X-Git-Url: http://git.megacz.com/?p=coq-hetmet.git;a=blobdiff_plain;f=examples%2FGArrowTikZ.hs;h=f877b42e7ecdf28b0c03dff61ab3673ba39fc13e;hp=1f629690079201bf2756d8d3b6b66af5380ad8ea;hb=013a93a8fbae4b8c8df290e9eff226f786770762;hpb=ff46afb5b5a682dd9f2e246afb889bb2f1be9f15 diff --git a/examples/GArrowTikZ.hs b/examples/GArrowTikZ.hs index 1f62969..f877b42 100644 --- a/examples/GArrowTikZ.hs +++ b/examples/GArrowTikZ.hs @@ -1,36 +1,349 @@ -{-# OPTIONS_GHC -XModalTypes -XMultiParamTypeClasses -ddump-types -XNoMonoPatBinds #-} -module GArrowTikZ +{-# LANGUAGE RankNTypes, MultiParamTypeClasses, GADTs, FlexibleContexts, FlexibleInstances, TypeOperators #-} +----------------------------------------------------------------------------- +-- | +-- Module : GArrowTikZ +-- Copyright : none +-- License : public domain +-- +-- Maintainer : Adam Megacz +-- Stability : experimental +-- +-- | Renders a @GArrowSkeleton@ using TikZ; the result is LaTeX code +-- + +module GArrowTikZ (tikz, tikz') where -import Prelude hiding ( id, (.) ) +import Prelude hiding ( id, (.), lookup ) +import Control.Category +import GHC.HetMet.GArrow +import Data.List hiding (lookup, insert) +import Data.Map hiding (map, (!)) +import Unify +import GArrowSkeleton +import GHC.HetMet.Private + +data UPort = + UPortVar UVar + | UPortPair UPort UPort + +instance Unifiable UPort where + unify' (UPortPair vl1a vl1b) (UPortPair vl2a vl2b) = mergeU (unify vl1a vl2a) (unify vl1b vl2b) + unify' _ _ = error "impossible" + inject = UPortVar + project (UPortVar v) = Just v + project _ = Nothing + occurrences (UPortVar v) = [v] + occurrences (UPortPair x y) = occurrences x ++ occurrences y + +-- | Resolves a unification variable; the answer to this query will change if subsequent unifications are performed +getU' :: Unifier UPort -> UPort -> UPort +getU' u (UPortPair x y) = UPortPair (getU' u x) (getU' u y) +getU' u x@(UPortVar v) = case Unify.getU u v of + Nothing -> x + Just x' -> getU' u x' + + + -- --- Render a fully-polymorphic GArrow term as a boxes-and-wires diagram using TikZ +-- | Render a fully-polymorphic GArrow term as a boxes-and-wires diagram using TikZ -- -{- -instance GArrow GArrowTikZ (,) where - ga_id = - ga_comp f g = - ga_second f = - ga_cancell f = - ga_cancelr f = - ga_uncancell f = - ga_uncancelr f = - ga_assoc f = - ga_unassoc f = - -instance GArrowDrop GArrowTikZ (,) where - ga_drop = - -instance GArrowCopy GArrowTikZ (,) where - ga_copy = - -instance GArrowSwap GArrowTikZ (,) where - ga_swap = - -instance GArrowLoop GArrowTikZ (,) where - ga_loop = - -instance GArrowLiteral GArrowTikZ (,) where - ga_literal = --} +type Constraints = [(UPort, Int, UPort)] + +-- the unification monad +data UyM t a = UyM (([UVar],Unifier UPort,Constraints) -> ([UVar],Unifier UPort,Constraints,a)) +instance Monad (UyM t) + where + return x = UyM $ \(i,u,k) -> (i,u,k,x) + (UyM f) >>= g = UyM $ \(i,u,k) -> let (i',u',k',x) = f (i,u,k) in let UyM g' = g x in g' (i',u',k') + + +getU = UyM $ \(i,u,k) -> (i,u,k,u) +getM v = UyM $ \(i,u,k) -> (i,u,k,getU' u v) +occursU v x = UyM $ \(i,u,k) -> (i,u,k,occurs u v x) +unifyM :: Eq t => UPort -> UPort -> UyM t () +unifyM v1 v2 = UyM $ \(i,u,k) -> (i,mergeU u (unify v1 v2),k,()) +freshU :: UyM t UVar +freshU = UyM $ \(i:is,u,k) -> (is,u,k,i) +constrain :: UPort -> Int -> UPort -> UyM t () +constrain v1 d v2 = UyM $ \(i,u,k) -> (i,u,((v1,d,v2):k),()) +getK :: UyM t [(UPort, Int, UPort)] +getK = UyM $ \(i,u,k) -> (i,u,k,k) +runU :: UyM t a -> ([UVar],Unifier UPort,Constraints,a) +runU (UyM f) = (f (uvarSupply,emptyUnifier,[])) + + + +name :: GArrowSkeleton m a b -> String +name GAS_id = "id" +name (GAS_const i) = "const " ++ show i +name (GAS_comp _ _) = "comp" +name (GAS_first _ ) = "first" +name (GAS_second _ ) = "second" +name GAS_cancell = "cancell" +name GAS_cancelr = "cancelr" +name GAS_uncancell = "uncancell" +name GAS_uncancelr = "uncancelr" +name GAS_drop = "drop" +name GAS_copy = "copy" +name GAS_swap = "swap" +name (GAS_loopl _ ) = "loopl" +name (GAS_loopr _ ) = "loopr" +name GAS_assoc = "assoc" +name GAS_unassoc = "unassoc" +name GAS_merge = "merge" +name (GAS_misc _) = "misc" + +fresh :: Int -> UyM () [Ports] +fresh 0 = return [] +fresh n = do { xs <- fresh (n-1) + ; x <- freshU + ; case xs of + [] -> return [UPortVar x] + (x':xs') -> do { constrain (UPortVar x) 1 x' + ; return $ (UPortVar x):x':xs' + } + } + +data Diagram p = DiagramComp (Diagram p) (Diagram p) + | DiagramPrim String p p p p (String -> Int -> Int -> Int -> p -> p -> Int -> String) + | DiagramBypassTop p (Diagram p) + | DiagramBypassBot (Diagram p) p + -- | DiagramLoopTop Diagram + -- | DiagramLoopBot Diagram + +type Ports = UPort + +getOut :: Diagram Ports -> Ports +getOut (DiagramComp f g) = getOut g +getOut (DiagramPrim s ptop pin pout pbot _) = pout +getOut (DiagramBypassTop p f) = UPortPair p (getOut f) +getOut (DiagramBypassBot f p) = UPortPair (getOut f) p + +getIn :: Diagram Ports -> Ports +getIn (DiagramComp f g) = getIn f +getIn (DiagramPrim s ptop pin pout pbot _) = pin +getIn (DiagramBypassTop p f) = UPortPair p (getIn f) +getIn (DiagramBypassBot f p) = UPortPair (getIn f) p + +-- constrain that Ports is at least Int units above the topmost portion of Diagram +constrainTop :: Ports -> Int -> Diagram Ports -> UyM () () +constrainTop v i (DiagramComp d1 d2) = do { constrainTop v i d1 ; constrainTop v i d2 ; return () } +constrainTop v i (DiagramBypassTop p d) = constrain v 2 p +constrainTop v i (DiagramBypassBot d p) = constrainTop v (i+1) d +constrainTop v i (DiagramPrim s ptop pin pout pbot _) = constrain v i ptop + +-- constrain that Ports is at least Int units below the bottommost portion of Diagram +constrainBot :: Diagram Ports -> Int -> Ports -> UyM () () +constrainBot (DiagramComp d1 d2) i v = do { constrainBot d1 i v ; constrainBot d2 i v ; return () } +constrainBot (DiagramBypassTop p d) i v = constrainBot d (i+1) v +constrainBot (DiagramBypassBot d p) i v = constrain p 2 v +constrainBot (DiagramPrim s ptop pin pout pbot _) i v = constrain pbot i v + +ga2diag :: GArrowSkeleton m a b -> UyM () (Diagram Ports) +ga2diag (GAS_id ) = do { [top,x,bot] <- fresh 3 ; return $ DiagramPrim "id" top x x bot defren } +ga2diag (GAS_comp f g) = do { f' <- ga2diag f + ; g' <- ga2diag g + ; unifyM (getOut f') (getIn g') + ; return $ DiagramComp f' g' } +ga2diag (GAS_first f) = do { [x] <- fresh 1; f' <- ga2diag f ; constrainBot f' 1 x ; return $ DiagramBypassBot f' x } +ga2diag (GAS_second f) = do { [x] <- fresh 1; f' <- ga2diag f ; constrainTop x 1 f' ; return $ DiagramBypassTop x f' } +ga2diag GAS_cancell = do { [top,x,y ,bot] <- fresh 4 ; return $ DiagramPrim "cancell" top (UPortPair x y) y bot defren } +ga2diag GAS_cancelr = do { [top,x,y ,bot] <- fresh 4 ; return $ DiagramPrim "cancelr" top (UPortPair x y) x bot defren } +ga2diag GAS_uncancell = do { [top,x,y ,bot] <- fresh 4 ; return $ DiagramPrim "uncancell" top y (UPortPair x y) bot defren } +ga2diag GAS_uncancelr = do { [top,x,y ,bot] <- fresh 4 ; return $ DiagramPrim "uncancelr" top x (UPortPair x y) bot defren } +ga2diag GAS_drop = do { [top,x ,bot] <- fresh 3 ; return $ DiagramPrim "drop" top x x bot defren } +ga2diag (GAS_const i) = do { [top,x ,bot] <- fresh 3 ; return $ DiagramPrim ("const " ++ show i) top x x bot defren } +ga2diag GAS_copy = do { [top,x,y,z,bot] <- fresh 5 + ; return $ DiagramPrim "copy" top y (UPortPair x z) bot defren } +ga2diag GAS_merge = do { [top,x,y,z,bot] <- fresh 5 + ; return $ DiagramPrim "merge" top (UPortPair x z) y bot defren } +ga2diag GAS_swap = do { [top,x,y ,bot] <- fresh 4 + ; return $ DiagramPrim "swap" top (UPortPair x y) (UPortPair x y) bot defren } +ga2diag GAS_assoc = do { [top,x,y,z,bot] <- fresh 5 + ; return $ DiagramPrim "assoc" top (UPortPair (UPortPair x y) z) (UPortPair x (UPortPair y z)) bot defren } +ga2diag GAS_unassoc = do { [top,x,y,z,bot] <- fresh 5 + ; return $ DiagramPrim "unassoc" top (UPortPair x (UPortPair y z)) (UPortPair (UPortPair x y) z) bot defren } +ga2diag (GAS_loopl f) = error "not implemented" +ga2diag (GAS_loopr f) = error "not implemented" +ga2diag (GAS_misc f ) = error "not implemented" + +defren :: String -> Int -> Int -> Int -> Ports -> Ports -> Int -> String +defren s x w top p1 p2 bot + = drawBox x top (x+w) bot "black" s +-- ++ wires (x-1) p1 x "green" +-- ++ wires (x+w) p2 (x+w+1) "red" + +xscale = 1 +yscale = 1 + +textc x y text color = + "\\node[anchor=center,color="++color++"] at ("++show (x*xscale)++"cm,"++show (y*yscale)++"cm) "++ + "{{\\tt{"++text++"}}};\n" + +drawBox x1 y1 x2 y2 color text = + "\\node[anchor=north west] at ("++show (x1*xscale)++"cm,"++show (y1*yscale)++"cm) "++ + "{{\\tt{"++text++"}}};\n" + ++ + "\\path[draw,color="++color++"]"++ + " ("++show (x1*xscale)++","++show (y1*yscale)++") rectangle ("++ + show (x2*xscale)++","++show (y2*yscale)++");\n" + +drawLine x1 y1 x2 y2 color style = + "\\path[draw,color="++color++","++style++"] "++ + "("++show (x1*xscale)++","++show (y1*yscale)++") -- " ++ + "("++show (x2*xscale)++","++show (y2*yscale)++");\n" + +width :: Diagram Ports -> Int +width (DiagramComp d1 d2) = (width d1) + 1 + (width d2) +width (DiagramPrim s _ p1 p2 _ _) = 2 +width (DiagramBypassTop p d) = (width d) + 2 +width (DiagramBypassBot d p) = (width d) + 2 + +(!) :: Map UVar Int -> UVar -> Int +m ! x = case lookup x m of + Nothing -> 0 + Just y -> y + +tikZ :: Map UVar Int -> + Diagram Ports -> + Int -> -- horizontal position + String +tikZ m = tikZ' + where + tikZ' d@(DiagramComp d1 d2) x = tikZ' d1 x + ++ wires (x+width d1) (getOut d1) (x+width d1+1) "black" + ++ tikZ' d2 (x + width d1 + 1) + tikZ' d'@(DiagramBypassTop p d) x = let top = getTop d' in + let bot = getBot d' in + drawBox x top (x+width d') bot "gray!50" "second" + ++ wires x (getIn d) (x+1) "black" + ++ tikZ' d (x+1) + ++ wires (x+1+width d) (getOut d) (x+1+width d+1) "black" + ++ wires x p (x+1+width d+1) "black" + tikZ' d'@(DiagramBypassBot d p) x = let top = getTop d' in + let bot = getBot d' in + drawBox x top (x+width d') bot "gray!50" "first" + ++ wires x (getIn d) (x+1) "black" + ++ tikZ' d (x+1) + ++ wires (x+1+width d) (getOut d) (x+1+width d+1) "black" + ++ wires x p (x+1+width d+1) "black" + tikZ' d@(DiagramPrim s (UPortVar top) p1 p2 (UPortVar bot) r) x = r s x (width d) (m ! top) p1 p2 (m ! bot) + tikZ' _ _ = error "FIXME" + + wires :: Int -> Ports -> Int -> String -> String + wires x1 (UPortVar v) x2 color = drawLine x1 (m ! v) x2 (m ! v) color "->" + -- ++ textc ((x1+x2) `div` 2) (m!v) (show v) "purple" + wires x1 (UPortPair x y) x2 color = wires x1 x x2 color ++ wires x1 y x2 color + + getTop :: Diagram Ports -> Int + getTop (DiagramComp d1 d2) = min (getTop d1) (getTop d2) + getTop (DiagramBypassTop p d) = (m ! getleft p) - 1 + getTop (DiagramBypassBot d p) = getTop d - 1 + getTop (DiagramPrim s (UPortVar ptop) _ _ _ _) = m ! ptop + getTop _ = error "getTop failed" + + getBot :: Diagram Ports -> Int + getBot (DiagramComp d1 d2) = max (getBot d1) (getBot d2) + getBot (DiagramBypassTop p d) = getBot d + 1 + getBot (DiagramBypassBot d p) = (m ! getright p) + 1 + getBot (DiagramPrim s _ _ _ (UPortVar pbot) _) = m ! pbot + getBot _ = error "getTop failed" + +resolve' (DiagramComp d1 d2) = do { d1' <- resolve' d1 ; d2' <- resolve' d2 ; return $ DiagramComp d1' d2' } +resolve' (DiagramBypassTop p d) = do { p' <- getM p ; d' <- resolve' d ; return $ DiagramBypassTop p' d' } +resolve' (DiagramBypassBot d p) = do { p' <- getM p ; d' <- resolve' d ; return $ DiagramBypassBot d' p' } +resolve' (DiagramPrim s ptop pin pout pbot r) + = do { ptop' <- getM ptop + ; pbot' <- getM pbot + ; pin' <- getM pin + ; pout' <- getM pout + ; return $ DiagramPrim s ptop' pin' pout' pbot' r } + +getleft (UPortVar v) = v +getleft (UPortPair a b) = getleft a + +getright (UPortVar v) = v +getright (UPortPair a b) = getright b + +strip :: [(Ports,Int,Ports)] -> [(UVar,Int,UVar)] +strip = map (\(v1,x,v2) -> (getright v1, x, getleft v2)) + + +-- must use bubblesort because the ordering isn't transitive +sortit :: [(UVar,Int,UVar)] -> [(UVar,Int,UVar)] +sortit x = let x' = stupidSort x [] in if x==x' then x else sortit x' + where + stupidSort [] x = x + stupidSort (h:t) x = stupidSort t (stupidInsert h x) + + stupidInsert t [] = [t] + stupidInsert t@(_,_,t') ((a@(_,_,a')):b) = if cmp' x t' a' == LT + then t:a:b + else a:(stupidInsert t b) + + cmp' :: [(UVar,Int,UVar)] -> UVar -> UVar -> Ordering + cmp' [] a b = EQ -- compare a b + cmp' ((v1,_,v2):r) a b = if a == v1 && b==v2 + then LT + else if a == v2 && b==v1 + then GT + else cmp' r a b + +lookup'' :: Map UVar Int -> UVar -> Int +lookup'' m x = case lookup x m of + Nothing -> 0 + Just y -> y + +valuatit :: Map UVar Int -> [(UVar,Int,UVar)] -> Map UVar Int +valuatit m [] = m +valuatit m ((v1,k,v2):r) = valuatit m' r + where + m' = insert v2 v2' m + v2' = max (lookup'' m v2) (k+(lookup'' m v1)) + +resolve'k :: UyM () [(Ports,Int,Ports)] +resolve'k = do { k <- getK + ; k' <- mapM (\(v1,x,v2) -> do { v1' <- getM v1 ; v2' <- getM v2 ; return (v1',x,v2') }) k + ; return k' + } + +toTikZ :: GArrowSkeleton m a b -> String +toTikZ g = tikZ m d 0 + where + (_,_,_,(d,k)) = runU $ do { d <- ga2diag g + ; d' <- resolve' d + ; k' <- resolve'k + ; return (d',k') } + s = sortit (strip k) + m = valuatit empty s +toTikZ' :: GArrowSkeleton m a b -> String +toTikZ' g = foldr (\x y -> x++"\\\\\n"++y) [] (map foo s) + where + (_,_,_,k) = runU $ ga2diag g >>= resolve' >>= \_ -> resolve'k + foo (v1,v,v2) = "x_{"++show v1++"} + "++show v++" \\leq x_{"++show v2++"} = " ++ (show $ lookup'' m v2) + s = sortit (strip k) + m = valuatit empty s + +tikz' :: (forall g a . + PGArrow g (GArrowUnit g) a -> + ( + forall b . PGArrow g (GArrowTensor g b b) b) -> + PGArrow g (GArrowUnit g) a) -> IO () +tikz' x = tikz $ optimize $ unG (x (PGArrowD { unG = GAS_const 12 }) (PGArrowD { unG = GAS_merge }) ) +main = do putStrLn "hello" +tikz example + = do putStrLn "\\documentclass{article}" + putStrLn "\\usepackage[landscape,paperwidth=20in,textheight=19in,paperheight=40in,textwidth=39in]{geometry}" + putStrLn "\\usepackage{tikz}" + putStrLn "\\usepackage{amsmath}" + putStrLn "\\begin{document}" + putStrLn $ "\\begin{tikzpicture}[every on chain/.style={join=by ->},yscale=-1]" + putStrLn (toTikZ example) + putStrLn "\\end{tikzpicture}" + --putStrLn "\\pagebreak" + --putStrLn "\\begin{align*}" + --putStr (toTikZ' example) + --putStrLn "\\end{align*}" + putStrLn "\\end{document}"