forked from GitHub/gf-core
Founding the newly structured GF2.0 cvs archive.
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aarne
210
src/GF/Grammar/TC.hs
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210
src/GF/Grammar/TC.hs
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module TC where
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import Operations
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import Abstract
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import AbsCompute
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import Monad
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-- Thierry Coquand's type checking algorithm that creates a trace
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data AExp =
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AVr Ident Val
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| ACn QIdent Val
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| AType
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| AInt Int
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| AStr String
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| AMeta MetaSymb Val
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| AApp AExp AExp Val
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| AAbs Ident Val AExp
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| AProd Ident AExp AExp
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| AEqs [([Exp],AExp)] ---
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deriving (Eq,Show)
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type Theory = QIdent -> Err Val
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lookupConst :: Theory -> QIdent -> Err Val
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lookupConst th f = th f
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lookupVar :: Env -> Ident -> Err Val
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lookupVar g x = maybe (prtBad "unknown variable" x) return $ lookup x ((IW,uVal):g)
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-- wild card IW: no error produced, ?0 instead.
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type TCEnv = (Int,Env,Env)
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emptyTCEnv :: TCEnv
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emptyTCEnv = (0,[],[])
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whnf :: Val -> Err Val
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whnf v = ---- errIn ("whnf" +++ prt v) $ ---- debug
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case v of
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VApp u w -> do
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u' <- whnf u
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w' <- whnf w
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app u' w'
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VClos env e -> eval env e
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_ -> return v
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app :: Val -> Val -> Err Val
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app u v = case u of
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VClos env (Abs x e) -> eval ((x,v):env) e
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_ -> return $ VApp u v
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eval :: Env -> Exp -> Err Val
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eval env e = ---- errIn ("eval" +++ prt e +++ "in" +++ prEnv env) $
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case e of
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Vr x -> lookupVar env x
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Q m c -> return $ VCn (m,c)
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Sort c -> return $ VType --- the only sort is Type
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App f a -> join $ liftM2 app (eval env f) (eval env a)
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_ -> return $ VClos env e
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eqVal :: Int -> Val -> Val -> Err [(Val,Val)]
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eqVal k u1 u2 = ---- errIn (prt u1 +++ "<>" +++ prBracket (show k) +++ prt u2) $
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do
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w1 <- whnf u1
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w2 <- whnf u2
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let v = VGen k
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case (w1,w2) of
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(VApp f1 a1, VApp f2 a2) -> liftM2 (++) (eqVal k f1 f2) (eqVal k a1 a2)
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(VClos env1 (Abs x1 e1), VClos env2 (Abs x2 e2)) ->
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eqVal (k+1) (VClos ((x1,v x1):env1) e1) (VClos ((x2,v x1):env2) e2)
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(VClos env1 (Prod x1 a1 e1), VClos env2 (Prod x2 a2 e2)) ->
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liftM2 (++)
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(eqVal k (VClos env1 a1) (VClos env2 a2))
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(eqVal (k+1) (VClos ((x1,v x1):env1) e1) (VClos ((x2,v x1):env2) e2))
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(VGen i _, VGen j _) -> return [(w1,w2) | i /= j]
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_ -> return [(w1,w2) | w1 /= w2]
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-- invariant: constraints are in whnf
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checkType :: Theory -> TCEnv -> Exp -> Err (AExp,[(Val,Val)])
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checkType th tenv e = checkExp th tenv e vType
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checkExp :: Theory -> TCEnv -> Exp -> Val -> Err (AExp, [(Val,Val)])
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checkExp th tenv@(k,rho,gamma) e ty = do
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typ <- whnf ty
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let v = VGen k
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case e of
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Meta m -> return $ (AMeta m typ,[])
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Abs x t -> case typ of
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VClos env (Prod y a b) -> do
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a' <- whnf $ VClos env a ---
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(t',cs) <- checkExp th
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(k+1,(x,v x):rho, (x,a'):gamma) t (VClos ((y,v x):env) b)
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return (AAbs x a' t', cs)
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_ -> prtBad ("function type expected for" +++ prt e +++ "instead of") typ
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Eqs es -> do
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bcs <- mapM (\b -> checkBranch th tenv b typ) es
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let (bs,css) = unzip bcs
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return (AEqs bs, concat css)
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Prod x a b -> do
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testErr (typ == vType) "expected Type"
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(a',csa) <- checkType th tenv a
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(b',csb) <- checkType th (k+1, (x,v x):rho, (x,VClos rho a):gamma) b
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return (AProd x a' b', csa ++ csb)
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_ -> checkInferExp th tenv e typ
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checkInferExp :: Theory -> TCEnv -> Exp -> Val -> Err (AExp, [(Val,Val)])
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checkInferExp th tenv@(k,_,_) e typ = do
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(e',w,cs1) <- inferExp th tenv e
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cs2 <- eqVal k w typ
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return (e',cs1 ++ cs2)
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inferExp :: Theory -> TCEnv -> Exp -> Err (AExp, Val, [(Val,Val)])
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inferExp th tenv@(k,rho,gamma) e = case e of
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Vr x -> mkAnnot (AVr x) $ noConstr $ lookupVar gamma x
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Q m c -> mkAnnot (ACn (m,c)) $ noConstr $ lookupConst th (m,c)
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Sort _ -> return (AType, vType, [])
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App f t -> do
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(f',w,csf) <- inferExp th tenv f
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typ <- whnf w
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case typ of
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VClos env (Prod x a b) -> do
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(a',csa) <- checkExp th tenv t (VClos env a)
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b' <- whnf $ VClos ((x,VClos rho t):env) b
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return $ (AApp f' a' b', b', csf ++ csa)
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_ -> prtBad ("Prod expected for function" +++ prt f +++ "instead of") typ
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_ -> prtBad "cannot infer type of expression" e
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checkBranch :: Theory -> TCEnv -> Equation -> Val -> Err (([Exp],AExp),[(Val,Val)])
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checkBranch th tenv b@(ps,t) ty = errIn ("branch" +++ show b) $
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chB tenv' ps' ty
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where
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(ps',_,rho2,_) = ps2ts k ps
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tenv' = (k,rho2++rho, gamma)
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(k,rho,gamma) = tenv
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chB tenv@(k,rho,gamma) ps ty = case ps of
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p:ps2 -> do
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typ <- whnf ty
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case typ of
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VClos env (Prod y a b) -> do
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a' <- whnf $ VClos env a
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(p', sigma, binds, cs1) <- checkP tenv p y a'
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let tenv' = (length binds, sigma ++ rho, binds ++ gamma)
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((ps',exp),cs2) <- chB tenv' ps2 (VClos ((y,p'):env) b)
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return ((p:ps',exp), cs1 ++ cs2) -- don't change the patt
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_ -> prtBad ("Product expected for definiens" +++prt t +++ "instead of") typ
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[] -> do
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(e,cs) <- checkExp th tenv t ty
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return (([],e),cs)
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checkP env@(k,rho,gamma) t x a = do
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(delta,cs) <- checkPatt th env t a
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let sigma = [(x, VGen i x) | ((x,_),i) <- zip delta [k..]]
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return (VClos sigma t, sigma, delta, cs)
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ps2ts k = foldr p2t ([],0,[],k)
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p2t p (ps,i,g,k) = case p of
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PV IW -> (meta (MetaSymb i) : ps, i+1,g,k)
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PV x -> (vr x : ps, i, upd x k g,k+1)
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---- PL s -> (cn s : ps, i, g, k)
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PP m c xs -> (mkApp (qq (m,c)) xss : ps, j, g',k')
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where (xss,j,g',k') = foldr p2t ([],i,g,k) xs
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_ -> error $ "undefined p2t case" +++ prt p +++ "in checkBranch"
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upd x k g = (x, VGen k x) : g --- hack to recognize pattern variables
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checkPatt :: Theory -> TCEnv -> Exp -> Val -> Err (Binds,[(Val,Val)])
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checkPatt th tenv exp val = do
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(aexp,_,cs) <- checkExpP tenv exp val
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let binds = extrBinds aexp
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return (binds,cs)
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where
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extrBinds aexp = case aexp of
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AVr i v -> [(i,v)]
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AApp f a _ -> extrBinds f ++ extrBinds a
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_ -> [] -- no other cases are possible
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--- ad hoc, to find types of variables
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checkExpP tenv@(k,rho,gamma) exp val = case exp of
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Meta m -> return $ (AMeta m val, val, [])
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Vr x -> return $ (AVr x val, val, [])
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Q m c -> do
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typ <- lookupConst th (m,c)
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return $ (ACn (m,c) typ, typ, [])
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App f t -> do
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(f',w,csf) <- checkExpP tenv f val
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typ <- whnf w
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case typ of
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VClos env (Prod x a b) -> do
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(a',_,csa) <- checkExpP tenv t (VClos env a)
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b' <- whnf $ VClos ((x,VClos rho t):env) b
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return $ (AApp f' a' b', b', csf ++ csa)
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_ -> prtBad ("Prod expected for function" +++ prt f +++ "instead of") typ
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_ -> prtBad "cannot typecheck pattern" exp
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-- auxiliaries
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noConstr :: Err Val -> Err (Val,[(Val,Val)])
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noConstr er = er >>= (\v -> return (v,[]))
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mkAnnot :: (Val -> AExp) -> Err (Val,[(Val,Val)]) -> Err (AExp,Val,[(Val,Val)])
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mkAnnot a ti = do
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(v,cs) <- ti
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return (a v, v, cs)
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