1 files changed, 173 insertions, 0 deletions
diff --git a/Term.hs b/Term.hs
new file mode 100644
index 0000000..626b91c
--- /dev/null
+++ b/Term.hs
@@ -0,0 +1,173 @@
+module Term (
+    Term(..),
+
+    alphaEquiv,
+    alphaConvert,
+    alphaConvertList,
+    substitute,
+    containsVars,
+    rename,
+    typeOf,
+    mkEquals,
+    isEq,
+    getlhs,
+    getrhs
+    ) where
+
+
+
+import Data.List
+import TypeVar
+
+
+
+data Term = TVar { tVar :: Var }
+          | TConst { tConst :: Const
+                   , tConstType :: Type }
+          | TApp { tAppLeft :: Term
+                 , tAppRight :: Term }
+          | TAbs { tAbsVar :: Term
+                 , tAbsTerm :: Term }
+
+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 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 ([],[(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 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 == (fst x))
+                                then snd x
+                                else TVar v
+                    (TAbs v a) -> let safe = rename (TAbs v a) (union [fst x] (containsVars . 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
+
+
+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
+
+
+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