r q x y where
+ ga_reflect :: g r q -> (x -> y)
-class GArrow g (**) => GArrowLiteral g (**) a where
- ga_literal :: a -> g () a
--- not sure -- subject to change
-class GArrow g (**) => GArrowReify g (**) where
- ga_reify :: (x -> y) -> g x y
--- not sure -- subject to change
-class GArrow g (**) => GArrowReflect g (**) where
- ga_reflect :: g x y -> (x -> y)
+------------------------------------------------------------------------
+-- Apply and Curry
+class GArrow g (**) u => GArrowApply g (**) u (~>) where
+ ga_applyl :: g (x**(x~>y) ) y
+ ga_applyr :: g ( (x~>y)**x) y
+class GArrow g (**) u => GArrowCurry g (**) u (~>) where
+ ga_curryl :: g (x**y) z -> g x (y~>z)
+ ga_curryr :: g (x**y) z -> g y (x~>z)
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