-{-# 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 <megacz@acm.org>
+-- 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}"
projects / coq-hetmet.git / blobdiff