import Data.Char as Char import Control.Monad import qualified Table import EnvCont import Parser import Repl import Debug.Trace type Symbol = String data Value = VNum Integer | VUnd Location | VRef Location | VCtor Symbol Int [Location] | VRec (Table.T Symbol Location) | VFun Symbol Environment Expr | VMod Environment | VCnt ContVS data Type = TInt | TName Symbol [Type] | TFun Type Type | TVar (Table.T Symbol [Type]) | TRec (Table.T Symbol Type) | TMod TypeDefs data Expr = EId Symbol | ENum Integer | EPlus Expr Expr | ETimes Expr Expr | EFun Symbol (Maybe Type) Expr | EApp Expr Expr | EDecl Decl Expr | ERecord [(Symbol, Expr)] | EMember Expr Symbol | ECase Expr [(Pattern, Expr)] | EAssign Expr Expr | ESeq Expr Expr | EPrint String Expr | EUnify Expr Expr | EWhile Expr Expr | EFor Symbol Expr Expr Expr | EReturn Expr | EBreak | EContinue | ELetCC Symbol Expr | ETry Expr Symbol Expr | EThrow Expr data Decl = DEmpty | DModule Symbol [Decl] | DImport Expr | DLet Symbol (Maybe Type) (Maybe Expr) | DTypeVar Symbol [Symbol] [(Symbol, [Type])] | DTypeRec Symbol [Symbol] [(Symbol, Type)] | DTypeDef Symbol [Symbol] Type data Pattern = ElsePat | VarPat Symbol | CtorPat Symbol [Symbol] | NumPat Integer -- memory type Location = Int type Continuation a = a -> (String, String) type CPS a = Continuation a -> (String, String) type ContVS = Continuation (Value, Store) type Environment = Env Location (Value, Store) instance Eq Value where (VNum n1) == (VNum n2) = n1 == n2 (VRef l1) == (VRef l2) = l1 == l2 (VUnd l1) == (VUnd l2) = l1 == l2 (VCtor c1 n1 a1) == (VCtor c2 n2 a2) = c1 == c2 && n1 == n2 && all (\(x,y) -> x == y) (zip a1 a2) (VRec f1) == (VRec f2) = f1 == f2 (VFun x1 e1 b1) == (VFun x2 e2 b2) = False -- x1 == x2 && e1 == e2 && b1 == b2 -- XXX we should at least use alpha-equivalence here (VMod d1) == (VMod d2) = d1 == d2 (VCnt _) == (VCnt _) = True _ == _ = False data Store = S Int (Table.T Location Value) String [ContVS] empty_store :: Store empty_store = S 0 Table.empty "" [\(v,_) -> error ("uncaught exception " ++ show v)] read_mem :: Store -> Location -> Value read_mem (S _ t _ _) l = Table.lookup t l set_mem :: Store -> Location -> Value -> Store set_mem (S n t out es) l v = S n (Table.bind t l v) out es get_value :: Store -> Value -> Value get_value st (VUnd _) = error "reading uninitialised variable" get_value st (VRef l) = get_value st (read_mem st l) get_value st v = v new_loc :: Store -> (Location, Store) new_loc (S n t out es) = (n, S (n+1) (Table.bind t n (VUnd n)) out es) add_output :: Store -> String -> Store add_output (S n t out es) str = S n t (out ++ str) es get_output :: Store -> String get_output (S _ _ out _) = out push_exception :: Store -> ContVS -> Store push_exception (S n t out es) k = S n t out (k:es) raise_exception :: Store -> ContVS raise_exception (S n t out (k:es)) (v,_) = k (v, S n t out es) store_value :: Store -> Value -> (Store, Location) store_value st v = let (l, st2) = new_loc st in case v of VUnd p -> (set_mem st2 l (VRef p), l) _ -> (set_mem st2 l v, l) bind_value :: (Store, Environment) -> (Symbol, Value) -> (Store, Environment) bind_value (st, env) (x, v) = let (st2, l) = store_value st v in (st2, bind_variable env x l) unit_value = VCtor "()" 0 [] -- value unification vunify :: Store -> Value -> Value -> Store vunify st v1 v2 = fst (vunify_rec Table.empty st v1 v2) vunify_rec :: Table.T (Value,Value) () -> Store -> Value -> Value -> (Store, Table.T (Value,Value) ()) vunify_rec seen st v1 v2 = case Table.maybe_lookup seen (v1, v2) of Nothing -> compare (Table.bind seen (v1,v2) ()) st v1 v2 Just () -> (st, seen) where compare seen st (VRef l) v = compare seen st (read_mem st l) v compare seen st v (VRef l) = compare seen st v (read_mem st l) compare seen st (VUnd l1) (VUnd l2) = if l1 == l2 then (st, seen) else (set_mem st l1 (VRef l2), seen) compare seen st (VUnd l) v = (set_mem st l v, seen) compare seen st v (VUnd l) = (set_mem st l v, seen) compare seen st (VNum n1) (VNum n2) | n1 == n2 = (st, seen) compare seen st (VCtor c1 n1 args1) (VCtor c2 n2 args2) | c1 == c2 && n1 == n2 = foldl (\(st, seen) (a1,a2) -> vunify_rec seen st (read_mem st a1) (read_mem st a2)) (st, seen) (zip args1 args2) compare seen st (VRec fields1) (VRec fields2) | Table.same_keys fields1 fields2 = Table.fold2 (\_ f1 f2 (st, seen) -> vunify_rec seen st (read_mem st f1) (read_mem st f2)) (st, seen) fields1 fields2 compare _ _ u v = error ("cannot unify " ++ show u ++ " and " ++ show v) -- evaluation eval :: Store -> Environment -> Expr -> CPS (Value, Store) eval st env (ENum n) k = k (VNum n, st) eval st env (EId id) k = k (read_mem st (lookup_variable env id), st) eval st env (EFun arg _ body) k = k (VFun arg env body, st) eval st env (EPlus e1 e2) k = eval st env e1 (\(v1, st1) -> eval st1 env e2 (\(v2, st2) -> case (get_value st2 v1, get_value st2 v2) of (VNum x1, VNum x2) -> k (VNum (x1 + x2), st2) _ -> error "addition of non-numbers")) eval st env (ETimes e1 e2) k = eval st env e1 (\(v1, st1) -> eval st1 env e2 (\(v2, st2) -> case (get_value st2 v1, get_value st2 v2) of (VNum x1, VNum x2) -> k (VNum (x1 * x2), st2) _ -> error "multiplication of non-numbers")) eval st env (EApp f a) k = eval st env f (\(fv, st1) -> eval st1 env a (\(av, st2) -> case get_value st2 fv of VFun p e b -> let (st3, new_env) = bind_value (st2, e) (p, av) in eval st3 (set_return_cont new_env k) b k VCnt cnt -> cnt (av, st2) VCtor ctor 0 args -> error "constructor applied to too many arguments" VCtor ctor ar args -> let (st3, l) = store_value st2 av in k (VCtor ctor (ar-1) (args ++ [l]), st3) _ -> error "application of non-function")) eval st env (EDecl d e) k = eval_decl st env d (\(st2, env2) -> eval st2 env2 e k) eval st env (ERecord fields) k = let add_value f e k (new_state, vals) = eval new_state env e (\(v, st2) -> let (st3, l) = store_value st2 v in k (st3, Table.bind vals f l)) in (foldr (\(f,e) k -> add_value f e k) (\(new_state, vals) -> k (VRec vals, new_state)) fields) (st, Table.empty) eval st env (EMember e f) k = eval st env e (\(v, st2) -> case get_value st2 v of VRec fields -> k (read_mem st2 (Table.lookup fields f), st2) VMod fields -> k (read_mem st2 (lookup_variable fields f), st2) _ -> error "value has no fields") eval st env (ECase e pats) k = eval st env e (\(val, st2) -> iter val st2 pats) where iter val st2 [] = error "no matching pattern in case expression" iter val st2 ((ElsePat, e):ps) = eval st2 env e k iter val st2 ((VarPat x, e):ps) = case maybe_lookup_variable env x of -- check whether x is a constructor or a variable Nothing -> let (st3, new_env) = bind_value (st2, env) (x, val) in eval st3 new_env e k Just l -> case get_value st2 (read_mem st2 l) of (VCtor c 0 []) -> case val of VCtor d 0 [] | c == d -> eval st2 env e k _ -> iter val st2 ps iter val st2 ((NumPat n, e):ps) = case val of VNum m | n == m -> eval st2 env e k _ -> iter val st2 ps iter val st2 ((CtorPat c xs,e):ps) = case val of VCtor d 0 args | c == d && length xs == length args -> eval st2 new_env e k where new_env = foldl (\env (x,l) -> bind_variable env x l) env (zip xs args) _ -> iter val st2 ps eval st env (EAssign x e) k = eval_lvalue st env x (\(l, st1) -> eval st1 env e (\(v, st2) -> k (unit_value, set_mem st2 l v))) eval st env (ESeq e1 e2) k = eval st env e1 (\(_, st1) -> eval st1 env e2 k) eval st env (EPrint str e) k = eval st env e (\(v, st1) -> k (unit_value, add_output st1 ("\n" ++ str ++ " " ++ show_value st1 v))) eval st env (EUnify x y) k = eval st env x (\(u, st1) -> eval st1 env y (\(v, st2) -> k (unit_value, vunify st2 u v))) eval st env (EWhile c b) k = iter st where loop_env = set_break_cont env k iter st = eval st env c (\(v,st2) -> case get_value st2 v of VCtor "False" 0 [] -> k (unit_value, st2) VCtor "True" 0 [] -> let cc (_, st3) = iter st3 in eval st2 (set_continue_cont loop_env cc) b cc _ -> error "type error in while loop") eval st env (EFor x l u b) k = eval st env l (\(lv, st2) -> eval st2 env u (\(uv, st3) -> let first = case get_value st3 lv of VNum n -> n _ -> error "type error in for loop" in let last = case get_value st3 uv of VNum n -> n _ -> error "type error in for loop" in iter st3 first last)) where loop_env = set_break_cont env k iter st i last = if i > last then k (unit_value, st) else let (st2, new_env) = bind_value (st, loop_env) (x, VNum i) in let cc (_, st3) = iter st3 (i + 1) last in eval st2 (set_continue_cont new_env cc) b cc eval st env (EReturn e) k = eval st env e (get_return_cont env) eval st env EBreak k = (get_break_cont env) (unit_value, st) eval st env EContinue k = (get_continue_cont env) (unit_value, st) eval st env (ELetCC x e) k = let (st2, new_env) = bind_value (st, env) (x, VCnt k) in eval st2 new_env e k eval st env (ETry e x h) k = let ec (v,st2) = let (st3, new_env) = bind_value (st2, env) (x, v) in eval st3 new_env h k in eval (push_exception st ec) env e k eval st env (EThrow e) k = eval st env e (raise_exception st) eval_lvalue :: Store -> Environment -> Expr -> CPS (Location, Store) eval_lvalue st env (EId id) k = k (lookup_variable env id, st) eval_lvalue st env (EMember e f) k = eval st env e (\(v, st2) -> case v of VRec fields -> k (Table.lookup fields f, st2) VMod fields -> k (lookup_variable fields f, st2) _ -> error "value has no fields") eval_lvalue st env (EDecl d e) k = eval_decl st env d (\(st2, env2) -> eval_lvalue st2 env2 e k) eval_lvalue st env (ESeq e1 e2) k = eval st env e1 (\(_, st1) -> eval_lvalue st1 env e2 k) eval_lvalue st env _ _ = error "expression is not an l-value" eval_decl :: Store -> Environment -> Decl -> CPS (Store, Environment) eval_decl st env (DLet x _ e) k = let (l, st2) = new_loc st in --- note this is now non-recursive let new_env = bind_variable env x l in case e of Nothing -> k (st2, new_env) Just e -> eval st2 new_env e (\(v, st3) -> k (set_mem st3 l v, new_env)) eval_decl st env (DTypeVar _ _ ctors) k = k (foldl (\st_env (c,args) -> bind_value st_env (c, VCtor c (length args) [])) (st, env) ctors) eval_decl st env (DTypeRec _ _ _) k = k (st, env) eval_decl st env (DTypeDef _ _ _) k = k (st, env) eval_decl st env (DModule name decls) k = let add_decl d k (new_st, new_env) = eval_decl new_st (merge_declarations env (variable_table new_env)) d k in (foldr (\d k -> add_decl d k) (\(new_st, new_env) -> k (bind_value (new_st, env) (name, VMod new_env))) decls) (st, empty_env) eval_decl st env (DImport e) k = eval st env e (\(v, st2) -> case v of VMod menv -> k (st2, merge_declarations env (variable_table menv)) _ -> error "not a module in import statement") -- data structures for type information data TypeScheme = TS [Symbol] Type type TypeDefs = Table.T Symbol TypeScheme type Declarations = Table.T Symbol Type type TypeSubst = Table.T Symbol Type data Types = TY TypeDefs TypeSubst Int -- type definitions, variable values, number of used variables new_type_info defs = TY defs Table.empty 0 lookup_type :: Types -> Symbol -> TypeScheme lookup_type (TY defs _ _) name = Table.lookup defs name maybe_lookup_type :: Types -> Symbol -> Maybe TypeScheme maybe_lookup_type (TY defs _ _) name = Table.maybe_lookup defs name define_type :: Types -> Symbol -> TypeScheme -> Types define_type (TY defs vars n) name typ = TY (Table.bind defs name typ) vars n lookup_type_variable :: Types -> Symbol -> Type lookup_type_variable (TY _ vars _) name = iter (Table.lookup vars name) where iter (TName n []) = case Table.maybe_lookup vars n of Just t -> iter t Nothing -> TName n [] iter typ = typ maybe_lookup_type_variable :: Types -> Symbol -> Maybe Type maybe_lookup_type_variable (TY _ vars _) name = iter (Table.maybe_lookup vars name) where iter Nothing = Nothing iter (Just (TName n [])) = case Table.maybe_lookup vars n of Just t -> iter (Just t) Nothing -> Just (TName n []) iter (Just typ) = Just typ is_variable :: Types -> Symbol -> Bool is_variable (TY defs _ _) n = case Table.maybe_lookup defs n of Just _ -> False Nothing -> True set_variable :: Types -> Symbol -> Type -> Types set_variable (TY defs vars n) name typ = TY defs (Table.bind vars name typ) n new_variable :: Types -> (Symbol, Types) new_variable (TY defs vars n) = ("a[" ++ show n ++ "]", TY defs vars (n+1)) -- utility functions for types uncurry_type :: Type -> ([Type], Type) uncurry_type (TFun a b) = let (arg_types, ret_type) = uncurry_type b in (a:arg_types, ret_type) uncurry_type a = ([], a) substitute :: Table.T Symbol Type -> Type -> Type substitute subst (TName n []) = case Table.maybe_lookup subst n of Nothing -> TName n [] Just t -> t substitute subst (TName n args) = TName n (map (substitute subst) args) substitute _ TInt = TInt substitute subst (TFun a b) = TFun (substitute subst a) (substitute subst b) substitute subst (TVar vars) = TVar (Table.map (\_ args -> map (substitute subst) args) vars) substitute subst (TRec fields) = TRec (Table.map (\ _ t -> substitute subst t) fields) instantiate :: Types -> [Symbol] -> Type -> (Type, Types) instantiate types params typ = let (subst, new_types) = foldl (\(subst, types) p -> let (var, new_types) = new_variable types in (Table.bind subst p (TName var []), new_types)) (Table.empty, types) params in (substitute subst typ, new_types) occurs :: Symbol -> Type -> Bool occurs x TInt = False occurs x (TName n []) = n == x occurs x (TName _ args) = any (occurs x) args occurs x (TFun a b) = occurs x a || occurs x b occurs x (TVar vars) = Table.fold (\_ args occ -> occ || any (occurs x) args) False vars occurs x (TRec fields) = Table.fold (\_ t occ -> occ || occurs x t) False fields; extract_parameters :: Types -> Type -> [Symbol] extract_parameters types TInt = [] extract_parameters types (TName n []) = case maybe_lookup_type types n of Nothing -> [n] Just _ -> [] extract_parameters types (TName n args) = foldl (++) [] (map (extract_parameters types) args) extract_parameters types (TFun a b) = extract_parameters types a ++ extract_parameters types b extract_parameters types (TVar vars) = Table.fold (\ _ args params -> foldl (++) params (map (extract_parameters types) args)) [] vars extract_parameters types (TRec fields) = Table.fold (\_ t params -> params ++ extract_parameters types t) [] fields expand_type_variable :: Types -> Type -> Type expand_type_variable types (TName n []) = case maybe_lookup_type_variable types n of Nothing -> TName n [] Just _ -> expand_type_variable types (lookup_type_variable types n) expand_type_variable _ typ = typ expand_type :: Types -> Type -> Type expand_type types TInt = TInt expand_type types (TName n []) = case maybe_lookup_type_variable types n of Nothing -> TName n [] Just _ -> expand_type types (lookup_type_variable types n) expand_type types (TName n args) = TName n (map (expand_type types) args) expand_type types (TFun a b) = TFun (expand_type types a) (expand_type types b) expand_type types (TVar vars) = TVar (Table.map (\ _ args -> map (expand_type types) args) vars) expand_type types (TRec fields) = TRec (Table.map (\_ t -> expand_type types t) fields) -- type unification unify :: Types -> Type -> Type -> Types unify types t1 t2 = -- trace ("unifying types " ++ show t1 ++ " [" ++ pp_type types t1 ++ "] and " ++ show t2 -- ++ " [" ++ pp_type types t2 ++ "]") $ unify_step types (expand_type_variable types t1) (expand_type_variable types t2) unify_step types (TName n []) t2 | is_variable types n = case maybe_lookup_type_variable types n of Just t -> unify types t t2 Nothing -> case t2 of TName n2 [] -> if n2 == n then types else if occurs n t2 then error "recursive type" else set_variable types n t2 _ -> if occurs n t2 then error "recursive type" else set_variable types n t2 unify_step types t1 (TName n []) | is_variable types n = case maybe_lookup_type_variable types n of Nothing -> set_variable types n t1 -- XXX occurs check Just t -> unify types t1 t unify_step types (TName n1 args1) (TName n2 args2) = if n1 == n2 then unify_lists types args1 args2 else error ("type error: trying to unify nominal types " ++ n1 ++ " and " ++ n2) unify_step types TInt TInt = types unify_step types (TFun a1 b1) (TFun a2 b2) = unify (unify types a1 a2) b1 b2 unify_step types (TVar vars1) (TVar vars2) = if Table.same_keys vars1 vars2 then Table.fold2 (\_ ct1 ct2 types -> unify_lists types ct1 ct2) types vars1 vars2 else error "type error" unify_step types (TRec f1) (TRec f2) = if Table.same_keys f1 f2 then Table.fold2 (\_ t1 t2 types -> unify types t1 t2) types f1 f2 else error "type error" unify_step _ t1 t2 = error ("type error: trying to unify " ++ show t1 ++ " and " ++ show t2) unify_lists types lst1 lst2 = if length lst1 == length lst2 then foldl (\types (t1,t2) -> unify types t1 t2) types (zip lst1 lst2) else error "type error" -- type checking type_check types decl expr = type_check_step types decl expr -- trace ("## type checking " ++ show expr ++ "\n") $ -- let (typ, new_types) = type_check_step types decl expr in -- (trace ("## type of " ++ show expr ++ " is " ++ show (expand_type types typ) -- ++ " [" ++ pp_type types typ ++ "]") $ -- (typ, new_types)) type_check :: Types -> TypeDefs -> Expr -> (Type, Types) type_check_step types decl (ENum n) = (TInt, types) type_check_step types decl (EId id) = let TS params typ = Table.lookup decl id in instantiate types params typ type_check_step types decl (EFun x t body) = let (x_type, new_types) = case t of Just t -> (t, types) Nothing -> let (n, new_types) = new_variable types in (TName n [], new_types) in let (typ, new_types2) = type_check new_types (Table.bind decl x (TS [] x_type)) body in (TFun x_type typ, new_types2) type_check_step types decl (EPlus e1 e2) = let (et1, new_types1) = type_check types decl e1 in let (et2, new_types2) = type_check new_types1 decl e2 in let new_types3 = unify new_types2 TInt et1 in let new_types4 = unify new_types3 TInt et2 in (TInt, new_types4) type_check_step types decl (ETimes e1 e2) = let (et1, new_types1) = type_check types decl e1 in let (et2, new_types2) = type_check new_types1 decl e2 in let new_types3 = unify new_types2 TInt et1 in let new_types4 = unify new_types3 TInt et2 in (TInt, new_types4) type_check_step types decl (EApp f a) = let (ft, new_types) = type_check types decl f in let (at, new_types2) = type_check new_types decl a in let (var, new_types3) = new_variable new_types2 in let rt = TName var [] in (rt, unify new_types3 ft (TFun at rt)) type_check_step types decl (EDecl d e) = let (new_types, new_decl) = type_check_decl types decl d in type_check new_types new_decl e type_check_step types decl (ERecord fields) = let (field_types, new_types) = foldl (\(table, types) (f,e) -> let (t, new_types) = type_check types decl e in (Table.bind table f t, new_types)) (Table.empty, types) fields in (TRec field_types, new_types) type_check_step types decl (EMember e f) = let (e_type, new_types) = type_check types decl e in case expand_type_variable types e_type of TRec fields -> (Table.lookup fields f, new_types) TName n [] -> case maybe_lookup_type new_types n of Just (TS [] (TMod fields)) -> let TS params typ = Table.lookup fields f in let (ityp, new_types2) = instantiate types params typ in (ityp, new_types2) _ -> error "type error: type inference for record types is not supported. Please use an explicit type annotation." _ -> error "type error" type_check_step types decl (ECase e pats) = let (typ, new_types) = type_check types decl e in let (pat_types, new_types2) = foldl (\(pt,types) p -> let (ptyp, new_types) = check_pat types typ p in (ptyp : pt, new_types)) ([], new_types) pats in case pat_types of [] -> error "malformed case statement" (p:ps) -> let new_types3 = foldl (\types pat -> unify types p pat) new_types2 ps in (p, new_types3) where check_pat types typ (g, b) = let (new_types, new_decl) = check_guard types typ g in type_check new_types new_decl b check_guard types typ ElsePat = (types, decl) check_guard types typ (NumPat n) = (unify types typ TInt, decl) check_guard types typ (VarPat x) = case Table.maybe_lookup decl x of -- check whether x is a constructor or a variable Nothing -> (types, Table.bind decl x (TS [] typ)) Just (TS params ct) -> let (ctor_typ, new_types) = instantiate types params ct in let (arg_typ, ret_typ) = uncurry_type ctor_typ in case arg_typ of [] -> (unify new_types typ ret_typ, decl) _ -> error "type error" check_guard types typ (CtorPat c xs) = let TS params ct = Table.lookup decl c in let (ctor_typ, new_types) = instantiate types params ct in let (arg_typ, ret_typ) = uncurry_type ctor_typ in let new_types2 = unify new_types typ ret_typ in if length xs == length arg_typ then let new_decl = foldl (\decl (x,t) -> Table.bind decl x (TS [] t)) decl (zip xs arg_typ) in (new_types2, new_decl) else error "type error" type_check_step types decl (EAssign x v) = let (t1, new_types1) = type_check types decl x in let (t2, new_types2) = type_check new_types1 decl v in (type_unit, unify new_types2 t1 t2) type_check_step types decl (ESeq e1 e2) = let (t1, new_types1) = type_check types decl e1 in let (t2, new_types2) = type_check new_types1 decl e2 in (t2, unify new_types2 t1 type_unit) type_check_step types decl (EPrint str e) = let (_, new_types) = type_check types decl e in (type_unit, new_types) type_check_step types decl (EUnify e1 e2) = let (t1, new_types1) = type_check types decl e1 in let (t2, new_types2) = type_check new_types1 decl e2 in (type_unit, unify new_types2 t1 t2) type_check_step types decl (EWhile c e) = let (t1, new_types1) = type_check types decl c in let (t2, new_types2) = type_check new_types1 decl e in let new_types3 = unify new_types2 t1 type_bool in let new_types4 = unify new_types3 t2 type_unit in (type_unit, new_types4) type_check_step types decl (EFor v l u e) = let new_decl = Table.bind decl v (TS [] TInt) in let (t1, new_types1) = type_check types decl l in let (t2, new_types2) = type_check new_types1 decl u in let (t3, new_types3) = type_check new_types2 new_decl e in let new_types4 = unify new_types3 t1 TInt in let new_types5 = unify new_types4 t2 TInt in let new_types6 = unify new_types5 t3 type_unit in (type_unit, new_types6) type_check_step types decl (EReturn e) = let (_, new_types) = type_check types decl e in (type_unit, new_types) type_check_step types decl EBreak = (type_unit, types) type_check_step types decl EContinue = (type_unit, types) type_check_step types decl (ELetCC k e) = let (n, new_types) = new_variable types in let new_decl = Table.bind decl k (TS ["a"] (TFun (TName n []) (TName "a" []))) in let (e_type, new_types2) = type_check new_types new_decl e in (e_type, unify new_types2 (TName n []) e_type) type_check_step types decl (ETry e x h) = let (e_type, new_types) = type_check types decl e in let (n, new_types2) = new_variable new_types in let new_decl = Table.bind decl x (TS [n] (TName n [])) in -- We should get the type of x from e_type. let (h_type, new_types3) = type_check new_types2 new_decl h in let new_types4 = unify new_types3 e_type h_type in (e_type, new_types4) type_check_step types decl (EThrow e) = let (e_type, new_types) = type_check types decl e in let (n, new_types2) = new_variable new_types in (TName n [], new_types2) -- We should record that the expression may throw an exception of type e_type. type_check_decl :: Types -> TypeDefs -> Decl -> (Types, TypeDefs) type_check_decl types decl (DLet x t e) = let (x_type, new_types) = case t of Just t -> (expand_type types t, types) Nothing -> let (n, new_types) = new_variable types in (TName n [], new_types) in let params = extract_parameters new_types x_type in let new_decl = Table.bind decl x (TS params x_type) in case e of Nothing -> (new_types, new_decl) Just e -> let (et, new_types2) = type_check new_types new_decl e in let new_types3 = unify new_types2 x_type et in let x_type2 = expand_type new_types3 x_type in let params2 = extract_parameters new_types3 x_type2 in let new_decl2 = Table.bind decl x (TS params2 x_type2) in (new_types3, new_decl2) type_check_decl types decl (DTypeVar name params variants) = let ctors = foldl (\table (c,args) -> Table.bind table c args) Table.empty variants in let typ = TVar ctors in let new_types = define_type types name (TS params typ) in let new_decl = foldl (\decl (c,args) -> Table.bind decl c (TS params (foldr (\t a -> TFun a t) typ args))) Table.empty variants in (new_types, new_decl) type_check_decl types decl (DTypeRec name params fields) = let field_types = foldl (\table (f,t) -> Table.bind table f t) Table.empty fields in let new_types = define_type types name (TS params (TRec field_types)) in (new_types, decl) type_check_decl types decl (DTypeDef name params t) = let new_types = define_type types name (TS params t) in (new_types, decl) type_check_decl types decl DEmpty = (types, decl) type_check_decl types decl (DModule n fields) = let (_, field_types) = foldl (\(types, decl) d -> type_check_decl types decl d) (types, decl) fields in let new_types = define_type types n (TS [] (TMod field_types)) in let new_decl = Table.bind decl n (TS [] (TName n [])) in (new_types, new_decl) type_check_decl types decl (DImport (EId n)) = let new_decl = case lookup_type types n of TS [] (TMod field_types) -> Table.fold (\id typ decl -> Table.bind decl id typ) decl field_types _ -> error "type error: import does not refer to a module" in (types, decl) type_check_decl types decl (DImport (EMember e n)) = let new_types = iter types e where iter :: Types -> Expr -> Types iter types (EMember e n) = let new_types = iter types e in case lookup_type new_types n of TS [] (TMod field_types) -> Table.fold (\id typ types -> define_type types id typ) types field_types _ -> error "type error: import does not refer to a module" iter types _ = types in let new_decl = case lookup_type new_types n of TS [] (TMod field_types) -> Table.fold (\id typ decl -> Table.bind decl id typ) decl field_types _ -> error "type error: import does not refer to a module" in (types, new_decl) type_check_decl types decl (DImport _) = error "syntax error: not a valid module expression in import statement" desugar :: PExpr -> Expr desugar (PId id) = EId id desugar (PNum n) = ENum n desugar (PPlus e1 e2) = EPlus (desugar e1) (desugar e2) desugar (PTimes e1 e2) = ETimes (desugar e1) (desugar e2) desugar (PMinus e1 e2) = EPlus (desugar e1) (ETimes (ENum (-1)) (desugar e2)) desugar (PEqual e1 e2) = ECase (desugar (PMinus e1 e2)) [ (NumPat 0, EId "%True"), (ElsePat, EId "%False") ] desugar (PFun [] b) = EFun "()" (Just (TName "unit" [])) (desugar b) desugar (PFun [(p,t)] b) = EFun p (liftM desugar_type t) (desugar b) desugar (PFun ((p,t):args) b) = EFun p (liftM desugar_type t) (desugar (PFun args b)) desugar (PApp f []) = EApp (desugar f) (EId "()") desugar (PApp f [a]) = EApp (desugar f) (desugar a) desugar (PApp f args) = foldl (\f a -> EApp f a ) (desugar f) (map desugar args) desugar (PRecord fields) = ERecord (map (\(f,e) -> (f, desugar e)) fields) desugar (PMember e f) = EMember (desugar e) f desugar (PSeq e1 e2) = ESeq (desugar e1) (desugar e2) desugar (PAssign e f) = EAssign (desugar e) (desugar f) desugar (PUnify e1 e2) = EUnify (desugar e1) (desugar e2) desugar (PPrint str e) = EPrint str (desugar e) desugar (PDecl d e) = EDecl (desugar_decl d) (desugar e) desugar (PIf c t e) = ECase (desugar c) [ (VarPat "%True", desugar t), (ElsePat, desugar e) ] desugar (PCase e pats) = ECase (desugar e) (map (\(p,e) -> (desugar_pat p, desugar e)) pats) desugar (PWhile c b) = EWhile (desugar c) (desugar b) desugar (PFor x l u b) = EFor x (desugar l) (desugar u) (desugar b) desugar (PReturn e) = EReturn (desugar e) desugar PBreak = EBreak desugar PContinue = EContinue desugar (PLetCC x e) = ELetCC x (desugar e) desugar (PTry e x h) = ETry (desugar e) x (desugar h) desugar (PThrow e) = EThrow (desugar e) desugar (PListLit es t) = foldr (\x y -> EApp (EApp (EId "%Cons") (desugar x)) y) (case t of Nothing -> EId "%Nil" Just e -> desugar e) es desugar _ = error "unsupported syntactic construct\n" desugar_pat :: PPattern -> Pattern desugar_pat PElsePat = ElsePat desugar_pat (PVarPat x) = VarPat x desugar_pat (PCtorPat c xs) = CtorPat c xs desugar_pat (PNumPat n) = NumPat n desugar_type :: PExpr -> Type desugar_type (PId "int") = TInt desugar_type (PId n) = TName n [] desugar_type (PApp (PId n) args) = TName n (map desugar_type args) desugar_type (PArrow a b) = TFun (desugar_type a) (desugar_type b) desugar_type _ = error "invalid type annotation" desugar_decl (PModule name [] decls) = DModule name (map desugar_decl decls) desugar_decl (PImport e) = DImport (desugar e) desugar_decl (PLet x t e) = DLet x (liftM desugar_type t) (Just (desugar e)) desugar_decl (PLetUnIni x t) = DLet x (liftM desugar_type t) Nothing desugar_decl (PLetFun f args t b) = DLet f (liftM desugar_type ft) (Just (desugar (PFun args b))) where ft = foldr arr t (map snd args) arr Nothing _ = Nothing arr _ Nothing = Nothing arr (Just a) (Just b) = Just (PArrow a b) desugar_decl (PTypeVar name params ctors) = DTypeVar name params (map (\(c,args) -> (c, map desugar_type args)) ctors) desugar_decl (PTypeRec name params fields) = DTypeRec name params (map (\(f,t) -> (f, desugar_type t)) fields) desugar_decl (PTypeDef t params t2) = DTypeDef t params (desugar_type t2) show_list :: Show a => String -> String -> (a -> String) -> [a] -> String show_list l r sh [] = "" show_list l r sh xs = l ++ foldl1 (\ x y -> x ++ ", " ++ y) (map sh xs) ++ r show_list_acc :: String -> String -> (b -> a -> (String, b)) -> b -> [a] -> (String, b) show_list_acc l r sh acc [] = ("", acc) show_list_acc l r sh acc (x:xs) = let (str,new_acc) = foldl (\(str,acc) y -> let (s,a) = sh acc y in (str ++ ", " ++ s, a)) (sh acc x) xs in (l ++ str ++ r, new_acc) instance Show Value where show (VUnd l) = "" show (VRef l) = "" show (VNum n) = show n show (VCtor c _ args) = c ++ show_list "(" ")" show args show (VRec fields) = show_list "[" "]" (\(f,v) -> f ++ " = " ++ show v) (Table.to_list fields) show (VFun a _ b) = "fun (" ++ a ++ ") { " ++ show b ++ " }" show (VMod env) = "module {" ++ show_list "" "" (\(f,v) -> "let " ++ f ++ " = " ++ show v ++ ";\n") (Table.to_list (variable_table env)) ++ "}" show (VCnt _) = "" show_value st (VUnd l) = "" show_value st (VRef l) = show_value st (read_mem st l) show_value st (VNum n) = show n show_value st (VCtor c _ args) = c ++ show_list "(" ")" (show_value st) (map (read_mem st) args) show_value st (VRec fields) = show_list "[" "]" (\(f,l) -> f ++ " = " ++ show_value st (read_mem st l)) (Table.to_list fields) show_value st (VFun a _ b) = "fun (" ++ a ++ ") { " ++ show b ++ " }" show_value st (VMod env) = "module {" ++ show_list "" "" (\(f,l) -> "let " ++ f ++ " = " ++ show_value st (read_mem st l) ++ ";\n") (Table.to_list (variable_table env)) ++ "}" show_value st (VCnt _) = "" -- pp_type types typ = fst (pretty_print_type Table.empty (expand_type types typ)) pretty_print_type :: Table.T Symbol String -> Type -> (String, Table.T Symbol String) pretty_print_type names TInt = ("int", names) pretty_print_type names (TName n []) = case n of ('a' : '[' : _) -> case Table.maybe_lookup names n of Just str -> (str, names) Nothing -> let used = Table.size names in let str = if used < 26 then [Char.chr (97 + used)] else if used < 26 * 26 then [Char.chr (97 + used `div` 26), Char.chr (97 + used `mod` 26)] else [Char.chr (97 + used `div` 26), Char.chr (97 + used `mod` 26)] ++ show (used `div` (26 * 26)) in (str, Table.bind names n str) _ -> (n, names) pretty_print_type names (TName n args) = let (str, new_names) = show_list_acc "(" ")" pretty_print_type names args in (n ++ str, new_names) pretty_print_type names (TFun a b) = let (str1, names1) = pretty_print_type names a in let (str2, names2) = pretty_print_type names1 b in ("(" ++ str1 ++ " -> " ++ str2 ++ ")", names2) pretty_print_type names (TVar vars) = foldl (\(str,names) (c,fields) -> let (str, new_names) = show_list_acc "(" ")" pretty_print_type names fields in (str ++ "| " ++ c, new_names)) ("", names) (Table.to_list vars) pretty_print_type names (TRec fields) = show_list_acc "[" "]" (\names (f,t) -> let (str, new_names) = pretty_print_type names t in (f ++ " : " ++ str, new_names)) names (Table.to_list fields) instance Show Type where show TInt = "int" show (TName n []) = n show (TName n args) = n ++ show_list "(" ")" show args show (TFun a b) = "(" ++ show a ++ " -> " ++ show b ++ ")" show (TVar vars) = foldl (\str (c,fields) -> str ++ "| " ++ c ++ show_list "(" ")" show fields) "" (Table.to_list vars) show (TRec fields) = show_list "[" "]" (\(f,t) -> f ++ " : " ++ show t) (Table.to_list fields) instance Show Expr where show (EId x) = x show (ENum n) = show n show (EPlus e1 e2) = "(" ++ show e1 ++ " + " ++ show e2 ++ ")" show (ETimes e1 e2) = "(" ++ show e1 ++ " * " ++ show e2 ++ ")" show (EFun a Nothing b) = "fun (" ++ a ++ ") { " ++ show b ++ " }" show (EFun a (Just t) b) = "fun (" ++ a ++ " : " ++ show t ++ ") { " ++ show b ++ " }" show (EApp f a) = show fn ++ show_list "(" ")" show args where (fn, args) = collect_args f [a] collect_args (EApp g b) args = collect_args g (b:args) collect_args g args = (g, args) show (ERecord fields) = show_list "[" "]" (\(f,e) -> f ++ " = " ++ show e) fields show (EMember e f) = show e ++ "." ++ f show (ESeq a b) = show a ++ "; " ++ show b show (EAssign e f) = show e ++ " := " ++ show f show (EPrint str e) = "print " ++ show str ++ " " ++ show e show (EDecl d e) = show d ++ " " ++ show e show (ECase e pats) = foldl (++) ("case " ++ show e) (map (\(p,e) -> " | " ++ show p ++ " => " ++ show e) pats) show (EWhile c b) = "while " ++ show c ++ " " ++ show b show (EFor x l u b) = "for " ++ x ++ " = " ++ show l ++ " .. " ++ show u ++ " " ++ show b show (EReturn e) = "return " ++ show e show EBreak = "break" show EContinue = "continue" show (ELetCC k e) = "letcc " ++ k ++ " { " ++ show e ++ " }" show (ETry e x h) = "try " ++ show e ++ " catch " ++ x ++ " => " ++ show h show (EThrow e) = "throw " ++ show e instance Show Decl where show DEmpty = ";" show (DLet x Nothing b) = case b of Nothing -> "let " ++ x ++ ";" Just e -> "let " ++ x ++ " = " ++ show e ++ ";" show (DLet x (Just t) b) = case b of Nothing -> "let " ++ x ++ " :" ++ show t ++ ";" Just e -> "let " ++ x ++ " :" ++ show t ++ " = " ++ show e ++ ";" show (DTypeVar n ps ctors) = foldl (++) ("type " ++ n ++ show_list "(" ")" id ps ++ " =") (map (\(c,args) -> " | " ++ c ++ show_list "(" ")" show args) ctors) ++ ";" show (DTypeRec n ps fields) = "type " ++ n ++ show_list "(" ")" id ps ++ " = {" ++ show_list "(" ")" (\(c,t) -> c ++ " : " ++ show t) fields ++ "};" show (DTypeDef n ps t) = "type " ++ n ++ show_list "(" ")" id ps ++ " = " ++ show t ++ ";" show (DModule name decls) = foldl (++) ("module " ++ name ++ " ") (map show decls) ++ ";" show (DImport e) = "import " ++ show e ++ ";" instance Show Pattern where show ElsePat = "else" show (VarPat x) = x show (NumPat n) = show n show (CtorPat c xs) = c ++ show_list "(" ")" id xs -- builtin types and functions type_unit = TName "unit" [] type_bool = TName "bool" [] type_pair = TName "pair" [TName "a" [], TName "b" []] type_list = TName "list" [TName "a" []] type_unit_def = TVar Table.empty type_bool_def = TVar (Table.bind (Table.bind Table.empty "True" []) "False" []) type_pair_def = TVar (Table.bind Table.empty "pair" [TName "a" [], TName "b" []]) type_list_def = TVar (Table.bind (Table.bind Table.empty "Nil" []) "Cons" [TName "a" [], type_list]) builtin_types = foldl (\types (n,t) -> Table.bind types n t) Table.empty [("unit", TS [] type_unit_def), ("bool", TS [] type_bool_def), ("product", TS ["a", "b"] type_pair_def), ("list", TS ["a"] type_list_def)] ((initial_store, builtin_env), builtin_decls) = foldl (\(st_env, decls) (ctor, val, typ) -> (bind_value st_env (ctor, val), Table.bind decls ctor typ)) ((empty_store, empty_env), Table.empty) [("()", VCtor "()" 0 [], TS [] type_unit), ("True", VCtor "True" 0 [], TS [] type_bool), ("False", VCtor "False" 0 [], TS [] type_bool), ("Pair", VCtor "Pair" 2 [], TS ["a", "b"] (TFun (TName "a" []) (TFun (TName "b" []) type_pair))), ("Nil", VCtor "Nil" 0 [], TS ["a"] type_list), ("Cons", VCtor "Cons" 2 [], TS ["a"] (TFun (TName "a" []) (TFun type_list type_list))), ("%True", VCtor "True" 0 [], TS [] type_bool), ("%False", VCtor "False" 0 [], TS [] type_bool), ("%Nil", VCtor "Nil" 0 [], TS ["a"] type_list), ("%Cons", VCtor "Cons" 2 [], TS ["a"] (TFun (TName "a" []) (TFun type_list type_list)))] run str = eval initial_store builtin_env (desugar (parse str)) (\(val, st) -> (get_output st, show_value st val)) run_tc str = let (typ, types) = type_check (new_type_info builtin_types) builtin_decls (desugar (parse str)) in expand_type types typ main :: IO () main = repl run (Just (fst . pretty_print_type Table.empty . run_tc))