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+
+open Ast
+
+type assoc = L | R | N
+
+let level = function
+ | "--" -> 70,L
+ | "=" -> 70,N
+ | "+" -> 60,L
+ | "++" -> 60,R
+ | "+++" -> 60,R
+ | "-" -> 60,L
+ | "*" -> 50,L
+ | "/" -> 50,L
+ | "**" -> 40,R
+ | ":" -> (100,R)
+ | "->" -> (90,R)
+ | s -> failwith ("unknowm operator '"^s^"'")
+
+let fixity = function
+ | "--" -> [L]
+ | "=" -> [N]
+ | ("+"|"-"|"*"|"/") -> [L;N]
+ | "++" -> [R]
+ | _ -> [L;N;R]
+
+let ground_oper = function
+ ("-"|"+") -> true
+ | _ -> false
+
+let is_prefix op = List.mem L (fixity op)
+let is_infix op = List.mem N (fixity op)
+let is_postfix op = List.mem R (fixity op)
+
+let mk_inf op t1 t2 =
+ if not (is_infix op) then failwith (op^" not infix");
+ Infix(op,t1,t2)
+
+let mk_post op t =
+ if not (is_postfix op) then failwith (op^" not postfix");
+ Postfix(op,t)
+
+
+(* Pb avec ground_oper: pas de diff entre -1 et -(1) *)
+let mk_pre op t =
+ if not (is_prefix op) then failwith (op^" not prefix");
+ if ground_oper op then
+ match t with
+ | Int i -> Int (op^i)
+ | _ -> Prefix(op,t)
+ else Prefix(op,t)
+
+(* teste si on peut reduire op suivi d'un op de niveau (n,a)
+ si la reponse est false, c'est que l'op (n,a) doit se reduire
+ avant *)
+let red_left_op (nl,al) (nr,ar) =
+ if nl < nr then true
+ else
+ if nl = nr then
+ match al,ar with
+ | (L|N), L -> true
+ | R, (R|N) -> false
+ | R, L -> failwith "conflit d'assoc: ambigu"
+ | (L|N), (R|N) -> failwith "conflit d'assoc: blocage"
+ else false
+
+
+type level = int * assoc
+type stack =
+ | PrefixOper of string list
+ | Term of constr_ast * stack
+ | Oper of string list * string * constr_ast * stack
+
+let rec str_ast = function
+ | Infix(op,t1,t2) -> str_ast t1 ^ " " ^ op ^ " " ^ str_ast t2
+ | Postfix(op,t) -> str_ast t ^ " " ^ op
+ | Prefix(op,t) -> op ^ " " ^ str_ast t
+ | _ -> "_"
+
+let rec str_stack = function
+ | PrefixOper ops -> String.concat " " (List.rev ops)
+ | Term (t,s) -> str_stack s ^ " (" ^ str_ast t ^ ")"
+ | Oper(ops,lop,t,s) ->
+ str_stack (Term(t,s)) ^ " " ^ lop ^ " " ^
+ String.concat " " (List.rev ops)
+
+let pps s = prerr_endline (str_stack s)
+let err s stk = failwith (s^": "^str_stack stk)
+
+
+let empty = PrefixOper []
+
+let check_fixity_term stk =
+ match stk with
+ Term _ -> err "2 termes successifs" stk
+ | _ -> ()
+
+let shift_term t stk =
+ check_fixity_term stk;
+ Term(t,stk)
+
+let shift_oper op stk =
+ match stk with
+ | Oper(ops,lop,t,s) -> Oper(op::ops,lop,t,s)
+ | Term(t,s) -> Oper([],op,t,s)
+ | PrefixOper ops -> PrefixOper (op::ops)
+
+let is_reducible lv stk =
+ match stk with
+ | Oper([],iop,_,_) -> red_left_op (level iop) lv
+ | Oper(op::_,_,_,_) -> red_left_op (level op) lv
+ | PrefixOper(op::_) -> red_left_op (level op) lv
+ | _ -> false
+
+let reduce_head (t,stk) =
+ match stk with
+ | Oper([],iop,t1,s) ->
+ (Infix(iop,t1,t), s)
+ | Oper(op::ops,lop,t',s) ->
+ (mk_pre op t, Oper(ops,lop,t',s))
+ | PrefixOper(op::ops) ->
+ (Prefix(op,t), PrefixOper ops)
+ | _ -> assert false
+
+let rec reduce_level lv (t,s) =
+ if is_reducible lv s then reduce_level lv (reduce_head (t, s))
+ else (t, s)
+
+let reduce_post op (t,s) =
+ let (t',s') = reduce_level (level op) (t,s) in
+ (mk_post op t', s')
+
+let reduce_posts stk =
+ match stk with
+ Oper(ops,iop,t,s) ->
+ let pts1 = reduce_post iop (t,s) in
+ List.fold_right reduce_post ops pts1
+ | Term(t,s) -> (t,s)
+ | PrefixOper _ -> failwith "reduce_posts"
+
+
+let shift_infix op stk =
+ let (t,s) = reduce_level (level op) (reduce_posts stk) in
+ Oper([],op,t,s)
+
+let is_better_infix op stk =
+ match stk with
+ | Oper(ops,iop,t,s) ->
+ is_postfix iop &&
+ List.for_all is_postfix ops &&
+ (not (is_prefix op) || red_left_op (level iop) (level op))
+ | Term _ -> false
+ | _ -> assert false
+
+let parse_oper op stk =
+ match stk with
+ | PrefixOper _ ->
+ if is_prefix op then shift_oper op stk else failwith "prefix_oper"
+ | Oper _ ->
+ if is_infix op then
+ if is_better_infix op stk then shift_infix op stk
+ else shift_oper op stk
+ else if is_prefix op then shift_oper op stk
+ else if is_postfix op then
+ let (t,s) = reduce_post op (reduce_posts stk) in
+ Term(t,s)
+ else assert false
+ | Term(t,s) ->
+ if is_infix op then shift_infix op stk
+ else if is_postfix op then
+ let (t2,s2) = reduce_post op (t,s) in Term(t2,s2)
+ else failwith "infix/postfix"
+
+let parse_term = shift_term
+
+let rec close_stack stk =
+ match stk with
+ Term(t,PrefixOper []) -> t
+ | PrefixOper _ -> failwith "expression sans atomes"
+ | _ ->
+ let (t,s) = reduce_head (reduce_posts stk) in
+ close_stack (Term(t,s))
+