{-# OPTIONS_GHC -XModalTypes -XMultiParamTypeClasses -XNoMonoPatBinds -XKindSignatures -XGADTs -XFlexibleContexts -XFlexibleInstances -XTypeOperators -XUndecidableInstances -XTypeFamilies #-} module GArrowTikZ (tikz, tikz', GArrowTikZ(..)) where 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 GHC.HetMet.Private {- TO DO: - have "resolve" turn a (Diagram UnifVal) into (Diagram Int) - custom rendering - bias right now is for all edges to be uppermost; try for bias towards smallest nodes? - curvy boxes (like XOR gates) -} -- a unification value is basically a LISP-ish expression data UVal = UVVar UVar | UVVal [UVal] instance Unifiable UVal where unify' (UVVal vl1) (UVVal vl2) | length vl1 /= length vl2 = error "length mismatch during unification" | otherwise = foldr mergeU emptyUnifier (map (\(x,y) -> unify x y) $ zip vl1 vl2) unify' _ _ = error "impossible" inject = UVVar project (UVVar v) = Just v project _ = Nothing occurrences (UVVar v) = [v] occurrences (UVVal vl) = concatMap occurrences vl -- | Resolves a unification variable; the answer to this query will change if subsequent unifications are performed getU' :: Unifier UVal -> UVal -> UVal getU' u (UVVal vl) = UVVal $ map (getU' u) vl getU' u x@(UVVar 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 -- type Constraints = [(UVal, Int, UVal)] -- the unification monad data UyM t a = UyM (([UVar],Unifier UVal,Constraints) -> ([UVar],Unifier UVal,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 => UVal -> UVal -> 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 :: UVal -> Int -> UVal -> UyM t () constrain v1 d v2 = UyM $ \(i,u,k) -> (i,u,((v1,d,v2):k),()) getK :: UyM t [(UVal, Int, UVal)] getK = UyM $ \(i,u,k) -> (i,u,k,k) runU :: UyM t a -> ([UVar],Unifier UVal,Constraints,a) runU (UyM f) = (f (uvarSupply,emptyUnifier,[])) data GArrowTikZ :: * -> * -> * where TikZ_const :: Int -> GArrowTikZ () Int TikZ_id :: GArrowTikZ x x TikZ_comp :: GArrowTikZ y z -> GArrowTikZ x y -> GArrowTikZ x z TikZ_first :: GArrowTikZ x y -> GArrowTikZ (x**z) (y**z) TikZ_second :: GArrowTikZ x y -> GArrowTikZ (z**x) (z**y) TikZ_cancell :: GArrowTikZ (()**x) x TikZ_cancelr :: GArrowTikZ (x**()) x TikZ_uncancell :: GArrowTikZ x (()**x) TikZ_uncancelr :: GArrowTikZ x (x**()) TikZ_assoc :: GArrowTikZ ((x**y)**z) (x**(y**z)) TikZ_unassoc :: GArrowTikZ (x**(y**z)) ((x**y)**z) TikZ_drop :: GArrowTikZ x () TikZ_copy :: GArrowTikZ x (x**x) TikZ_swap :: GArrowTikZ (x**y) (y**x) TikZ_merge :: GArrowTikZ (x**y) z TikZ_loopl :: GArrowTikZ (x**z) (y**z) -> GArrowTikZ x y TikZ_loopr :: GArrowTikZ (z**x) (z**y) -> GArrowTikZ x y -- -- Technically this instance violates the laws (and RULEs) for -- Control.Category; the compiler might choose to optimize (f >>> id) -- into f, and this optimization would produce a change in behavior -- below. In practice this means that the user must be prepared for -- the rendered TikZ diagram to be merely *equivalent to* his/her -- term, rather than structurally exactly equal to it. -- instance Category GArrowTikZ where id = TikZ_id (.) = TikZ_comp instance GArrow GArrowTikZ (**) () where ga_first = TikZ_first ga_second = TikZ_second ga_cancell = TikZ_cancell ga_cancelr = TikZ_cancelr ga_uncancell = TikZ_uncancell ga_uncancelr = TikZ_uncancelr ga_assoc = TikZ_assoc ga_unassoc = TikZ_unassoc instance GArrowDrop GArrowTikZ (**) () where ga_drop = TikZ_drop instance GArrowCopy GArrowTikZ (**) () where ga_copy = TikZ_copy instance GArrowSwap GArrowTikZ (**) () where ga_swap = TikZ_swap instance GArrowLoop GArrowTikZ (**) () where ga_loopl = TikZ_loopl ga_loopr = TikZ_loopr type instance GArrowTensor GArrowTikZ = (,) type instance GArrowUnit GArrowTikZ = () type instance GArrowExponent GArrowTikZ = (->) instance GArrowSTKC GArrowTikZ name :: GArrowTikZ a b -> String name TikZ_id = "id" name (TikZ_const i) = "const " ++ show i name (TikZ_comp _ _) = "comp" name (TikZ_first _ ) = "first" name (TikZ_second _ ) = "second" name TikZ_cancell = "cancell" name TikZ_cancelr = "cancelr" name TikZ_uncancell = "uncancell" name TikZ_uncancelr = "uncancelr" name TikZ_drop = "drop" name TikZ_copy = "copy" name TikZ_swap = "swap" name (TikZ_loopl _ ) = "loopl" name (TikZ_loopr _ ) = "loopr" name TikZ_assoc = "assoc" name TikZ_unassoc = "unassoc" fresh1 :: UyM () Ports fresh1 = do { x <- freshU ; return $ UVVar x } fresh2 :: UyM () (Ports,Ports) fresh2 = do { x <- freshU ; y <- freshU ; constrain (UVVar x) 1 (UVVar y) ; return $ (UVVar x,UVVar y) } fresh3 :: UyM () (Ports,Ports,Ports) fresh3 = do { x <- freshU ; y <- freshU ; z <- freshU ; constrain (UVVar x) 1 (UVVar y) ; constrain (UVVar y) 1 (UVVar z) ; return $ (UVVar x,UVVar y,UVVar z) } fresh4 :: UyM () (Ports,Ports,Ports,Ports) fresh4 = do { x1 <- freshU ; x2 <- freshU ; x3 <- freshU ; x4 <- freshU ; constrain (UVVar x1) 1 (UVVar x2) ; constrain (UVVar x2) 1 (UVVar x3) ; constrain (UVVar x3) 1 (UVVar x4) ; return $ (UVVar x1,UVVar x2,UVVar x3,UVVar x4) } fresh5 :: UyM () (Ports,Ports,Ports,Ports,Ports) fresh5 = do { x1 <- freshU ; x2 <- freshU ; x3 <- freshU ; x4 <- freshU ; x5 <- freshU ; constrain (UVVar x1) 1 (UVVar x2) ; constrain (UVVar x2) 1 (UVVar x3) ; constrain (UVVar x3) 1 (UVVar x4) ; constrain (UVVar x4) 1 (UVVar x5) ; return $ (UVVar x1,UVVar x2,UVVar x3,UVVar x4,UVVar x5) } --example = ga_first ga_drop >>> ga_cancell >>> ga_first id >>> ga_swap >>> ga_first id >>> TikZ_merge --example :: forall x y z. forall g. (GArrow g (,) (), GArrowCopy g (,) (), GArrowSwap g (,) ()) => g x ((x,x),x) --example = ga_copy >>> ga_second ga_copy >>> ga_second (ga_first id) >>> ga_unassoc >>> ga_first ga_swap --example = ga_copy >>> ga_second ga_copy >>> ga_second (ga_second id) >>> ga_unassoc >>> ga_first id >>> ga_first ga_swap --example :: forall x. forall g. (GArrow g (,) (), GArrowCopy g (,) (), GArrowSwap g (,) ()) => g x x --example = id >>> id 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 = UVal getOut :: Diagram Ports -> Ports getOut (DiagramComp f g) = getOut g getOut (DiagramPrim s ptop pin pout pbot _) = pout getOut (DiagramBypassTop p f) = UVVal [p, (getOut f)] getOut (DiagramBypassBot f p) = UVVal [(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) = UVVal [p, (getIn f)] getIn (DiagramBypassBot f p) = UVVal [(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 :: GArrowTikZ a b -> UyM () (Diagram Ports) ga2diag (TikZ_id ) = do { (top,x,bot) <- fresh3 ; return $ DiagramPrim "id" top x x bot defren } ga2diag (TikZ_comp g f) = do { f' <- ga2diag f ; g' <- ga2diag g ; unifyM (getOut f') (getIn g') ; return $ DiagramComp f' g' } ga2diag (TikZ_first f) = do { x <- fresh1; f' <- ga2diag f ; constrainBot f' 1 x ; return $ DiagramBypassBot f' x } ga2diag (TikZ_second f) = do { x <- fresh1; f' <- ga2diag f ; constrainTop x 1 f' ; return $ DiagramBypassTop x f' } ga2diag TikZ_cancell = do { (top,x,y ,bot) <- fresh4 ; return $ DiagramPrim "cancell" top (UVVal [x,y]) y bot defren } ga2diag TikZ_cancelr = do { (top,x,y ,bot) <- fresh4 ; return $ DiagramPrim "cancelr" top (UVVal [x,y]) x bot defren } ga2diag TikZ_uncancell = do { (top,x,y ,bot) <- fresh4 ; return $ DiagramPrim "uncancell" top y (UVVal [x,y]) bot defren } ga2diag TikZ_uncancelr = do { (top,x,y ,bot) <- fresh4 ; return $ DiagramPrim "uncancelr" top x (UVVal [x,y]) bot defren } ga2diag TikZ_drop = do { (top,x ,bot) <- fresh3 ; return $ DiagramPrim "drop" top x x bot defren } ga2diag (TikZ_const i) = do { (top,x ,bot) <- fresh3 ; return $ DiagramPrim ("const " ++ show i) top x x bot defren } ga2diag TikZ_copy = do { (top,x,y,z,bot) <- fresh5 ; return $ DiagramPrim "copy" top y (UVVal [x,z]) bot defren } ga2diag TikZ_merge = do { (top,x,y,z,bot) <- fresh5 ; return $ DiagramPrim "merge" top (UVVal [x,z]) y bot defren } ga2diag TikZ_swap = do { (top,x,y ,bot) <- fresh4 ; return $ DiagramPrim "swap" top (UVVal [x,y]) (UVVal [x,y]) bot defren } ga2diag TikZ_assoc = do { (top,x,y,z,bot) <- fresh5 ; return $ DiagramPrim "assoc" top (UVVal [UVVal [x,y],z])(UVVal [x,UVVal [y,z]]) bot defren } ga2diag TikZ_unassoc = do { (top,x,y,z,bot) <- fresh5 ; return $ DiagramPrim "unassoc" top (UVVal [x,UVVal [y,z]])(UVVal [UVVal [x,y],z]) bot defren } ga2diag (TikZ_loopl f) = error "not implemented" ga2diag (TikZ_loopr 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" ++ drawLine x (top+1) (x+width d') (top+1) "black" "->" ++ wires x (getIn d) (x+1) "black" ++ tikZ' d (x+1) ++ wires (x+1+width d) (getOut d) (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" ++ drawLine x (bot-1) (x+width d') (bot-1) "black" "->" ++ wires x (getIn d) (x+1) "black" ++ tikZ' d (x+1) ++ wires (x+1+width d) (getOut d) (x+1+width d+1) "black" tikZ' d@(DiagramPrim s (UVVar top) p1 p2 (UVVar bot) r) x = r s x (width d) (m ! top) p1 p2 (m ! bot) wires :: Int -> Ports -> Int -> String -> String wires x1 (UVVar v) x2 color = drawLine x1 (m ! v) x2 (m ! v) color "->" -- ++ textc ((x1+x2) `div` 2) (m!v) (show v) "purple" wires x1 (UVVal vl) x2 color = foldr (\x y -> x ++ " " ++ y) [] (map (\v -> wires x1 v x2 color) vl) 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 (UVVar ptop) _ _ _ _) = m ! ptop 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 _ _ _ (UVVar pbot) _) = m ! pbot 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 (UVVar v) = v getleft (UVVal vl) = getleft (head vl) getright (UVVar v) = v getright (UVVal vl) = getright (last vl) 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 = stupidSort 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 :: GArrowTikZ 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' :: GArrowTikZ 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 -> PGArrow g (GArrowUnit g) a) -> IO () tikz' x = tikz $ unG (x (PGArrowD { unG = TikZ_const 12 })) main = do putStrLn "hello" tikz example = do putStrLn "\\documentclass{article}" putStrLn "\\usepackage[landscape,paperheight=20in,textwidth=19in]{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 "\\begin{align*}" -- putStr (toTikZ' example) -- putStrLn "\\end{align*}" putStrLn "\\end{document}"