X-Git-Url: http://git.megacz.com/?p=coq-hetmet.git;a=blobdiff_plain;f=examples%2FGArrowSkeleton.hs;h=dd7937ba61ab5412cd4669a4f2514a9e702763f5;hp=8775d4af31bdff04d5dbf43f7a6a2cb2a96038bf;hb=6e1e4b67d01a6447f7dd44f7b5450ddc400000d9;hpb=542be54b8968c631f0c397272cf05871ccef425b diff --git a/examples/GArrowSkeleton.hs b/examples/GArrowSkeleton.hs index 8775d4a..dd7937b 100644 --- a/examples/GArrowSkeleton.hs +++ b/examples/GArrowSkeleton.hs @@ -119,7 +119,7 @@ instance Eq ((GArrowSkeleton m) a b) -- laws, but no guarantees about which optimizations actually happen. -- optimize :: (GArrowSkeleton m) a b -> (GArrowSkeleton m) a b -optimize = repeat (gasl2gas . optimizel . gas2gasl) +optimize = repeat (gasl2gas . optimizel . {- FIXME -} optimizel . gas2gasl) {- optimize x = let x' = optimize' x in if x == x' then x' else optimize x' @@ -206,15 +206,17 @@ repeat f x = let x' = f x in -- | Recursively turns @(ga_first x >>> first y)@ into @(ga_first (x >>> y))@, likewise for ga_second. -- beautify :: (GArrowSkeleton m) a b -> (GArrowSkeleton m) a b -beautify = optimize . (repeat beautify') +beautify = repeat beautify' where beautify' :: (GArrowSkeleton m) a b -> (GArrowSkeleton m) a b - beautify' (GAS_comp (GAS_comp f g) h) = GAS_comp f $ GAS_comp g h - beautify' (GAS_comp f (GAS_comp (GAS_comp g h) k)) = GAS_comp f $ GAS_comp g $ GAS_comp h k + beautify' (GAS_comp (GAS_comp f g) h) = beautify' $ GAS_comp f $ GAS_comp g h + beautify' (GAS_comp f (GAS_comp (GAS_comp g h) k)) = beautify' $ GAS_comp f $ GAS_comp g $ GAS_comp h k beautify' (GAS_comp f (GAS_comp g h)) = case (beautify' f, beautify' g) of (GAS_first f' , GAS_first g') -> beautify' $ GAS_comp (GAS_first (GAS_comp f' g')) h (GAS_second f', GAS_second g') -> beautify' $ GAS_comp (GAS_second (GAS_comp f' g')) h (f' , g' ) -> GAS_comp f' (beautify' (GAS_comp g h)) + beautify' (GAS_comp f GAS_id) = f + beautify' (GAS_comp GAS_id f) = f beautify' (GAS_comp f g) = case (beautify' f, beautify' g) of (GAS_first f' , GAS_first g') -> GAS_first (GAS_comp f' g') (GAS_second f', GAS_second g') -> GAS_second (GAS_comp f' g') @@ -277,6 +279,8 @@ data GArrowSkeletonY m :: * -> * -> * GASY_X :: GArrowSkeletonX m x y -> GArrowSkeletonY m x y GASY_first :: GArrowSkeletonY m x y -> GArrowSkeletonY m (x,z) (y,z) GASY_second :: GArrowSkeletonY m x y -> GArrowSkeletonY m (z,x) (z,y) + GASY_atomicl :: GArrowSkeletonY m () x -> GArrowSkeletonY m y (x,y) + GASY_atomicr :: GArrowSkeletonY m () x -> GArrowSkeletonY m y (y,x) data GArrowSkeletonX m :: * -> * -> * where @@ -305,6 +309,8 @@ gasy2gas :: GArrowSkeletonY m x y -> GArrowSkeleton m x y gasy2gas (GASY_X gx) = gasx2gas gx gasy2gas (GASY_first gy) = GAS_first (gasy2gas gy) gasy2gas (GASY_second gy) = GAS_second (gasy2gas gy) +gasy2gas (GASY_atomicl gy) = GAS_comp GAS_uncancell (GAS_first $ gasy2gas gy) +gasy2gas (GASY_atomicr gy) = GAS_comp GAS_uncancelr (GAS_second $ gasy2gas gy) gasx2gas :: GArrowSkeletonX m x y -> GArrowSkeleton m x y gasx2gas (GASX_const k) = GAS_const k @@ -327,10 +333,10 @@ gasx2gas (GASX_loopr gl) = GAS_loopr $ gasl2gas gl optimizel :: GArrowSkeletonL m x y -> GArrowSkeletonL m x y optimizel (GASL_id ) = GASL_id optimizel (GASL_Y gy ) = GASL_Y $ optimizey gy -optimizel (GASL_comp gy (GASL_comp gy' gl)) | pushright gy, not (pushright gy'), Just x <- pushpair gy gy' = optimizel $ gaslcat x gl -optimizel (GASL_comp gy (GASL_Y gy')) | pushright gy, not (pushright gy'), Just x <- pushpair gy gy' = GASL_comp (optimizey gy) (GASL_Y gy') optimizel (GASL_comp gy (GASL_comp gy' gl)) | Just x <- optpair gy gy' = optimizel $ gaslcat x gl -optimizel (GASL_comp gy (GASL_Y gy')) | Just x <- optpair gy gy' = GASL_comp (optimizey gy) (GASL_Y gy') +optimizel (GASL_comp gy (GASL_Y gy')) | Just x <- optpair gy gy' = x +optimizel (GASL_comp gy (GASL_comp gy' gl)) | pushright gy, not (pushright gy'), Just x <- swappair gy gy' = optimizel $ gaslcat x gl +optimizel (GASL_comp gy (GASL_Y gy')) | pushright gy, not (pushright gy'), Just x <- swappair gy gy' = GASL_comp (optimizey gy) (GASL_Y gy') optimizel (GASL_comp gy gl) = GASL_comp (optimizey gy) (optimizel gl) --optimize' (GAS_loopl GAS_id ) = GAS_id @@ -353,53 +359,118 @@ optimizel (GASL_comp gy gl) -} optpair :: GArrowSkeletonY m x y -> GArrowSkeletonY m y z -> Maybe (GArrowSkeletonL m x z) -optpair (GASY_first gy1) (GASY_first gy2) = liftM gasl_firstify $ optpair gy1 gy2 -optpair (GASY_second gy1) (GASY_second gy2) = liftM gasl_secondify $ optpair gy1 gy2 + +optpair (GASY_atomicl g) (GASY_X GASX_cancelr) = Just $ GASL_Y g +optpair (GASY_atomicr g) (GASY_X GASX_cancell) = Just $ GASL_Y g + optpair (GASY_X GASX_uncancell) (GASY_X GASX_cancell) = Just $ GASL_id optpair (GASY_X GASX_uncancelr) (GASY_X GASX_cancelr) = Just $ GASL_id optpair (GASY_X GASX_cancell) (GASY_X GASX_uncancell) = Just $ GASL_id optpair (GASY_X GASX_cancelr) (GASY_X GASX_uncancelr) = Just $ GASL_id optpair (GASY_X GASX_uncancelr) (GASY_X GASX_cancell) = Just $ GASL_id optpair (GASY_X GASX_uncancell) (GASY_X GASX_cancelr) = Just $ GASL_id -optpair _ _ = Nothing - -pushpair :: GArrowSkeletonY m x y -> GArrowSkeletonY m y z -> Maybe (GArrowSkeletonL m x z) -pushpair (GASY_first gy1) (GASY_first gy2) = liftM gasl_firstify $ pushpair gy1 gy2 -pushpair (GASY_second gy1) (GASY_second gy2) = liftM gasl_secondify $ pushpair gy1 gy2 -pushpair (GASY_first gy1) (GASY_second gy2) = Just $ GASL_comp (GASY_second gy2) (GASL_Y $ GASY_first gy1) -pushpair (GASY_second gy1) (GASY_first gy2) = Just $ GASL_comp (GASY_first gy2) (GASL_Y $ GASY_second gy1) -pushpair (GASY_first gy1) (GASY_X GASX_unassoc) = Just $ GASL_comp(GASY_X GASX_unassoc) (GASL_Y $ GASY_first (GASY_first gy1)) -pushpair (GASY_second gy1) (GASY_X GASX_assoc ) = Just $ GASL_comp(GASY_X GASX_assoc ) (GASL_Y $ GASY_second (GASY_second gy1)) -pushpair (GASY_second (GASY_X GASX_uncancelr)) (GASY_X GASX_unassoc ) = Just $ GASL_Y $ GASY_X GASX_uncancelr -pushpair (GASY_first (GASY_X GASX_uncancell)) (GASY_X GASX_assoc ) = Just $ GASL_Y $ GASY_X GASX_uncancell -pushpair (GASY_X GASX_uncancelr) (GASY_first gy) = Just $ GASL_comp gy (GASL_Y $ GASY_X $ GASX_uncancelr) -pushpair (GASY_X GASX_uncancell) (GASY_second gy) = Just $ GASL_comp gy (GASL_Y $ GASY_X $ GASX_uncancell) -pushpair (GASY_first (GASY_second gy)) (GASY_X GASX_assoc ) = Just $ GASL_comp (GASY_X GASX_assoc ) $ GASL_Y (GASY_second (GASY_first gy)) -pushpair (GASY_second (GASY_first gy)) (GASY_X GASX_unassoc ) = Just $ GASL_comp (GASY_X GASX_unassoc) $ GASL_Y (GASY_first (GASY_second gy)) -pushpair (GASY_second (GASY_second gy)) (GASY_X GASX_unassoc ) = Just $ GASL_comp (GASY_X GASX_unassoc) $ GASL_Y (GASY_second gy) -pushpair (GASY_first (GASY_first gy)) (GASY_X GASX_assoc ) = Just $ GASL_comp (GASY_X GASX_assoc) $ GASL_Y (GASY_first gy) -pushpair (GASY_X GASX_uncancell) (GASY_X GASX_unassoc ) = Just $ GASL_Y $ GASY_first $ GASY_X GASX_uncancell -pushpair (GASY_X GASX_uncancelr) (GASY_X GASX_assoc ) = Just $ GASL_Y $ GASY_second $ GASY_X GASX_uncancelr -pushpair (GASY_first (GASY_X GASX_uncancelr)) (GASY_X GASX_assoc ) = Just $ GASL_Y $ GASY_second $ GASY_X GASX_uncancell -pushpair (GASY_second (GASY_X GASX_uncancell)) (GASY_X GASX_unassoc ) = Just $ GASL_Y $ GASY_first $ GASY_X GASX_uncancelr -pushpair (GASY_first gy) (GASY_X GASX_swap ) = Just $ GASL_comp (GASY_X GASX_swap) $ GASL_Y (GASY_second gy) -pushpair (GASY_second gy) (GASY_X GASX_swap ) = Just $ GASL_comp (GASY_X GASX_swap) $ GASL_Y (GASY_first gy) -pushpair (GASY_X GASX_uncancell) (GASY_X GASX_swap ) = Just $ GASL_Y $ GASY_X $ GASX_uncancelr -pushpair (GASY_X GASX_uncancelr) (GASY_X GASX_swap ) = Just $ GASL_Y $ GASY_X $ GASX_uncancell -pushpair _ _ = Nothing +optpair (GASY_X GASX_assoc) (GASY_X GASX_cancell) = Just $ GASL_Y $ GASY_first $ GASY_X GASX_cancell +optpair (GASY_X GASX_unassoc) (GASY_X GASX_cancelr) = Just $ GASL_Y $ GASY_second $ GASY_X GASX_cancelr +optpair (GASY_second (GASY_X GASX_uncancelr)) (GASY_X GASX_unassoc ) = Just $ GASL_Y $ GASY_X GASX_uncancelr +optpair (GASY_first (GASY_X GASX_uncancell)) (GASY_X GASX_assoc ) = Just $ GASL_Y $ GASY_X GASX_uncancell +optpair (GASY_X GASX_uncancell) (GASY_X GASX_unassoc ) = Just $ GASL_Y $ GASY_first $ GASY_X GASX_uncancell +optpair (GASY_X GASX_uncancelr) (GASY_X GASX_assoc ) = Just $ GASL_Y $ GASY_second $ GASY_X GASX_uncancelr +optpair (GASY_first (GASY_X GASX_uncancelr)) (GASY_X GASX_assoc ) = Just $ GASL_Y $ GASY_second $ GASY_X GASX_uncancell +optpair (GASY_second (GASY_X GASX_uncancell)) (GASY_X GASX_unassoc ) = Just $ GASL_Y $ GASY_first $ GASY_X GASX_uncancelr +optpair (GASY_X GASX_assoc) (GASY_second (GASY_X GASX_cancelr)) = Just $ GASL_Y $ GASY_X $ GASX_cancelr +optpair (GASY_X GASX_unassoc) (GASY_first (GASY_X GASX_cancell)) = Just $ GASL_Y $ GASY_X $ GASX_cancell +optpair (GASY_first g) (GASY_X GASX_cancelr) = Just $ GASL_comp (GASY_X GASX_cancelr) $ GASL_Y $ g +optpair (GASY_second g) (GASY_X GASX_cancell) = Just $ GASL_comp (GASY_X GASX_cancell) $ GASL_Y $ g +optpair (GASY_X GASX_uncancelr) (GASY_first g) = Just $ GASL_comp g $ GASL_Y (GASY_X GASX_uncancelr) +optpair (GASY_X GASX_uncancell) (GASY_second g) = Just $ GASL_comp g $ GASL_Y (GASY_X GASX_uncancell) + +-- swap with an {un}cancel{l,r} before/after it +optpair (GASY_X GASX_uncancell) (GASY_X GASX_swap ) = Just $ GASL_Y $ GASY_X $ GASX_uncancelr +optpair (GASY_X GASX_uncancelr) (GASY_X GASX_swap ) = Just $ GASL_Y $ GASY_X $ GASX_uncancell +optpair (GASY_X GASX_swap) (GASY_X GASX_cancell) = Just $ GASL_Y $ GASY_X $ GASX_cancelr +optpair (GASY_X GASX_swap) (GASY_X GASX_cancelr) = Just $ GASL_Y $ GASY_X $ GASX_cancell + +{- +optpair (GASY_X GASX_uncancelr) (GASY_X (GASX_loopl gl)) = + Just $ GASL_Y $ (GASY_X $ GASX_loopl $ GASL_comp (GASY_second $ GASY_X GASX_uncancelr) gl) +optpair (GASY_X GASX_uncancell) (GASY_X (GASX_loopl gl)) = + Just $ GASL_Y $ (GASY_X $ GASX_loopl $ GASL_comp (GASY_second $ GASY_X GASX_uncancell) gl) +optpair (GASY_X GASX_uncancelr) (GASY_X (GASX_loopr gl)) = + Just $ GASL_Y $ (GASY_X $ GASX_loopr $ GASL_comp (GASY_first $ GASY_X GASX_uncancelr) gl) +optpair (GASY_X GASX_uncancell) (GASY_X (GASX_loopr gl)) = + Just $ GASL_Y $ (GASY_X $ GASX_loopr $ GASL_comp (GASY_first $ GASY_X GASX_uncancell) gl) +-} +optpair q (GASY_X (GASX_loopl gl)) | pushin q = Just $ GASL_Y $ (GASY_X $ GASX_loopl $ GASL_comp (GASY_second $ q) gl) +optpair q (GASY_X (GASX_loopr gl)) | pushin q = Just $ GASL_Y $ (GASY_X $ GASX_loopr $ GASL_comp (GASY_first $ q) gl) + +optpair a@(GASY_X GASX_uncancell) (GASY_first b@(GASY_X (GASX_const c))) = Just $ GASL_Y $ GASY_atomicl b +optpair a@(GASY_X GASX_uncancelr) (GASY_second b@(GASY_X (GASX_const c))) = Just $ GASL_Y $ GASY_atomicr b + +optpair (GASY_first gy1) (GASY_second gy2) | pushleft gy2, not (pushleft gy1) + = Just $ GASL_comp (GASY_second gy2) $ GASL_Y $ GASY_first gy1 +optpair (GASY_second gy1) (GASY_first gy2) | pushleft gy2, not (pushleft gy1) + = Just $ GASL_comp (GASY_first gy2) $ GASL_Y $ GASY_second gy1 + +optpair (GASY_first gy1) (GASY_first gy2) = liftM gasl_firstify $ optpair gy1 gy2 +optpair (GASY_second gy1) (GASY_second gy2) = liftM gasl_secondify $ optpair gy1 gy2 +optpair _ _ = Nothing + +swappair :: GArrowSkeletonY m x y -> GArrowSkeletonY m y z -> Maybe (GArrowSkeletonL m x z) + +swappair q (GASY_atomicl g) = Just $ GASL_comp (GASY_atomicl g) $ GASL_Y $ GASY_second q +swappair q (GASY_atomicr g) = Just $ GASL_comp (GASY_atomicr g) $ GASL_Y $ GASY_first q + +swappair (GASY_first gy1) (GASY_second gy2) = Just $ GASL_comp (GASY_second gy2) (GASL_Y $ GASY_first gy1) +swappair (GASY_second gy1) (GASY_first gy2) = Just $ GASL_comp (GASY_first gy2) (GASL_Y $ GASY_second gy1) +swappair (GASY_first gy1) (GASY_X GASX_unassoc) = Just $ GASL_comp(GASY_X GASX_unassoc) (GASL_Y $ GASY_first (GASY_first gy1)) +swappair (GASY_second gy1) (GASY_X GASX_assoc ) = Just $ GASL_comp(GASY_X GASX_assoc ) (GASL_Y $ GASY_second (GASY_second gy1)) +swappair (GASY_X GASX_uncancelr) (GASY_first gy) = Just $ GASL_comp gy (GASL_Y $ GASY_X $ GASX_uncancelr) +swappair (GASY_X GASX_uncancell) (GASY_second gy) = Just $ GASL_comp gy (GASL_Y $ GASY_X $ GASX_uncancell) +swappair (GASY_first (GASY_second gy)) (GASY_X GASX_assoc ) = Just $ GASL_comp (GASY_X GASX_assoc ) $ GASL_Y (GASY_second (GASY_first gy)) +swappair (GASY_second (GASY_first gy)) (GASY_X GASX_unassoc ) = Just $ GASL_comp (GASY_X GASX_unassoc) $ GASL_Y (GASY_first (GASY_second gy)) +swappair (GASY_second (GASY_second gy)) (GASY_X GASX_unassoc ) = Just $ GASL_comp (GASY_X GASX_unassoc) $ GASL_Y (GASY_second gy) +swappair (GASY_first (GASY_first gy)) (GASY_X GASX_assoc ) = Just $ GASL_comp (GASY_X GASX_assoc) $ GASL_Y (GASY_first gy) +swappair (GASY_first gy) (GASY_X GASX_swap ) = Just $ GASL_comp (GASY_X GASX_swap) $ GASL_Y (GASY_second gy) +swappair (GASY_second gy) (GASY_X GASX_swap ) = Just $ GASL_comp (GASY_X GASX_swap) $ GASL_Y (GASY_first gy) +swappair gy (GASY_X (GASX_loopl gl)) = Just $ GASL_Y $ GASY_X $ GASX_loopl $ GASL_comp (GASY_second gy) gl +swappair gy (GASY_X (GASX_loopr gl)) = Just $ GASL_Y $ GASY_X $ GASX_loopr $ GASL_comp (GASY_first gy) gl + +swappair (GASY_first gy1) (GASY_first gy2) = liftM gasl_firstify $ swappair gy1 gy2 +swappair (GASY_second gy1) (GASY_second gy2) = liftM gasl_secondify $ swappair gy1 gy2 +swappair _ _ = Nothing -- pushright can only return True for central morphisms pushright :: GArrowSkeletonY m x y -> Bool pushright (GASY_first gy) = pushright gy pushright (GASY_second gy) = pushright gy +pushright (GASY_atomicl _) = False +pushright (GASY_atomicr _) = False pushright (GASY_X GASX_uncancell) = True pushright (GASY_X GASX_uncancelr) = True pushright (GASY_X _ ) = False +-- says if we should push it into a loopl/r +pushin :: GArrowSkeletonY m x y -> Bool +pushin gy = pushright gy || pushin' gy + where + pushin' :: GArrowSkeletonY m a b -> Bool + pushin' (GASY_first gy) = pushin' gy + pushin' (GASY_second gy) = pushin' gy + pushin' (GASY_atomicl _) = False + pushin' (GASY_atomicr _) = False + + -- not sure if these are a good idea + pushin' (GASY_X GASX_copy) = True + pushin' (GASY_X GASX_swap) = True + + pushin' (GASY_X _ ) = False + optimizey :: GArrowSkeletonY m x y -> GArrowSkeletonY m x y optimizey (GASY_X gx) = GASY_X $ optimizex gx optimizey (GASY_first gy) = GASY_first (optimizey gy) optimizey (GASY_second gy) = GASY_second (optimizey gy) +optimizey (GASY_atomicl gy) = GASY_atomicl $ optimizey gy +optimizey (GASY_atomicr gy) = GASY_atomicr $ optimizey gy optimizex :: GArrowSkeletonX m x y -> GArrowSkeletonX m x y optimizex (GASX_const k) = GASX_const k @@ -414,5 +485,16 @@ optimizex (GASX_copy) = GASX_copy optimizex (GASX_swap) = GASX_swap optimizex (GASX_merge) = GASX_merge optimizex (GASX_misc m) = GASX_misc m +optimizex (GASX_loopl (GASL_comp (GASY_first gy) gl))| pushleft gy = GASX_loopl $ gaslcat gl (GASL_Y $ GASY_first gy) +optimizex (GASX_loopr (GASL_comp (GASY_second gy) gl))| pushleft gy = GASX_loopr $ gaslcat gl (GASL_Y $ GASY_second gy) optimizex (GASX_loopl gl) = GASX_loopl $ optimizel gl optimizex (GASX_loopr gl) = GASX_loopr $ optimizel gl + +pushleft :: GArrowSkeletonY m x y -> Bool +pushleft (GASY_first gy) = pushleft gy +pushleft (GASY_second gy) = pushleft gy +pushleft (GASY_atomicl _) = False +pushleft (GASY_atomicr _) = False +pushleft (GASY_X GASX_cancell) = True +pushleft (GASY_X GASX_cancelr) = True +pushleft (GASY_X _ ) = False