1 {-# OPTIONS -XRankNTypes -XMultiParamTypeClasses -XNoMonomorphismRestriction -XTypeOperators -XFlexibleInstances -XFunctionalDependencies #-}
2 -----------------------------------------------------------------------------
4 -- Module : GHC.HetMet.GArrow
6 -- License : public domain
8 -- Maintainer : Adam Megacz <megacz@acm.org>
9 -- Stability : experimental
10 -- Portability : portable
12 module GHC.HetMet.GArrow (
22 GArrowLiteral(..), -- should be implemented, but never invoked, by user code
24 GArrowSum(..), ga_inl, ga_inr,
38 import Control.Category
40 ------------------------------------------------------------------------
41 -- The main GArrow class
43 class Category g => GArrow g (**) u | (**) -> u where
45 --comp :: g x y -> g y z -> g x z
46 ga_first :: g x y -> g (x ** z) (y ** z)
47 ga_second :: g x y -> g (z ** x) (z ** y)
48 ga_cancell :: g (u**x) x
49 ga_cancelr :: g (x**u) x
50 ga_uncancell :: g x (u**x)
51 ga_uncancelr :: g x (x**u)
52 ga_assoc :: g ((x** y)**z ) ( x**(y **z))
53 ga_unassoc :: g ( x**(y **z)) ((x** y)**z )
56 ------------------------------------------------------------------------
57 -- The three context-manipulation classes
59 class GArrow g (**) u => GArrowCopy g (**) u where
62 class GArrow g (**) u => GArrowDrop g (**) u where
65 class GArrow g (**) u => GArrowSwap g (**) u where
66 ga_swap :: g (x**y) (y**x)
69 ga_swap >>> ga_first f >>> ga_swap
70 -- implementation of ga_second for GArrowSwap
72 -- http://haskell.org/haskellwiki/Class_system_extension_proposal
73 -- "Allowing superclass methods to be overridden in derived classes";
74 -- if we had this we could do a better job here
78 ------------------------------------------------------------------------
79 -- Products, Coproducts, etc
82 class (GArrow g (**) u,
84 GArrowProd g (**) u (<*>) v where
85 ga_prod_copy :: g x (x<*>x)
88 class (GArrow g (**) u,
90 GArrowSum g (**) u (<+>) v where
91 ga_merge :: g (x<+>x) x
94 ga_inl = ga_uncancelr >>> ga_second ga_never
95 ga_inr = ga_uncancell >>> ga_first ga_never
97 ------------------------------------------------------------------------
100 class GArrow g (**) u => GArrowLoop g (**) u where
101 ga_loopl :: g (x**z) (y**z) -> g x y
102 ga_loopr :: g (z**x) (z**y) -> g x y
105 ------------------------------------------------------------------------
106 -- Literal. Note that ga_literal should never appear in (unflattened)
107 -- Haskell programs, though the user may wish to write implementations
108 -- of this function (I haven't yet found a way to enforce this
109 -- restriction using exports)
111 class GArrow g (**) u => GArrowLiteral g (**) u t r where
112 ga_literal :: t -> g u r
117 ------------------------------------------------------------------------
118 -- Constant and Run, which are dual to each other
120 class GArrow g (**) u => GArrowEval g (**) u r t where
121 ga_eval :: g u r -> t
123 class GArrow g (**) u => GArrowConstant g (**) u t r where
124 ga_constant :: t -> g u r
128 ------------------------------------------------------------------------
129 -- Reify and Reflect, which are "curried" versions
131 -- If you have this for R the identity map on types, you're basically
132 -- a Control.Arrow; you can also define essentially all the other
133 -- methods of GArrow, GArrowDrop, GArrowCopy, etc in terms of this.
134 class GArrow g (**) u => GArrowReify g (**) u x y r q where
135 ga_reify :: (x -> y) -> g r q
137 class GArrow g (**) u => GArrowReflect g (**) u r q x y where
138 ga_reflect :: g r q -> (x -> y)
143 ------------------------------------------------------------------------
146 class GArrow g (**) u => GArrowApply g (**) u (~>) where
147 ga_applyl :: g (x**(x~>y) ) y
148 ga_applyr :: g ( (x~>y)**x) y
150 class GArrow g (**) u => GArrowCurry g (**) u (~>) where
151 ga_curryl :: g (x**y) z -> g x (y~>z)
152 ga_curryr :: g (x**y) z -> g y (x~>z)
157 ------------------------------------------------------------------------
158 -- Commonly Implemented Collections of Classes
161 -- The simply typed KAPPA calculus; see Hasegawa, __Decomposing Typed
162 -- Lambda Calculus into a Couple of Categorical Programming
163 -- Languages__, http://dx.doi.org/10.1007/3-540-60164-3_28
165 class (GArrowDrop g (**) u,
167 GArrowSwap g (**) u) =>
170 -- The simply typed LAMBDA calculus
171 class (GArrowSTKC g (**) u,
172 GArrowCurry g (**) u (~>),
173 GArrowApply g (**) u (~>)) =>
174 GArrowSTLC g (**) u (~>)
176 -- Programming Language for Computable Functions (w/o integers and booleans)
177 class (GArrowSTLC g (**) u (~>),
178 GArrowLoop g (**) u) =>
179 GArrowPCF g (**) u (~>)