Ajout des fonctions.
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@ -3,8 +3,7 @@ open Expr
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let rec affiche_val v = match v with
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| VInt k -> print_int k
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| VBool b -> print_string (if b then "Vrai" else "Faux")
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| VFunc (v,e) -> print_string "fun ";print_string v;print_string " -> ";affiche_expr e
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| VFunc (v,e) -> print_string "Fun(";print_string v;print_string " -> ";affiche_expr e;print_string ")"
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(* fonction d'affichage *)
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and affiche_expr e =
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@ -44,3 +43,35 @@ and affiche_expr e =
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| LetIn(x,e0,e1) -> print_string "LetIn(";print_string x;print_string ",";affiche_expr e0;print_string ",";affiche_expr e1;print_string ")"
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| Fun(v,e) -> affiche_val (VFunc(v,e))
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| App(e1,e2) -> aff_aux "App(" e1 e2
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let dump_env_line x =
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let (e,v) = x in
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begin
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print_string e;
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print_string " -> ";
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affiche_val v
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end
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let dump_env env =
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begin
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print_string "[";
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let rec aux l =
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begin
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match l with
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| [] -> ()
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| [e] -> dump_env_line e
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| e::t ->
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begin
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dump_env_line e;
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print_string ";";
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aux t
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end
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end
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in aux env;
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print_string "]"
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end
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@ -1,3 +1,5 @@
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open List
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(* définition des différents types : tout est à reprendre et étendre *)
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type expr =
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Const of int
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@ -25,24 +27,56 @@ type env = (string*valeur) list
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let empty_env = []
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exception InvalidTypeException
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exception UnknownVariableException
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exception InvalidTypeException of (string*valeur) (** expected, given **)
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exception UnknownVariableException of (string*env) (** query, env **)
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let valToConstExpr v = match v with
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| VInt(k) -> Const(k)
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| VBool(b) -> BConst(b)
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| VFunc(var,e) -> Fun(var,e)
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let rec readVar env v0 e = match env with
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| [] -> raise e
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| (v,x)::t -> if (v0 = v) then x else readVar t v0 e
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let rec decontextifier e env = match e with
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| Const(_) | BConst(_)-> e
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| Fun(v,e) -> Fun(v,decontextifier e (filter (fun (var,x)->not (v=var)) env)) (* On enlève de l'environnement toutes les occurences de v *)
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| Add(e1,e2) -> Add(decontextifier e1 env, decontextifier e2 env)
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| Mul(e1,e2) -> Mul(decontextifier e1 env, decontextifier e2 env)
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| Min(e1,e2) -> Min(decontextifier e1 env, decontextifier e2 env)
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| Gt(e1,e2) -> Gt(decontextifier e1 env, decontextifier e2 env)
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| Lt(e1,e2) -> Lt(decontextifier e1 env, decontextifier e2 env)
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| Gte(e1,e2) -> Gte(decontextifier e1 env, decontextifier e2 env)
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| Lte(e1,e2) -> Lte(decontextifier e1 env, decontextifier e2 env)
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| Eq(e1,e2) -> Eq(decontextifier e1 env, decontextifier e2 env)
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| Band(e1,e2) -> Band(decontextifier e1 env, decontextifier e2 env)
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| Bor(e1,e2) -> Bor(decontextifier e1 env, decontextifier e2 env)
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| ITE(ec,e1,e2) -> ITE(decontextifier ec env, decontextifier e1 env, decontextifier e2 env)
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| PrInt e1 -> PrInt(decontextifier e1 env)
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| Var(v) ->
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begin
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try
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valToConstExpr (readVar env v (UnknownVariableException (v,env)))
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with UnknownVariableException(_,_) -> Var(v) (* Si ce n'est pas dans le contexte, on ne décontextualise pas *)
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end
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| LetIn(v,e0,e1) -> LetIn(v,decontextifier e0 env, decontextifier e1 (filter (fun (var,x)->not (v=var)) env))
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| App(e0,e1) -> App(decontextifier e0 env, decontextifier e1 env)
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let rec intIntOp op e1 e2 env = match (eval e1 env, eval e2 env) with
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| VInt k1,VInt k2 -> VInt(op k1 k2)
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| _ -> raise InvalidTypeException
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| x,VInt k2 -> raise (InvalidTypeException ("Int",x))
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| _,y -> raise (InvalidTypeException ("Int",y))
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and intBoolOp op e1 e2 env = match (eval e1 env, eval e2 env) with
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| VInt k1,VInt k2 -> VBool(op k1 k2)
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| _ -> raise InvalidTypeException
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| x,VInt k2 -> raise (InvalidTypeException ("Int",x))
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| _,y -> raise (InvalidTypeException ("Int",y))
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(* sémantique opérationnelle à grands pas *)
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and eval e env = match e with
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| Const(k) -> VInt k
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| BConst(b) -> VBool b
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| Fun(v,e) -> VFunc(v,e)
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| Fun(v,e) -> VFunc(v,decontextifier e (filter (fun (var,_)->not (v=var)) env)) (* On enlève de l'environnement toutes les occurences de v *)
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| Add(e1,e2) -> intIntOp ( + ) e1 e2 env
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| Mul(e1,e2) -> intIntOp ( * ) e1 e2 env
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| Min(e1,e2) -> intIntOp ( - ) e1 e2 env
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@ -53,21 +87,24 @@ and eval e env = match e with
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| Eq(e1,e2) -> (match (eval e1 env, eval e2 env) with
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| VInt k1,VInt k2 -> VBool (k1=k2)
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| VBool k1,VBool k2 -> VBool (k1=k2)
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| _ -> raise InvalidTypeException)
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| (x,y) -> raise (InvalidTypeException ("mismatch",x)))
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| Band(e1,e2) -> (match (eval e1 env, eval e2 env) with
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| VBool b1,VBool b2 -> VBool (b1 && b2)
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| _ -> raise InvalidTypeException)
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| x,VBool k2 -> raise (InvalidTypeException ("Bool",x))
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| _,y -> raise (InvalidTypeException ("Bool",y)))
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| Bor(e1,e2) -> (match (eval e1 env, eval e2 env) with
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| VBool b1,VBool b2 -> VBool (b1 || b2)
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| _ -> raise InvalidTypeException)
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| x,VBool k2 -> (raise (InvalidTypeException ("Bool",x)))
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| _,y -> raise (InvalidTypeException ("Bool",y)))
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| ITE(ec,e1,e2) -> (match (eval ec env) with
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| VBool bc -> eval (if bc then e1 else e2) env
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| _ -> raise InvalidTypeException)
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| x -> raise (InvalidTypeException ("Bool",x)))
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| PrInt e1 -> (match (eval e1 env) with
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| VInt k -> VInt k
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| _ -> raise InvalidTypeException)
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| Var(v) -> readVar env v UnknownVariableException
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| x -> raise (InvalidTypeException ("Int",x)))
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| Var(v) -> readVar env v (UnknownVariableException (v,env))
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| LetIn(v,e0,e1) -> eval e1 ((v,eval e0 env)::env)
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| App(e0,e1) -> (match (eval e0 env) with
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| VFunc(v,e) -> eval (LetIn(v,e1,e)) env (* On utilise l'équivalence (fun x->e) y <=> let x=y in e *)
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| _ -> raise InvalidTypeException)
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| x -> raise (InvalidTypeException ("Func",x)))
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@ -43,20 +43,24 @@ let rec affiche_printexpr e env = begin
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match e with
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| PrInt e -> (match (eval e env) with
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| VInt(k) -> print_int k;print_newline ()
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| _ -> raise InvalidTypeException)
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| x -> raise (InvalidTypeException ("Int",x)))
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| _ -> ()
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end
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(* le traitement d'une expression en entrée *)
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let execute e =
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try
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begin
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affiche_expr e;
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print_newline();
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print_newline ();
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affiche_printexpr e Expr.empty_env;
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print_newline();
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print_newline ();
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let v = Expr.eval e Expr.empty_env in
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affiche_val v;
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print_newline()
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print_newline ()
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end
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with
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| InvalidTypeException(expected, valeur) -> print_string "La valeur ";affiche_val valeur;print_string " a été donnée alors que on souhaitait avoir le type ";print_string expected;print_newline ()
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| UnknownVariableException(varname, env) -> print_string "Impossible de trouver la variable '";print_string varname;print_string "' dans l'environnement ";dump_env env;print_newline ()
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(* la boucle principale *)
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let calc () =
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