+
+
+-- 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
+
+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 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}"
projects / coq-hetmet.git / blobdiff