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Diffstat (limited to 'Term.hs')
| -rw-r--r-- | Term.hs | 193 |
1 files changed, 0 insertions, 193 deletions
diff --git a/Term.hs b/Term.hs deleted file mode 100644 index 8abdeb4..0000000 --- a/Term.hs +++ /dev/null @@ -1,193 +0,0 @@ -module Term ( - Term(..), - Substitution, - - alphaEquiv, - alphaConvert, - alphaConvertList, - substitute, - boundVars, - freeVars, - rename, - typeOf, - typeVarsInTerm, - mkEquals, - isEq, - getlhs, - getrhs - ) where - - - -import Data.List -import qualified Data.Set as Set -import qualified Data.Map as Map -import TypeVar - - - -data Term = TVar { tVar :: Var } - | TConst { tConst :: Const - , tConstType :: Type } - | TApp { tAppLeft :: Term - , tAppRight :: Term } - | TAbs { tAbsVar :: Term - , tAbsTerm :: Term } deriving (Ord) - -type Substitution = ( [(Name,Type)], [(Var,Term)] ) - - -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 Eq Term where - a == b = a `alphaEquiv` b - - - -alphaEquiv :: Term -> Term -> Bool -alphaEquiv a b = - let equiv = \term1 term2 varmap1 varmap2 depth -> - case (term1,term2) of - (TConst a1 b1, TConst a2 b2) -> - a1 == a2 && b1 == b2 - - (TApp a1 b1, TApp a2 b2) -> - equiv a1 a2 varmap1 varmap2 depth && - equiv b1 b2 varmap1 varmap2 depth - - (TAbs (TVar (Var name1 type1)) b1, TAbs (TVar (Var name2 type2)) b2) -> - type1 == type2 && - equiv b1 b2 newmap1 newmap2 (depth+1) - where newmap1 = Map.insert (Var name1 type1) depth varmap1 - newmap2 = Map.insert (Var name2 type2) depth varmap2 - - (TVar a1, TVar a2) -> - a1 == a2 && Map.notMember a1 varmap1 && Map.notMember a2 varmap2 || - Map.lookup a1 varmap1 == Map.lookup a2 varmap2 - - (_,_) -> False - in equiv a b Map.empty Map.empty 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 ([],[(tVar v1,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 == (TypeVar . fst $ x)) - then TConst a (snd x) - else TConst a ty - (TApp a b) -> TApp (typesub x a) (typesub x b) - (TAbs (TVar (Var n ty)) a) -> if (ty == (TypeVar . fst $ x)) - then TAbs (TVar (Var n (snd x))) (typesub x a) - else TAbs (TVar (Var n ty)) (typesub x a) - (TVar (Var n ty)) -> if (ty == (TypeVar . fst $ x)) - then TVar (Var n (snd x)) - else TVar (Var n ty)) - 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 == (fst x)) - then snd x - else TVar v - (TAbs v a) -> let safe = rename (TAbs v a) (Set.insert (fst x) (freeVars . snd $ 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 - - -boundVars :: Term -> Set.Set Var -boundVars (TConst a b) = Set.empty -boundVars (TApp a b) = Set.union (boundVars a) (boundVars b) -boundVars (TVar a) = Set.empty -boundVars (TAbs a b) = Set.insert (tVar a) (boundVars b) - - -freeVars :: Term -> Set.Set Var -freeVars (TConst a b) = Set.empty -freeVars (TApp a b) = Set.union (freeVars a) (freeVars b) -freeVars (TVar a) = Set.singleton a -freeVars (TAbs a b) = Set.delete (tVar a) (freeVars b) - - -rename :: Term -> Set.Set Var -> Term -rename (TAbs (TVar v) t) vars = - 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 (Set.member x 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 (Set.member v vars) - then doRename (TAbs (TVar v) t) v (findSafe v vars) - else TAbs (TVar v) t - - -typeOf :: Term -> Type -typeOf (TConst _ 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 - - -typeVarsInTerm :: Term -> Set.Set Type -typeVarsInTerm (TConst _ ty) = typeVarsInType ty -typeVarsInTerm (TVar v) = typeVarsInType . varTy $ v -typeVarsInTerm (TAbs v t) = Set.union (typeVarsInType . varTy . tVar $ v) (typeVarsInTerm t) -typeVarsInTerm (TApp f x) = Set.union (typeVarsInTerm f) (typeVarsInTerm x) - - -mkEquals :: Term -> Term -> Term -mkEquals lhs rhs = - let eqConst = TConst (Const (Name [] "=")) (mkEqualsType (typeOf lhs)) - in TApp (TApp eqConst lhs) rhs - - -getlhs :: Term -> Term -getlhs (TApp (TApp eq lhs) _) - | (isEq eq) = lhs - - -getrhs :: Term -> Term -getrhs (TApp (TApp eq _) rhs) - | (isEq eq) = rhs - - -isEq :: Term -> Bool -isEq (TConst (Const (Name [] "=")) _) = True -isEq _ = False |