diff options
Diffstat (limited to 'Semantic.hs')
| -rw-r--r-- | Semantic.hs | 238 |
1 files changed, 11 insertions, 227 deletions
diff --git a/Semantic.hs b/Semantic.hs index 7de8dee..d50905c 100644 --- a/Semantic.hs +++ b/Semantic.hs @@ -1,89 +1,12 @@ import Control.Monad( liftM ) import System( getArgs ) import Data.List +import TypeVar +import Term +import Theorem +import Object -data Object = ObjNum { objNum :: Number } - | ObjName { objName :: Name } - | ObjList { objList :: List } - | ObjTyOp { objTyOp :: TypeOp } - | ObjType { objType :: Type } - | ObjConst { objConst :: Const } - | ObjVar { objVar :: Var } - | ObjTerm { objTerm :: Term } - | ObjThm { objThm :: Theorem } deriving (Eq) - -type Number = Int - -data Name = Name { nameSpace :: [String] - , nameId :: String } deriving (Eq) - -type List = [Object] - -data TypeOp = TypeOp { tyOp :: Name } deriving (Eq) - -data Type = TypeVar { typeVar :: Name } - | AType { aType :: [Type] - , aTypeOp :: TypeOp } deriving (Eq) - -data Const = Const { constName :: Name } deriving (Eq) - -data Var = Var { varName :: Name - , varTy :: Type } deriving (Eq) - -data Term = TVar { tVar :: Var } - | TConst { tConst :: Const - , tConstType :: Type } - | TApp { tAppLeft :: Term - , tAppRight :: Term } - | TAbs { tAbsVar :: Term - , tAbsTerm :: Term } - -data Theorem = Theorem { thmHyp :: [Term] - , thmCon :: Term } deriving (Eq) - - -instance Show Object where - show (ObjNum a) = show a - show (ObjName a) = show a - show (ObjList a) = show a - show (ObjTyOp a) = show a - show (ObjType a) = show a - show (ObjConst a) = show a - show (ObjVar a) = show a - show (ObjTerm a) = show a - show (ObjThm a) = show a - -instance Show Name where - show a = intercalate "." (nameSpace a ++ [nameId a]) - -instance Show TypeOp where - show a = "typeOp " ++ (show $ tyOp a) - -instance Show Type where - show (TypeVar tyVar) = "typeVar " ++ (show tyVar) - show (AType list typeOp) = "type " ++ (show $ tyOp typeOp) ++ " " ++ (show list) - -instance Show Const where - show (Const a) = show a - -instance Show Var where - show (Var a _) = show a - -instance Show Term where - show (TVar a) = show a - show (TConst a _) = show a - show (TApp (TApp eq lhs) rhs) - | isEq eq = "(" ++ (show lhs) ++ " = " ++ (show rhs) ++ ")" - show (TApp a b) = "(" ++ (show a) ++ " " ++ (show b) ++ ")" - show (TAbs a b) = "(\\" ++ (show a) ++ " -> " ++ (show b) ++ ")" - -instance Show Theorem where - show a = (show . thmHyp $ a) ++ " |- " ++ (show . thmCon $ a) - -instance Eq Term where - a == b = a `alphaEquiv` b - data Stack = Stack { stackList :: [Object] } data Dictionary = Dictionary { dictionMap :: [(Int,Object)] } @@ -104,9 +27,6 @@ instance Show Theorems where show a = "Theorems:\n" ++ intercalate "\n" (map (show) (theoremList a)) ++ "\n\n" -type Substitution = [[[Object]]] - - data ArticleLine = Comment { commentString :: String } | Command { commandFunc :: ((Stack,Dictionary,Assumptions,Theorems)->(Stack,Dictionary,Assumptions,Theorems)) } @@ -225,7 +145,7 @@ betaConv :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumpt betaConv (s,d,a,t) = let stack = stackList s op = (\x -> Theorem [] (mkEquals x - (substitute [[], [[ObjVar . tVar . tAbsVar . tAppLeft $ x, ObjTerm . tAppRight $ x]]] + (substitute ([], [(tVar . tAbsVar . tAppLeft $ x, tAppRight $ x)]) (tAbsTerm . tAppLeft $ x)))) theorem = ObjThm $ op (objTerm $ stack!!0) s' = Stack $ theorem : (tail stack) @@ -380,7 +300,12 @@ subst (s,d,a,t) = let stack = stackList s op = (\x y -> Theorem (map (substitute y) (thmHyp x)) (substitute y (thmCon x))) - theorem = ObjThm $ op (objThm $ stack!!0) ((map (map objList)) . (map objList) . objList $ stack!!1) + substitution = + (\x -> let list = (map (map objList)) . (map objList) . objList $ x + f = (\g h x -> (g . head $ x, h . last $ x)) + in f (map (f objName objType)) (map (f objVar objTerm)) list) + + theorem = ObjThm $ op (objThm $ stack!!0) (substitution $ stack!!1) s' = Stack $ theorem : (drop 2 stack) in (s',d,a,t) @@ -434,147 +359,6 @@ varType (s,d,a,t) = - -alphaEquiv :: Term -> Term -> Bool -alphaEquiv a b = - let equiv = \term1 term2 varmap lambdaDepth -> - case (term1,term2) of - (TConst a1 b1, TConst a2 b2) -> - a1 == a2 && b1 == b2 - - (TApp a1 b1, TApp a2 b2) -> - equiv a1 a2 varmap lambdaDepth && - equiv b1 b2 varmap lambdaDepth - - (TAbs (TVar (Var name1 type1)) b1, TAbs (TVar (Var name2 type2)) b2) -> - type1 == type2 && - equiv b1 b2 newmap (lambdaDepth + 1) - where newmap = (lambdaDepth + 1, ((Var name1 type1),(Var name2 type2))) : varmap - - (TVar a1, TVar a2) -> - -- the order of the pair is important - (lambdaDepth, (a1,a2)) `elem` varmap || - not ((lambdaDepth, (a1,a2)) `elem` varmap) && a1 == a2 - - (_,_) -> False - in equiv a b [] 0 - - -alphaConvert :: Term -> Term -> Term -alphaConvert (TConst a ty) (TConst _ _) = TConst a ty -alphaConvert (TApp a1 b1) (TApp a2 b2) = TApp (alphaConvert a1 a2) (alphaConvert b1 b2) -alphaConvert (TVar v) (TVar _) = TVar v -alphaConvert (TAbs v1 a) (TAbs v2 b) = substitute [[],[[ObjVar $ tVar v1, ObjTerm $ v2]]] (TAbs v1 (alphaConvert a b)) - - -alphaConvertList :: [Term] -> [Term] -> [Term] -alphaConvertList a b = map (\x -> alphaConvert (fst x) (snd x)) (zip a b) - - -substitute :: Substitution -> Term -> Term -substitute [tymap, vmap] term = - let typesub = - (\x y -> - case y of - (TConst a ty) -> if (ty == (objType . head $ x)) - then TConst a (objType . last $ x) - else TConst a ty - (TApp a b) -> TApp (typesub x a) (typesub x b) - (TAbs v a) -> TAbs v (typesub x a) - (TVar v) -> TVar v) - varsub = - (\x y -> - case y of - (TConst a ty) -> TConst a ty - (TApp a b) -> TApp (varsub x a) (varsub x b) - (TVar v) -> if (v == (objVar . head $ x)) - then objTerm . last $ x - else TVar v - (TAbs v a) -> let safe = rename (TAbs v a) (union [(objVar . head $ x)] (containsVars (objTerm . last $ x))) - in case safe of - (TAbs m n) -> TAbs m (varsub x n)) - tydone = foldl' (\x y -> typesub y x) term tymap - vdone = foldl' (\x y -> varsub y x) tydone vmap - in vdone - - -containsVars :: Term -> [Var] -containsVars t = - let f = (\term list -> - case term of - (TConst a b) -> list - (TApp a b) -> union list ((f a list) ++ (f b list)) - (TVar a) -> union list [a] - (TAbs a b) -> union list ([tVar a] ++ (f b list))) - in f t [] - - -rename :: Term -> [Var] -> Term -rename (TAbs (TVar v) t) varlist = - let doRename = - (\x y z -> case x of - (TAbs (TVar a) b) -> if (a == y) - then TAbs (TVar z) (doRename b y z) - else TAbs (TVar a) (doRename b y z) - (TConst a b) -> TConst a b - (TApp a b) -> TApp (doRename a y z) (doRename b y z) - (TVar a) -> if (a == y) - then TVar z - else TVar a) - findSafe = - (\x y -> if (x `elem` y) - then case x of - (Var a b) -> - case a of - (Name c d) -> findSafe (Var (Name c (d ++ "'")) b) y - else x) - in if (v `elem` varlist) - then doRename (TAbs (TVar v) t) v (findSafe v varlist) - else TAbs (TVar v) t - - - - -typeOf :: Term -> Type -typeOf (TConst c ty) = ty -typeOf (TVar v) = varTy v -typeOf (TAbs v t) = typeFunc (typeOf v) (typeOf t) -typeOf (TApp f _) = - -- type of f is of the form [[a,b], "->"] - last . aType . typeOf $ f - - -mkEquals :: Term -> Term -> Term -mkEquals lhs rhs = - let eqConst = TConst (Const (Name [] "=")) (mkEqualsType (typeOf lhs)) - in TApp (TApp eqConst lhs) rhs - - -mkEqualsType :: Type -> Type -mkEqualsType ty = typeFunc (AType [] (TypeOp (Name [] "bool"))) (typeFunc ty ty) - - -getlhs :: Term -> Term -getlhs (TApp (TApp eq lhs) _) = - if (isEq eq) then lhs else error "Tried to get lhs from a non-eq term" - - -getrhs :: Term -> Term -getrhs (TApp (TApp eq _) rhs) = - if (isEq eq) then rhs else error "Tried to get rhs from a non-eq term" - - -isEq :: Term -> Bool -isEq (TConst (Const (Name [] "=")) _) = True -isEq _ = False - - -typeFunc :: Type -> Type -> Type -typeFunc ty1 ty2 = AType [ty1,ty2] (TypeOp (Name [] "->")) - - - - doSemanticCheck :: [String] -> (Stack,Dictionary,Assumptions,Theorems) doSemanticCheck = let s = Stack [] |