diff --git a/Data/LabeledTree.hs b/Data/LabeledTree.hs new file mode 100644 --- /dev/null +++ b/Data/LabeledTree.hs @@ -0,0 +1,34 @@ +{-# LANGUAGE TypeOperators #-} +module Data.LabeledTree where + +import Data.Traversable +import Data.Foldable +import Control.Applicative + +data Tree k a = Node { + rootLabel :: a, + subForest :: Forest k a +} deriving Show + +data k ::> a = k ::> a + deriving Show + +type Forest k a = [k ::> Tree k a] + +instance Functor ((::>) k) where + fmap = fmapDefault + +instance Foldable ((::>) k) where + foldMap = foldMapDefault + +instance Traversable ((::>) k) where + traverse f (k ::> v) = (::>) k <$> f v + +instance Functor (Tree k) where + fmap = fmapDefault + +instance Foldable (Tree k) where + foldMap = foldMapDefault + +instance Traversable (Tree k) where + traverse f (Node l sf) = Node <$> f l <*> (traverse (traverse (traverse f)) sf) diff --git a/DerivationTrees.hs b/DerivationTrees.hs new file mode 100644 --- /dev/null +++ b/DerivationTrees.hs @@ -0,0 +1,215 @@ +{-# LANGUAGE DisambiguateRecordFields, NamedFieldPuns, RecordWildCards, PostfixOperators, LiberalTypeSynonyms, TypeOperators #-} + +module DerivationTrees ( +-- * Basics +module Data.Monoid, +module Data.LabeledTree, + +-- * TeX extras +brace, paren, brack, tex, text, (!), + +-- * Derivation' building +-- axiom, rule, etc, aborted, +emptyDrv, haltDrv, haltDrv', abortDrv, delayPre, +dummy, rule, Derivation, Premise, Rule(..), + +-- * Figure building +Figure(..), + +-- * Engine +compile + +) where + +import DerivationTrees.Basics +import Data.List +import Data.Traversable hiding (mapM) +import Control.Monad.Writer +import Control.Monad.State +import Control.Applicative +import System.IO.Unsafe +import Data.LabeledTree +import Control.Applicative.State +import Data.Monoid + +data Rule tag = Rule {tag :: tag, style :: LineStyle, delimiter :: TeX, label :: TeX, conclusion :: TeX} + deriving Show + + +instance Monoid t => Applicative (Writer t) where + pure = return + (<*>) = ap + +type Premise = Link ::> Derivation' () +type Derivation' tag = Tree Link (Rule tag) +type Derivation = Derivation' () + +data Figure tag = Figure {ident :: Int, contents :: Derivation' tag} + +alloc = do + x <- get + put (x + 1) + return x + +------------------------------------------------------------ +-- Phase 1: Detach + +type Detach x = x -> Writer [Figure ()] x + +detachP :: Detach Premise +detachP (Detached{..} ::> d) = do + d'@(Node r ps) <- detachD d + tell [Figure {contents = Node r {delimiter = label} ps,..}] + return $ (defaultLink ::> haltDrv label d) +detachP (l ::> d) = (l ::>) <$> detachD d + +detachD :: Detach Derivation +detachD (Node n ps) = Node n <$> for ps detachP + +detachF :: Figure () -> Writer [Figure ()] () +detachF Figure{..} = do + contents <- detachD contents + tell [Figure{..}] + +detachTop :: [Figure ()] -> [Figure ()] +detachTop fs = snd $ runWriter $ for fs detachF + +-------------------------------------------------- +-- Phase 2: Delay + +insertAt n x xs = take n xs ++ x : drop n xs + +rm idx [] = [] +rm 0 (x:xs) = xs +rm n (x:xs) = x : rm (n-1) xs + +depth (Detached{} ::> _) = 2 +depth (Link{steps} ::> Node _ ps) = 1 + steps + maximum (0 : map depth ps) + +isDelayed :: Premise -> Bool +isDelayed (Delayed{} ::> _) = True +isDelayed _ = False + +delayPre a s (Link {..} ::> j) = Link {steps = s, align = a, ..} ::> j + +delayD :: Derivation -> Derivation +delayD (Node r ps0) = Node r [Link {..} ::> d | l ::> d <- ps, + let (steps,align) = case l of + Delayed{..} -> (1 + maximum (0 : map depth ps'),align) + Link{..} -> (steps,align)] + where style = Dotted + label = mempty + ps = fmap (fmap delayD) ps0 + ps' = filter (not . isDelayed) ps + + +delayF :: Figure () -> Figure () +delayF (Figure{..}) = Figure{contents = delayD contents,..} + +delayTop = map delayF + + + +--------------------------------------------------------- +-- Phase 3: Tag + +type Tag x = x () -> State Int (x Int) + +tagify :: Tag Rule +tagify (Rule {..}) = do + tag <- alloc + return $ Rule {..} + +tagifyFig :: Tag Figure +tagifyFig (Figure {..}) = Figure ident <$> traverse tagify contents + +tagifyTop :: [Figure ()] -> State Int [Figure Int] +tagifyTop = mapM tagifyFig + +---------------------------------------------------------- +-- Phase 4: Texify + +fromTeX :: TeX -> String +fromTeX (TeX s) = "\"" ++ s ++ "\"" + +mkTuple :: [String] -> String +mkTuple l = " (" ++ intercalate "," l ++ ") " + + +link (Link {..} ::> Node (Rule{tag}) _) + | steps == 0 = show tag + | otherwise = "MVD " ++ show tag ++ " " ++ + mkTuple [show steps,show "",fromTeX label,show align,show (fromEnum style)] + +type Stringize x = x Int -> Writer [String] () + +stringize :: Stringize Derivation' +stringize (Node Rule {tag = t, ..} premises) = do + traverse (traverse stringize) premises + tell ["jgm " ++ show t ++ " " ++ fromTeX conclusion ++ ";"] + tell ["Nfr " ++ show t ++ mkTuple (map link premises) ++ " " ++ + mkTuple [fromTeX label,fromTeX delimiter,fromTeX (TeX ""),show (fromEnum style)] ++ ";"] + +stringizeFig :: Figure Int -> Writer [String] () +stringizeFig (Figure {..}) = do + tell ["beginfig(" ++ show ident ++")"] + stringize contents + tell ["draw drv_tree;", + "endfig;"] + +preamble = ["outputtemplate := \"%j-%c.mps\";", + "input drv;", + "verbatimtex %&latex"] ++ lines texPreamble ++ + [ + "\\begin{document}", + "etex;", + "prologues:=3;" + ] + +texPreamble = unsafePerformIO $ readFile "preamble.tex" + +stringizeTop figs = do + tell preamble + mapM_ stringizeFig figs + tell ["end"] + +------------------------------------------ +-- Pipeline + +compile :: [Figure ()] -> [String] +compile j = snd $ runWriter $ stringizeTop $ fst $ flip runState 0 $ tagifyTop $ delayTop $ detachTop $ j + +----------------------- + +rule label conclusion = Rule {tag = (), delimiter = mempty, style = Simple, ..} + +dummy :: Rule () +dummy = (rule mempty mempty) {DerivationTrees.style = None} +emptyDrv = Node dummy [] + +abortDrv (Node Rule {..} _) = Node Rule {style = Waved, ..} [] + +-- | Used when the rest of the derivation is known. +haltDrv' :: TeX -> Derivation -> Derivation +haltDrv' tex (Node r _) = Node r {DerivationTrees.style = None} + [defaultLink {DerivationTrees.Basics.style = TeXDotted, steps = 1, DerivationTrees.Basics.label = tex} ::> emptyDrv] + +-- | More compact variant +haltDrv :: TeX -> Derivation -> Derivation +haltDrv t (Node r _) = Node r [defaultLink ::> Node dummy {conclusion = tex "vdots" [] <> tex "hspace" [TeX "2pt"] <> t} []] + + +------------------------- +brace :: TeX -> TeX +brace (TeX x) = TeX $ '{' : x ++ ['}'] +paren (TeX x) = TeX $ '(' : x ++ [')'] +brack (TeX x) = TeX $ "[" ++ x ++ "]" + +tex :: String -> [TeX] -> TeX +tex macro args = TeX ('\\' : macro) <> mconcat (map brace args) +text x = tex "text" [TeX x] + +f ! x = brace f <> TeX "_" <> brace x + + + diff --git a/DerivationTrees/Basics.hs b/DerivationTrees/Basics.hs new file mode 100644 --- /dev/null +++ b/DerivationTrees/Basics.hs @@ -0,0 +1,34 @@ +{-# LANGUAGE NoMonomorphismRestriction, GeneralizedNewtypeDeriving #-} + +module DerivationTrees.Basics + + where + +import Data.Monoid + +data LineStyle = None | Simple | Double | Dotted | Dashed | Waved | TeXDotted + deriving (Enum,Show) + +data Link = Link {label :: TeX, style :: LineStyle, align :: Alignment, steps :: Int} -- ^ Regular link + | Detached {ident :: Int, label :: TeX} -- ^ Detach the derivation as another figure + | Delayed {align :: Alignment} -- ^ automatic delaying + deriving Show + +defaultLink :: Link +defaultLink = Link mempty Dotted CenterA 0 + +data Alignment = LeftA | CenterA | RightA +instance Show Alignment where + show LeftA = "l" + show CenterA = "c" + show RightA = "r" + +newtype TeX = TeX String + deriving (Show, Monoid) + +(<>) = mappend + +void :: TeX -> Bool +void (TeX x) = null x + + diff --git a/DerivationTrees/CPTS.hs b/DerivationTrees/CPTS.hs new file mode 100644 --- /dev/null +++ b/DerivationTrees/CPTS.hs @@ -0,0 +1,296 @@ +{-# LANGUAGE RecordWildCards, DisambiguateRecordFields, GADTs, KindSignatures, GeneralizedNewtypeDeriving, TypeSynonymInstances #-} + +module DerivationTrees.CPTS where + +import Prelude hiding (abs, pi) +import Data.List +import DerivationTrees +import DerivationTrees.Basics +import Data.Monoid +import qualified DerivationTrees.ManualPTS as M +import Debug.Trace + +class Unifyable a where + (===) :: a -> a -> Bool + +class TeXable a where + texify :: a -> TeX + +instance Show (a -> b) where + show _ = "" + + +data V = V Name | Unbound + deriving (Eq, Show) + +type Name = String +type Sort = String +type Colour = String + + +data Binding :: * where + (:-) :: V -> Term -> Binding + Base :: Name -> Binding + Mult :: Binding -> Binding + deriving (Eq, Show) + +data Term :: * where + Lam :: Colour -> Binding -> Term -> Term + Pi :: Colour -> Binding -> Term -> Term + App :: Colour -> Term -> Term -> Term + Sub :: Term -> Binding -> Term + Var :: Name -> Term + Con :: Name -> Term + Sor :: Sort -> Term + Many :: Term -> Term + deriving (Eq, Show) + +-- Short notation (for colourless) +lam = Lam "" +(~~>) = Pi "" +($$) = App "" +subs = Sub +var = Var +(|=>) = Sub + +infixl |=> + + +-- TODO: BIG FAT HACK! +dS :: (Name,Term) -> Term -> Term +dS (n,s) t | s == t = Var n +dS s (Sub t b) = t +dS s (App k f a) = App k (dS s f) (dS s a) +dS s (Pi k f a) = Pi k f (dS s a) +dS s (Many t) = Many (dS s t) +dS s t = t + +-- Helper for non-dependent arrow +(Many t) --> u = Mult (Unbound :- t) ~~> u +t --> u = (Unbound :- t) ~~> u + +data Jug = Jug {value :: Term, typ :: Term, env :: Env} + deriving Show + +data Drv :: * where + Ax :: Drv + St :: Sort -> Drv -> Drv + Wk :: Int -> Sort -> Drv -> Drv -> Drv + Ab :: Sort -> Drv -> Drv -> Drv + Ap :: Binding -> Drv -> Drv -> Drv + Pr :: Colour -> (Sort,Sort) -> Drv -> Drv -> Drv + Co :: Sort -> Term -> Drv -> Drv -> Drv + An :: (Derivation -> Derivation) -> Drv -> Drv -- Arbitrary annotation / change + Ln :: Link -> Drv -> Drv + -- Ma :: Drv -> Drv + -- Re :: TeX -> Jug -> Drv -> Drv + deriving Show + +wk = Wk 0 + +type Env = [Binding] + +unbound :: Binding -> Bool +unbound (Mult x) = unbound x +unbound (Unbound :- _) = True +unbound (_ :- _) = False + +bound = not . unbound + + +instance Unifyable V where + Unbound === _ = True + _ === Unbound = True + x === y = x == y + +instance Unifyable Term where + (===) = (==) + +instance Unifyable Binding where + (x :- t) === (x' :- t') = (x === x') && (t === t') + Mult x === Mult x' = x === x' + x === x' = False + +instance TeXable Sort where + texify ('~':v) = M.tso (TeX v) + texify v = TeX v + + +interpV :: V -> TeX +interpV (V v) = texify v +interpV (Unbound) = TeX "?" + +interpB :: Binding -> TeX +interpB = interpB' (tex "IS" [mempty]) + +interpB' :: TeX -> Binding -> TeX +interpB' ass (x :- t) = interpV x <> ass <> interpT ColonRhs t +interpB' ass (Base x) = texify x +interpB' ass (Mult x) = M.many (interpB' ass x) + + +col :: Colour -> String -> [TeX] -> TeX +col "" macro args = tex macro args +col c macro args = tex (macro ++ "C") (TeX c:args) + +data Ctx = ArrowLhs | TopLvl | ColonRhs | BinderRhs | ApplLhs | ApplRhs | SubsLhs + +havePrn :: Ctx -> Term -> Bool +havePrn SubsLhs (Sub _ _) = False +havePrn ApplLhs (Sub _ _) = False +havePrn ApplLhs (App _ _ _) = False + +havePrn TopLvl _ = False +havePrn BinderRhs _ = False +havePrn ColonRhs (Lam _ _ _) = True +havePrn ColonRhs (Pi _ b _) | bound b = True +havePrn ColonRhs _ = False +havePrn _ _ = True + +parn context t = if havePrn context t then paren else id + +interpT :: Ctx -> Term -> TeX + +interpT d (App _ (Var ('\\':macroName)) t) = tex macroName [interpT TopLvl t] + +interpT d e@(Lam c a b) = parn d e $ col c "LAMBDA" [interpB a, interpT BinderRhs b] +interpT d e@(Pi c a b) | unbound a = parn d e $ col c "ARROW" [interpT ArrowLhs (bToT a), (interpT BinderRhs b)] +interpT d e@(Pi c a b) = parn d e $ col c "FORALL" [interpB a, interpT BinderRhs b] +interpT d e@(App c f a) = parn d e $ col c "APP" [interpT ApplLhs f, interpT ApplRhs a] +interpT d e@(Sub t b) = parn d e $ (interpT SubsLhs t <> brack (interpB' (tex "mapsto" [mempty]) b)) +interpT d e@(Var x) = texify x +interpT d e@(Con x) = texify x +interpT d e@(Many t) = M.many (interpT d t) +interpT d e@(Sor s) = texify s + +instance TeXable Term where + texify t = interpT ColonRhs t + +(+:) :: Binding -> Env -> Env +b +: e | unbound b = e +b +: e = b : e + +interpE :: Env -> [TeX] +interpE e = (map interpB $ reverse e) + +renam :: Term -> TeX +renam (Sor x) = texify x +renam x = (interpT ApplRhs x ! TeX "i") + +-- nterpret the non-context part of an assertion. +interpA :: Term -> Term -> (TeX,TeX) +interpA (Many x) (Many t) = (renam x, renam t) +interpA (Many x) (Sor t) = (renam x, texify t) +interpA x t = (texify x,texify t) + +interpJ :: Jug -> TeX +interpJ (Jug v t env) = M.assert (interpE env) v' t' + where (v',t') = interpA v t + +check :: Bool -> String -> (a -> a) +check True _ = id +check False msg = error msg + +-- Binding to 1 type. +bToT :: Binding -> Term +bToT (Mult b) = Many (bToT b) +bToT (_ :- t) = t +bToT _ = error "invalid binding for extraction" + +-- Reconstruct a binding, assuming the 1st term is a variable-like thing. +rebind :: Term -> Term -> Binding +rebind (Many x) (Many t) = Mult (rebind x t) +rebind (Many x) (Sor s) = Mult (rebind x (Sor s)) +rebind (Var x) t = V x :- t +rebind x t = error $ "Expected variable, but got: " ++ show x + +push (Many (App c f a)) = App c (push (Many f)) (push (Many a)) +push t = t + +subsOf (V x :- _ , t) = (x,t) +subsOf (Mult x,Many t) = subsOf (x,t) +subsOf _ = ("no variable",Con "no term") + + +jug' :: Term -> Sort -> Env -> Jug +jug' (Many x) s env = Jug (Many x) (Many (Sor s)) env +jug' x s env = Jug x (Sor s) env + +rtext = rule . text + +rm idx [] = [] +rm 0 (x:xs) = xs +rm n (x:xs) = x : rm (n-1) xs + +stp :: Drv -> Jug -> (TeX -> Rule (), [(Drv,Jug)]) +stp Ax _ = (\c -> (rtext "" c) {-DerivationTrees.style = None-}, []) +stp (St s d) (Jug v t (b':env)) = check (b === b') ("Start: bindings do not match: " ++ show (b, b')) + $ (rtext "st", [(d, Jug t (Sor s) env)]) + where b = rebind v t +stp (Wk idx s rest d) (Jug v t env) = (rtext label, [(rest,Jug v t env'), (d, jug' (bToT b) s env')]) + where env' = rm idx env + b = env !! idx + label | idx == 0 = "wk" + | otherwise = "wk (" ++ show idx ++ ")" + +stp (Co s typ d e) (Jug v t env) = + (rtext "conv", [(d,Jug v typ env), (e, jug' t s env)]) + where betaCond = rule mempty (interpT TopLvl typ <> TeX "=_\\beta " <> interpT TopLvl t) +stp (Ab s d e) (Jug (Lam k a bo) (Pi k' a' b) env) = check (k == k') ("Abstraction: colours do not match" ++ show (k,k')) $ + check (a === a') ("Abstraction: bindings do not match: " ++ show (a, a')) $ + (rtext "abs", [(d,Jug bo b (a:env)), (e,Jug (Pi k a' b) (Sor s) env)]) +stp (Pr k (s1,s2) d e) (Jug (Pi k' a b) (Sor s3) env) = check (k == k') ("Product: colours do not match" ++ show (k,k')) $ + (rule name, [(d,jug' (bToT a) s1 env),(e,jug' b s2 (a+:env))]) + where (cname,cargs) = if s2 == s3 then ("ptsrule",[s1,s2]) else ("prodrule",[s1,s2,s3]) + (fname,fargs) = if null k then (id,id) else ((++ "c"), (k:)) + name = tex (fname cname) (map texify $ fargs cargs) + +-- stp (Ma d) (Jug v t env) = (rule (text "many"), [(d,Jug (push v) (push t) env)]) + +-- if a substitution is there, eat it. +stp (Ap b d e) (Jug (App k f a) t env) = trace (show subst) $ + (rtext "app", [(d,Jug f (Pi k b (dS subst t)) env),(e,Jug a (bToT b) env)]) + + where subst = subsOf (b, a) +stp (Ap (Mult b) d e) (Jug (Many (App k f a)) (Many t) env) = + (rtext "app", [(d,Jug (Many f) (Many (Pi k b t)) env),(e,Jug (Many a) (Many (bToT b)) env)]) + -- Used only once in the product rule (many (f x)) + + + +-- stp (An f d) j = (rtext "usr", [(d,j)]) +-- stp (Re t j d) j' = (rule t, [(d,j)]) + + +stp r j = error $ "Unsupported: rule " ++ show r ++ " on judgement " ++ show j + +interp :: Drv -> Jug -> Derivation +interp (An f x) j = f $ interp x j +interp (Ln l x) j = interp x j +interp d j = Node (r (interpJ j)) [link d' ::> interp d' j' | (d',j') <- x] + where (r,x) = (stp d j) + link (Ln l _) = l + link _ = defaultLink + +------------------- + +dL = Ln (Delayed {align = LeftA}) +dC = Ln (Delayed {align = CenterA}) +dR = Ln (Delayed {align = RightA}) + +delay :: Alignment -> Int -> Drv -> Drv +delay align steps = Ln (Link {DerivationTrees.Basics.style = Dotted, ..}) + where label=mempty + +detach l ident = Ln (Detached {label = text ('(' : l ++ ")"),..}) + +halt :: String -> Drv +halt txt = An (haltDrv (text txt)) Ax + +named :: String -> Drv -> Drv +-- named txt = An (\(Node r ps) -> Node r [defaultLink ::> Node (rule mempty (text txt)) {DerivationTrees.style = Double} ps]) +named txt = An (\(Node r ps) -> Node r {delimiter = text txt} ps) + +abort :: Drv +abort = An abortDrv Ax -- (error "abort: Should stop") + diff --git a/DerivationTrees/ManualPTS.hs b/DerivationTrees/ManualPTS.hs new file mode 100644 --- /dev/null +++ b/DerivationTrees/ManualPTS.hs @@ -0,0 +1,19 @@ +module DerivationTrees.ManualPTS where + +import DerivationTrees +import DerivationTrees.Basics +import Data.List + +assert env val typ = tex "Assert" [mconcat $ intersperse (TeX ",") env,val,typ] +(-:) var typ = brace var <> tex "IS" [] <> brace typ + +lam binding body = tex "LAMBDA" [binding, body] +pi binding body = tex "FORALL" [binding, body] +subs term var s = tex "SUBS" [term,var,s] +($$) fun arg = tex "APP" [fun, arg] +tso s = tex "tsort" [s] +many x = tex "many" [x] +x --> y = brace x <> tex "to" [mempty] <> brace y + + + diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,340 @@ + GNU GENERAL PUBLIC LICENSE + Version 2, June 1991 + + Copyright (C) 1989, 1991 Free Software Foundation, Inc. + 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The licenses for most software are designed to take away your +freedom to share and change it. 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Of course, the commands you use may +be called something other than `show w' and `show c'; they could even be +mouse-clicks or menu items--whatever suits your program. + +You should also get your employer (if you work as a programmer) or your +school, if any, to sign a "copyright disclaimer" for the program, if +necessary. Here is a sample; alter the names: + + Yoyodyne, Inc., hereby disclaims all copyright interest in the program + `Gnomovision' (which makes passes at compilers) written by James Hacker. + + , 1 April 1989 + Ty Coon, President of Vice + +This General Public License does not permit incorporating your program into +proprietary programs. If your program is a subroutine library, you may +consider it more useful to permit linking proprietary applications with the +library. If this is what you want to do, use the GNU Library General +Public License instead of this License. diff --git a/Main.hs b/Main.hs new file mode 100644 --- /dev/null +++ b/Main.hs @@ -0,0 +1,236 @@ +{-# LANGUAGE RecordWildCards, DisambiguateRecordFields #-} +import Prelude hiding (abs) +import DerivationTrees +import DerivationTrees.Basics +import DerivationTrees.CPTS + + +translateE :: [Binding] -> [Binding] +translateE = concatMap translateB + +translateJ (Jug v t e) = Jug (translate v) (translate t $$ Many v) (translateE e) + +translateB :: Binding -> [Binding] +translateB (V x :- a) = [(V ("\\subR " ++ x) :- (translate a $$ Many (var x))), Mult (V x :- a)] +translateB (Base (x)) = [Base ("\\trans " ++ x)] + +translate :: Term -> Term +translate (Var x) = Var ("\\subR " ++ x) +translate (Con x) = Con ("\\trans " ++ x) +translate (Sor s) = (lam (Mult (V "A" :- Sor s)) ((Many $ var "A") --> Sor ('~':s))) + +translate (App k f a) = App (k++"_m") (App (k++"_i") (translate f) (Many a)) (translate a) +translate (Lam k a b) = Lam (k++"_i") w $ + Lam (k++"_m") w' $ + translate b + where [w',w] = translateB a +translate (Sub t (V x :- a)) = Sub (Sub (translate t) w) w' + where w = Mult (V x :- a) + w' = V ("\\subR " ++ x) :- translate a +translate t@(Pi k a@(V x :- _) b) + = lam (Mult (V "f" :- t)) $ + Pi (k++"_i") w $ + Pi (k++"_m") w' $ + (translate b $$ Many (App k (var "f") (var x))) + where [w',w] = translateB a + + + + +pr0 = Pr "" + +axiomJ = translateJ (Jug (Sor "s") (Sor "t") []) + where a = V "A" + a' = Many $ var "A" + + +axiomT = Co "~u" (Many (Sor "s") --> Sor "~t") + (Ab "~u" + (pr0 ("s","~t") + (St "t" Ax) + (wk "t" Ax Ax)) + + (pr0 ("t","~u") + Ax + Ax)) + (delay CenterA 4 $ Ap (Mult (Unbound :- Sor "t")) + (Ab "~v" + (pr0 ("t","~u") + (St "u" Ax) + (wk "u" Ax Ax)) + (pr0 ("u","~v") Ax Ax)) + + Ax) + +ind' = halt "ind'" +ind = halt "ind" +lem = halt "lem" +gamma = [Base "\\Gamma"] + +startJ = translateJ $ Jug (Var "x") (Con "A") [V "x" :- Con "A" ,Base ("\\Gamma")] +startT = St "~s" (Ap (Mult (Unbound :- Con "A")) + (wk "s~" ind' lem) + (St "s" lem)) + +weakJ = translateJ $ Jug (Con "A") (Con "B") [V "x" :- Con "C" ,Base ("\\Gamma")] +weakT = wk "~s" + (wk "s" + ind + lem) + (Ap (Mult (Unbound :- Con "C")) + (wk "s" ind' lem) + (St "s" lem)) + +protoPi = (Pi "k" (V "x" :- Con "A") (Con "B")) +protoLam = (Lam "k" (V "x" :- Con "A") (Con "b")) + +prodJ = translateJ $ Jug protoPi (Sor "s_3") gamma +prodT = Co "~t_3" (Many protoPi --> Sor "~s_3") + (dL $ + Ab "~t_3" + (dL $ Pr "k_i" ("s_1","~s_3") + (wk "s_3" lem lem) + (dR $ Pr "k_m" ("~s_1","~s_2") + (detach "1" 31 $ Ap (Mult (Unbound :- Con "A")) + (dL $ wk "s_1" + (wk "s_3" + ind' + lem) + lem) + (St "s_1" + (named "(2)" $ wk "s_3" + lem + lem)) + ) + (wk "~s_1" + (dL $ Ap (Mult (Unbound :- Con "B")) + (wk "s_1" + (wk "s_3" + ind' + lem) + lem) + (dR $ Ap (Mult (V "x" :- Con "A")) + (dC $wk "s_1" + (St "s_3" + lem) + (halt "(2)")) + (St "s_1" (halt "(2)"))) + ) + (halt "(1)")) + )) + (pr0 ("s_3","~t_3") lem Ax) + ) + (Ap (Mult (Unbound :- Sor "s_3")) + (dL $ Ab "~u_3" + (pr0 ("s_3","~t_3") + (St "t_3" Ax) + (wk "t_3" Ax Ax)) + (pr0 ("t_3", "~u_3") + Ax + Ax)) + (halt "lem")) + +{- +subst x a b = + +nf (App _ (Lam _ (Mult (V x :- _)) b) a) = subst x a b + +-} + + + + +applJ = translateJ $ Jug (App "k" (Con "F") (Con "a")) (Sub (Con "B") (V "x" :- Con "a")) gamma +applT = (Ap (V "\\subR x" :- (translate (Con "A") $$ (Many $ Con "a"))) + (Ap (Mult (V "x" :- Con "A")) + (dL $ Co "~s_B" (translate protoPi) + (dL $ ind) + (Pr "k_i" ("s_A","~s_B") + (lem) + (Pr "k_m" ("~s_A","~s_B") + (dL $ named "(1)" $ wk "s_A" + (Ap (Mult (Unbound :- Con "A")) (ind') (lem)) + lem) + (wk "~s_A" + (Ap (Mult (Unbound :- Con "B")) + (wk "s_A" + (ind') + (lem)) + (dC $ Ap (Mult (V "x" :- Con "A")) + (wk "s_A" lem lem) + (St "s_A" lem))) + (halt "(1)") + )) + )) + lem) + ind) + +abstJ = translateJ $ Jug protoLam protoPi gamma +abstT = Co "~s" (Pi "k_i" (Mult ((:-) (V "x") (Con "A"))) (Pi "k_m" ((:-) (V "\\subR x") (App "" (Con "\\trans A") (Many (Var "x")))) (App "" (Con "\\trans B") (Many $ Con "b")))) + (dL $ Ab "~s" + (dL $ Ab "~s" + (wk "~s_A" + (wk "s_A" ind lem) + (halt "(1)")) + (dR $ named "(3)" $ + Pr "k_m" ("~s_A","~s") + (named "(1)" $ Ap (Mult (Unbound :- Con "A")) + (wk "s_A" ind' lem) + (St "s_A" lem)) + (delay CenterA 3 $ wk "~s_A" + (wk "s_A" + (Ap (Mult (Unbound :- Con "B")) + ind' + lem) + lem) + (halt "(1)")) + ) + ) + (Pr "k_i" ("s_A","~s") + lem + (halt ("(3)")))) + (detach "S" 51 $ Ap (Mult (V "f" :- protoPi)) + (dL $ Ab "~t" + (dL $ Pr "k_i" ("s_A","~s") + (wk "s" lem lem) + (dR $ Pr "k_m" ("~s_A","~s") + (named "(2)" $ Wk 1 "s" + (halt "(1)") + (wk "s_A" lem lem)) + (dR $ wk "~s_A" + (dL $ Ap (Mult (Unbound :- Con "B")) + (wk "s_A" + (wk "~s" + ind' + lem) + -- (wk "s" lem lem) + (named "(4)" $ wk "s" lem lem) + ) + (dR $ Ap (Mult (V "x" :- Con "A")) + (dC $ wk "s_A" + (St "s" lem) + (halt "(4)") + ) + (St "s_A" (halt "(4)")) + )) + (halt "(2)")))) + (pr0 ("s","~t") lem + (wk "s" Ax lem))) + lem) + +convJ = translateJ $ Jug (Con "A") (Con "B'") gamma +convT = Co "~s" (translate (Con "B") $$ (Many $ Con "A")) + ind + (Ap (Mult (Unbound :- Con "B'")) + ind' + lem) + +main = writeFile "AbsProof.mp" $ unlines $ compile [Figure 0 (interp axiomT axiomJ), + Figure 1 (interp startT startJ), + Figure 2 (interp weakT weakJ), + Figure 3 (interp prodT prodJ), + Figure 4 (interp applT applJ), + Figure 5 (interp abstT abstJ), + Figure 6 (interp convT convJ) + ] + diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,4 @@ +#!/usr/bin/env runhaskell +import Distribution.Simple +main :: IO () +main = defaultMain diff --git a/derivation-trees.cabal b/derivation-trees.cabal new file mode 100644 --- /dev/null +++ b/derivation-trees.cabal @@ -0,0 +1,28 @@ +name: derivation-trees +version: 0.7.1 +category: Graphics, Math +synopsis: Typeset Derivation Trees via MetaPost +description: + A library to typeset derivation trees via Laurent Mehats metapost package. + Also contains a module to ease the generation of trees for (coloured) pure type systems. +license: GPL +license-file: LICENSE +author: Jean-Philippe Bernardy +maintainer: jeanphilippe.bernardy@gmail.com +Cabal-Version: >= 1.8 +tested-with: GHC==6.12.1 +build-type: Simple + +extra-source-files: Main.hs + +library + build-depends: base==4.* + build-depends: mtl==1.1.* + build-depends: applicative-extras==0.1.* + exposed-modules: + Data.LabeledTree + DerivationTrees + DerivationTrees.Basics + DerivationTrees.ManualPTS + DerivationTrees.CPTS +