| Line No. | Rev | Author | Line |
|---|---|---|---|
| 1 | 1 | paulosilva | |
| 2 | {-# LANGUAGE GADTs, TypeOperators, FlexibleContexts, Rank2Types #-} | ||
| 3 | {-# OPTIONS_GHC -Wall #-} | ||
| 4 | |||
| 5 | ------------------------------------------------------------------------------- | ||
| 6 | |||
| 7 | {- | | ||
| 8 | Module : Galculator.Engine.GcToLaw | ||
| 9 | Description : | ||
| 10 | Copyright : (c) Paulo Silva | ||
| 11 | License : LGPL | ||
| 12 | |||
| 13 | Maintainer : paufil@di.uminho.pt | ||
| 14 | Stability : experimental | ||
| 15 | Portability : portable | ||
| 16 | |||
| 17 | -} | ||
| 18 | |||
| 19 | ------------------------------------------------------------------------------- | ||
| 20 | |||
| 21 | module Galculator.Engine.GcToLaw ( | ||
| 22 | --gc2Rules, | ||
| 23 | rType2Law, | ||
| 24 | gcProperties, | ||
| 25 | gcPropertyFunc, | ||
| 26 | gcShunting, | ||
| 27 | gcDistributivityUpper, | ||
| 28 | gcDistributivityLower, | ||
| 29 | gcMonotonicityUpper, | ||
| 30 | gcMonotonicityLower, | ||
| 31 | gcPreservingBottom, | ||
| 32 | gcPreservingTop, | ||
| 33 | gcCancellationUpper, | ||
| 34 | gcCancellationLower | ||
| 35 | ) where | ||
| 36 | |||
| 37 | import Control.GalcError | ||
| 38 | import Control.Monad.Error | ||
| 39 | import Control.Monad.Fresh | ||
| 40 | import Data.Existential | ||
| 41 | --import Galculator.Engine.LawToRule | ||
| 42 | --import Galculator.Rule | ||
| 43 | import Language.Law.Syntax | ||
| 44 | import Language.R.Syntax | ||
| 45 | import Language.Type.Syntax | ||
| 46 | |||
| 47 | ------------------------------------------------------------------------------- | ||
| 48 | {- | ||
| 49 | gc2Rules :: Type (GC b a) -> R (GC b a) -> [Rule] | ||
| 50 | gc2Rules t gc = map getRule pp ++ | ||
| 51 | map getRuleInv pp | ||
| 52 | where pp = gcProperties t gc | ||
| 53 | -} | ||
| 54 | ------------------------------------------------------------------------------- | ||
| 55 | |||
| 56 | rType2Law :: (MonadFresh [String] String m, MonadError GalcError m) | ||
| 57 | => RType -> (forall a . Type a -> R a -> m Law) -> m Law | ||
| 58 | rType2Law (Exists t g) f = f t g | ||
| 59 | |||
| 60 | ------------------------------------------------------------------------------- | ||
| 61 | |||
| 62 | gcProperties :: Type (GC b a) -> R (GC b a) -> [Law] | ||
| 63 | gcProperties t gc = map (\f -> f t gc) gcPropertyFunc | ||
| 64 | |||
| 65 | ------------------------------------------------------------------------------- | ||
| 66 | |||
| 67 | gcPropertyFunc :: [Type (GC b a) -> R (GC b a) -> Law] | ||
| 68 | gcPropertyFunc = [] {- [ | ||
| 69 | gcShunting, | ||
| 70 | --gcDistributivityUpper, | ||
| 71 | --gcDistributivityLower, | ||
| 72 | gcMonotonicityUpper, | ||
| 73 | gcMonotonicityLower, | ||
| 74 | gcPreservingTop, | ||
| 75 | gcPreservingBottom, | ||
| 76 | gcCancellationUpper, | ||
| 77 | gcCancellationLower | ||
| 78 | ]-} | ||
| 79 | |||
| 80 | ------------------------------------------------------------------------------- | ||
| 81 | |||
| 82 | gcShunting :: (MonadFresh [String] String m, MonadError GalcError m) | ||
| 83 | => Type a -> R a -> m Law | ||
| 84 | gcShunting (GC b a) g = do | ||
| 85 | ladj <- lowerAdjoint g | ||
| 86 | uadj <- upperAdjoint g | ||
| 87 | lord <- lowerOrder g | ||
| 88 | uord <- upperOrder g | ||
| 89 | return $ | ||
| 90 | EQUIV (Meta "Shunting" (Just GCSHUNT)) | ||
| 91 | (Rel a b) | ||
| 92 | (COMP b (CONV ladj) (ORD lord)) | ||
| 93 | (COMP a (ORD uord) uadj) | ||
| 94 | gcShunting _ _ = throwError ImpossibleError | ||
| 95 | |||
| 96 | ------------------------------------------------------------------------------- | ||
| 97 | |||
| 98 | gcDistributivityUpper :: (MonadFresh [String] String m, MonadError GalcError m) | ||
| 99 | => Type a -> R a -> m Law | ||
| 100 | gcDistributivityUpper (GC b a) g = do | ||
| 101 | uadj <- upperAdjoint g | ||
| 102 | lord <- lowerOrder g | ||
| 103 | uord <- upperOrder g | ||
| 104 | return $ | ||
| 105 | EQUIV (Meta ("Distributivity (Upper adjoint)") (Just GCDISTR) ) | ||
| 106 | (Rel a (Prod b b)) | ||
| 107 | (COMP b uadj (FUN (OMeet lord))) | ||
| 108 | (COMP (Prod a a) (FUN (OMeet uord)) (PROD uadj uadj)) | ||
| 109 | gcDistributivityUpper _ _ = error "gcDistributivityUpper" | ||
| 110 | |||
| 111 | ------------------------------------------------------------------------------- | ||
| 112 | |||
| 113 | gcDistributivityLower :: (MonadFresh [String] String m, MonadError GalcError m) | ||
| 114 | => Type a -> R a -> m Law | ||
| 115 | gcDistributivityLower (GC b a) g = do | ||
| 116 | ladj <- lowerAdjoint g | ||
| 117 | lord <- lowerOrder g | ||
| 118 | uord <- upperOrder g | ||
| 119 | return $ | ||
| 120 | EQUIV (Meta ("Distributivity (Lower adjoint)") (Just GCDISTR) ) | ||
| 121 | (Rel b (Prod a a)) | ||
| 122 | (COMP a ladj (FUN (OJoin uord))) | ||
| 123 | (COMP (Prod b b) (FUN (OJoin lord)) (PROD ladj ladj)) | ||
| 124 | gcDistributivityLower _ _ = error "gcDistributivityLower" | ||
| 125 | |||
| 126 | ------------------------------------------------------------------------------- | ||
| 127 | |||
| 128 | gcMonotonicityUpper :: (MonadFresh [String] String m, MonadError GalcError m) | ||
| 129 | => Type a -> R a -> m Law | ||
| 130 | gcMonotonicityUpper (GC b a) g = do | ||
| 131 | uadj <- upperAdjoint g | ||
| 132 | lord <- lowerOrder g | ||
| 133 | uord <- upperOrder g | ||
| 134 | return $ | ||
| 135 | IMPL (Meta "Monotonicity (upper adjoint)" (Just GCMONOT)) | ||
| 136 | (Rel a b) | ||
| 137 | (COMP b uadj (ORD lord)) | ||
| 138 | (COMP a (ORD uord) uadj) | ||
| 139 | gcMonotonicityUpper _ _ = error "gcMonotonicityUpper" | ||
| 140 | |||
| 141 | ------------------------------------------------------------------------------- | ||
| 142 | |||
| 143 | gcMonotonicityLower :: (MonadFresh [String] String m, MonadError GalcError m) | ||
| 144 | => Type a -> R a -> m Law | ||
| 145 | gcMonotonicityLower (GC b a) g = do | ||
| 146 | ladj <- lowerAdjoint g | ||
| 147 | lord <- lowerOrder g | ||
| 148 | uord <- upperOrder g | ||
| 149 | return $ | ||
| 150 | IMPL (Meta "Monotonicity (lower adjoint)" (Just GCMONOT)) | ||
| 151 | (Rel b a) | ||
| 152 | (COMP a ladj (ORD uord)) | ||
| 153 | (COMP b (ORD lord) ladj) | ||
| 154 | gcMonotonicityLower _ _ = error "gcMonotonicityLower" | ||
| 155 | |||
| 156 | ------------------------------------------------------------------------------- | ||
| 157 | |||
| 158 | gcPreservingTop :: (MonadFresh [String] String m, MonadError GalcError m) | ||
| 159 | => Type a -> R a -> m Law | ||
| 160 | gcPreservingTop (GC b a) g = do | ||
| 161 | uadj <- upperAdjointF g | ||
| 162 | lord <- lowerOrder g | ||
| 163 | uord <- upperOrder g | ||
| 164 | return $ | ||
| 165 | EQUIV (Meta "Top preserving" (Just GCTOP)) | ||
| 166 | a | ||
| 167 | (APPLY b uadj (OMax lord)) | ||
| 168 | (OMax uord) | ||
| 169 | gcPreservingTop _ _ = error "gcPreservingTop" | ||
| 170 | |||
| 171 | ------------------------------------------------------------------------------- | ||
| 172 | |||
| 173 | gcPreservingBottom :: (MonadFresh [String] String m, MonadError GalcError m) | ||
| 174 | => Type a -> R a -> m Law | ||
| 175 | gcPreservingBottom (GC b a) g = do | ||
| 176 | ladj <- lowerAdjointF g | ||
| 177 | lord <- lowerOrder g | ||
| 178 | uord <- upperOrder g | ||
| 179 | return $ | ||
| 180 | EQUIV (Meta "Bottom preserving" (Just GCBOT)) | ||
| 181 | b | ||
| 182 | (APPLY a ladj (OMin uord)) | ||
| 183 | (OMin lord) | ||
| 184 | gcPreservingBottom _ _ = error "gcPreservingBottom" | ||
| 185 | |||
| 186 | ------------------------------------------------------------------------------- | ||
| 187 | |||
| 188 | gcCancellationUpper :: (MonadFresh [String] String m, MonadError GalcError m) | ||
| 189 | => Type a -> R a -> m Law | ||
| 190 | gcCancellationUpper (GC b a) g = do | ||
| 191 | ladj <- lowerAdjoint g | ||
| 192 | uadj <- upperAdjoint g | ||
| 193 | uord <- upperOrder g | ||
| 194 | return $ | ||
| 195 | IMPL (Meta "Cancellation (upper adjoint)" (Just GCCANC)) | ||
| 196 | (Rel a a) | ||
| 197 | (ORD uord) | ||
| 198 | (COMP a (ORD uord) (COMP b uadj ladj)) | ||
| 199 | gcCancellationUpper _ _ = error "gcCancellationUpper" | ||
| 200 | |||
| 201 | ------------------------------------------------------------------------------- | ||
| 202 | |||
| 203 | gcCancellationLower :: (MonadFresh [String] String m, MonadError GalcError m) | ||
| 204 | => Type a -> R a -> m Law | ||
| 205 | gcCancellationLower (GC b a) g = do | ||
| 206 | ladj <- lowerAdjoint g | ||
| 207 | uadj <- upperAdjoint g | ||
| 208 | lord <- lowerOrder g | ||
| 209 | return $ | ||
| 210 | IMPL (Meta "Cancellation (lowerAdjoint)" (Just GCCANC)) | ||
| 211 | (Rel b b) | ||
| 212 | (COMP b (COMP a ladj uadj) (ORD lord)) | ||
| 213 | (ORD lord) | ||
| 214 | gcCancellationLower _ _ = error "gcCancellationLower" | ||
| 215 | |||
| 216 | ------------------------------------------------------------------------------- | ||
| 217 | |||
| 218 | upperAdjoint :: MonadError GalcError m => R (GC b a) -> m (R (a :<->: b)) | ||
| 219 | upperAdjoint (GDef _ _ g _ _) = return $ FUN g | ||
| 220 | upperAdjoint GId = return ID | ||
| 221 | upperAdjoint (GComp t g1 g2) = do | ||
| 222 | g1' <- upperAdjoint g1 | ||
| 223 | g2' <- upperAdjoint g2 | ||
| 224 | return $ COMP t g2' g1' | ||
| 225 | upperAdjoint (GConv g) = lowerAdjoint g | ||
| 226 | upperAdjoint _ = throwError ImpossibleError | ||
| 227 | |||
| 228 | ------------------------------------------------------------------------------- | ||
| 229 | |||
| 230 | lowerAdjoint :: MonadError GalcError m => R (GC b a) -> m (R (b :<->: a)) | ||
| 231 | lowerAdjoint (GDef _ f _ _ _) = return $ FUN f | ||
| 232 | lowerAdjoint GId = return ID | ||
| 233 | lowerAdjoint (GComp t g1 g2) = do | ||
| 234 | g1' <- lowerAdjoint g1 | ||
| 235 | g2' <- lowerAdjoint g2 | ||
| 236 | return $ COMP t g1' g2' | ||
| 237 | lowerAdjoint (GConv g) = upperAdjoint g | ||
| 238 | lowerAdjoint _ = throwError ImpossibleError | ||
| 239 | |||
| 240 | ------------------------------------------------------------------------------- | ||
| 241 | |||
| 242 | upperAdjointF :: MonadError GalcError m => R (GC b a) -> m (R (a :<-: b)) | ||
| 243 | upperAdjointF (GDef _ _ g _ _) = return g | ||
| 244 | upperAdjointF GId = return FId | ||
| 245 | upperAdjointF (GComp t g1 g2) = do | ||
| 246 | g1' <- upperAdjointF g1 | ||
| 247 | g2' <- upperAdjointF g2 | ||
| 248 | return $ FComp t g2' g1' | ||
| 249 | upperAdjointF (GConv g) = lowerAdjointF g | ||
| 250 | upperAdjointF _ = throwError ImpossibleError | ||
| 251 | |||
| 252 | ------------------------------------------------------------------------------- | ||
| 253 | |||
| 254 | lowerAdjointF :: MonadError GalcError m => R (GC b a) -> m (R (b :<-: a)) | ||
| 255 | lowerAdjointF (GDef _ f _ _ _) = return f | ||
| 256 | lowerAdjointF GId = return FId | ||
| 257 | lowerAdjointF (GComp t g1 g2) = do | ||
| 258 | g1' <- lowerAdjointF g1 | ||
| 259 | g2' <- lowerAdjointF g2 | ||
| 260 | return $ FComp t g1' g2' | ||
| 261 | lowerAdjointF (GConv g) = upperAdjointF g | ||
| 262 | lowerAdjointF _ = throwError ImpossibleError | ||
| 263 | |||
| 264 | ------------------------------------------------------------------------------- | ||
| 265 | |||
| 266 | lowerOrder :: (MonadFresh [String] String m, MonadError GalcError m) | ||
| 267 | => R (GC b a) -> m (R (PO b)) | ||
| 268 | lowerOrder (GDef _ _ _ o _) = return o | ||
| 269 | lowerOrder GId = do | ||
| 270 | o <- getFresh | ||
| 271 | return $ Var ('o':o) | ||
| 272 | lowerOrder (GComp _ g1 _) = lowerOrder g1 | ||
| 273 | lowerOrder (GConv g) = do | ||
| 274 | g' <- upperOrder g | ||
| 275 | return $ OConv g' | ||
| 276 | lowerOrder _ = error "lowerOrder" | ||
| 277 | |||
| 278 | ------------------------------------------------------------------------------- | ||
| 279 | |||
| 280 | upperOrder :: (MonadFresh [String] String m, MonadError GalcError m) | ||
| 281 | => R (GC b a) -> m (R (PO a)) | ||
| 282 | upperOrder (GDef _ _ _ _ o) = return o | ||
| 283 | upperOrder GId = do | ||
| 284 | o <- getFresh | ||
| 285 | return $ Var ('o':o) | ||
| 286 | upperOrder (GComp _ _ g2) = upperOrder g2 | ||
| 287 | upperOrder (GConv g) = do | ||
| 288 | g' <- lowerOrder g | ||
| 289 | return $ OConv g' | ||
| 290 | upperOrder _ = error "upperOrder" | ||
| 291 | |||
| 292 | ------------------------------------------------------------------------------- | ||
| 293 |