1 files changed, 390 insertions, 78 deletions

diff --git a/abstract/abs_interp.ml b/abstract/abs_interp.ml
index a610843..8d5f1c9 100644
--- a/abstract/abs_interp.ml
+++ b/abstract/abs_interp.ml
@@ -4,42 +4,244 @@ open Formula
 open Typing
 
 open Util
-open Abs_domain
 open Num_domain
+open Enum_domain
 
-module I (E : ENVIRONMENT_DOMAIN) : sig
+
+module I (ED : ENUM_ENVIRONMENT_DOMAIN) (ND : NUMERICAL_ENVIRONMENT_DOMAIN) : sig
 
     type st
 
-    val do_prog     : int -> rooted_prog -> unit
+    val do_prog     : int -> (id -> bool) -> rooted_prog -> unit
 
 end = struct
 
+    (*  **************************
+            Disjunction domain 
+        **************************  *)
+
+    type case_v = ED.t * ND.t
+    type case = ED.item list
+
+    type dd_v = {
+        d_vars  : id list;
+        data    : (case, case_v) Hashtbl.t;
+    }
+
+    (*
+      print_dd : Formatter.t -> dd_v -> unit
+    *)
+    let print_aux fmt d_vars env =
+      let print_it q (enum, num) =
+        Format.fprintf fmt "@[<hov 4>";
+        List.iter2
+          (fun id  v -> Format.fprintf fmt "%a ≡ %s,@ "
+              Formula_printer.print_id id v)
+          d_vars q;
+        Format.fprintf fmt "@ %a,@ %a@]@."
+            ED.print enum ND.print num;
+      in
+      Hashtbl.iter print_it env
+    let print_dd fmt dd = print_aux fmt dd.d_vars dd.data
+
+
+    (*
+      dd_bot : id list -> dd_v
+    *)
+    let dd_bot d_vars = { d_vars; data = Hashtbl.create 12 }
+
+    (*
+      dd_add_case : dd_v -> case_v -> unit
+    *)
+    let dd_add_case env (enum, num) =
+      let rec aux enum vals = function
+        | [] ->
+          let case = List.rev vals in
+          begin try let e0, n0 = Hashtbl.find env.data case in
+            Hashtbl.replace env.data case (ED.join enum e0, ND.join num n0);
+          with Not_found ->
+            Hashtbl.add env.data case (enum, num);
+          end
+        | p::q ->
+          List.iter
+            (fun v -> match ED.apply_cons enum (E_EQ, p, EItem v) with
+              | [en] -> aux en (v::vals) q
+              | _ -> assert false)
+            (ED.project enum p)
+      in aux enum [] env.d_vars
+
+    (*
+      dd_singleton : id list -> case_v -> dd_v
+    *)
+    let dd_singleton d_vars d =
+      let v = { d_vars; data = Hashtbl.create 1 } in
+      dd_add_case v d;
+      v
+
+    (*
+      dd_extract_case : dd_v -> case -> dd_v
+    *)
+    let dd_extract_case v case =
+      try dd_singleton v.d_vars (Hashtbl.find v.data case)
+      with Not_found -> dd_bot v.d_vars
+
+
+    (*
+      dd_apply_ncons : dd_v -> num_cons list -> dd_v
+    *)
+    let dd_apply_ncl v ncl =
+        let vv = dd_bot v.d_vars in
+        Hashtbl.iter (fun case (enum, num) ->
+            let num = ND.apply_cl num ncl in
+            if not (ND.is_bot num) then
+              Hashtbl.add vv.data case (enum, num))
+          v.data;
+        vv
+
+    (*
+      dd_apply_econs : dd_v -> enum_cons -> dd_v
+    *)
+    let dd_apply_econs v cons =
+        let vv = dd_bot v.d_vars in
+        Hashtbl.iter (fun case (enum, num) ->
+            List.iter
+              (fun enum -> dd_add_case vv (enum, num))
+              (ED.apply_cons enum cons))
+          v.data;
+        vv
+
+    (*
+      dd_join : dd_v -> dd_v -> dd_v
+    *)
+    let dd_join a b =
+        let vv = { d_vars = a.d_vars; data = Hashtbl.copy a.data } in
+        Hashtbl.iter (fun case (enum, num) ->
+            try let e2, n2 = Hashtbl.find vv.data case in
+              Hashtbl.replace vv.data case (ED.join e2 enum, ND.join n2 num)
+            with Not_found -> Hashtbl.replace vv.data case (enum, num))
+          b.data;
+        vv
+
+    (*
+      dd_meet : dd_v -> dd_v -> dd_v
+    *)
+    let dd_meet a b =
+        let vv = dd_bot a.d_vars in
+        Hashtbl.iter (fun case (enum, num) ->
+            try let e2, n2 = Hashtbl.find b.data case in
+              let en, nn = ED.meet enum e2, ND.meet n2 num in
+              if not (ND.is_bot nn) then Hashtbl.add vv.data case (en, nn)
+            with _ -> ())
+          a.data;
+        vv
+
+    (*
+      dd_apply_cl : dd_v -> conslist -> dd_v
+    *)
+    let rec apply_cl env (ec, nc, r) =
+        match r with
+        | CLTrue ->
+          let env_ec = List.fold_left dd_apply_econs env ec in
+          let env_nc = dd_apply_ncl env_ec nc in
+          (* Format.printf "[[ %a -> %a ]]@."
+              print_dd env print_dd env_nc; *)
+          env_nc
+        | CLFalse -> dd_bot env.d_vars
+        | CLAnd(a, b) ->
+          let env = apply_cl env (ec, nc, a) in
+          apply_cl env (ec, nc, b)
+        | CLOr((eca, nca, ra), (ecb, ncb, rb)) ->
+          dd_join (apply_cl env (ec@eca, nc@nca, ra))
+                  (apply_cl env (ec@ecb, nc@ncb, rb))
+      
+
+    (*  ***************************
+          Abstract interpretation 
+        ***************************  *)
+
     type st = {
         rp          : rooted_prog;
         widen_delay : int;
-        env         : E.t;
+
+        enum_vars   : (id * ED.item list) list;
+        num_vars    : (id * bool) list;
+
+        (* program expressions *)
         f           : bool_expr;
         cl          : conslist;
         f_g         : bool_expr;
         cl_g        : conslist;
         guarantees  : (id * bool_expr) list;
+
+        (* abstract interpretation *)
+        cycle       : (id * id * typ) list;     (* s'(x) = s(y) *)
+        forget      : (id * typ) list;          (* s'(x) not specified *)
+        d_vars      : id list;                  (* disjunction variables *)
+        top         : case_v;
+        env         : (case, case_v) Hashtbl.t;
+        mutable delta : case list;
+        widen       : (case, int) Hashtbl.t;
     }
 
+    (*
+      print_st : Formatter.t -> st -> unit
+    *)
+    let print_st fmt st = print_aux fmt st.d_vars st.env
 
-    (* init state *)
-    let init_state widen_delay rp =
-      let env = List.fold_left
-        (fun env (_, id, ty) -> E.addvar env id ty)
-        E.init
-        rp.all_vars
-      in
+    (*
+      add_case : st -> case_v -> unit
+    *)
+    let add_case st (enum, num) =
+      let rec aux enum vals = function
+        | [] ->
+          let case = List.rev vals in
+          begin try let e0, n0 = Hashtbl.find st.env case in
+            if (not (ED.subset enum e0)) || (not (ND.subset num n0)) then begin
+              begin try
+                let n = Hashtbl.find st.widen case in
+                let jw = if n < st.widen_delay then ND.join else ND.widen in
+                Hashtbl.replace st.env case (ED.join e0 enum, jw n0 num);
+                Hashtbl.replace st.widen case (n+1);
+              with Not_found ->
+                Hashtbl.replace st.env case (ED.join enum e0, ND.join num n0);
+                Hashtbl.add st.widen case 0;
+              end;
+              if not (List.mem case st.delta) then st.delta <- case::st.delta
+            end
+          with Not_found ->
+            Hashtbl.add st.env case (enum, num);
+            if not (List.mem case st.delta) then st.delta <- case::st.delta
+          end
+        | p::q ->
+          List.iter
+            (fun v -> match ED.apply_cons enum (E_EQ, p, EItem v) with
+              | [en] -> aux en (v::vals) q
+              | _ -> assert false)
+            (ED.project enum p)
+      in aux enum [] st.d_vars
+
+
+
+    (*
+      init_state : int -> rooted_prog -> st
+    *)
+    let init_state widen_delay disj rp =
       Format.printf "Vars: @[<hov>%a@]@.@."
           (Ast_printer.print_list Ast_printer.print_typed_var ", ")
           rp.all_vars;
 
+      let enum_vars = List.fold_left
+          (fun v (_, id, t) -> match t with
+              | TEnum ch -> (id, ch)::v | _ -> v)
+          [] rp.all_vars in
+      let num_vars = List.fold_left
+          (fun v (_, id, t) -> match t with
+              | TInt -> (id, false)::v | TReal -> (id, true)::v | _ -> v)
+          [] rp.all_vars in
+
       let init_f = Transform.init_f_of_prog rp in
       Format.printf "Init formula: %a@.@." Formula_printer.print_expr init_f;
+      let init_cl = conslist_of_f init_f in
 
       let guarantees = Transform.guarantees_of_prog rp in
       Format.printf "Guarantees:@.";
@@ -51,96 +253,192 @@ end = struct
       let f = Formula.eliminate_not (Transform.f_of_prog rp false) in
       let f_g = Formula.eliminate_not (Transform.f_of_prog rp true) in
       Format.printf "Cycle formula:@.%a@.@." Formula_printer.print_expr f;
-      Format.printf "Cycle formula with guarantees:@.%a@.@." Formula_printer.print_expr f_g;
-
-      let env = E.set_disjunct env "/exit" DNever in
-      let env = E.apply_f env init_f in
+      Format.printf "Cycle formula with guarantees:@.%a@.@."
+          Formula_printer.print_expr f_g;
 
       let cl = Formula.conslist_of_f f in
       let cl_g = Formula.conslist_of_f f_g in
 
-      { rp; widen_delay;
-        f; cl; f_g; cl_g;
-        guarantees; env }
-
-    (*
-      pass_cycle : var_def list -> E.t -> E.t
-
-      Does :
-        - x <- Nx, for all x
-        - ignore x for all x such that Nx does not exist
-    *)
-    let pass_cycle vars e =
-      let tr_assigns = List.fold_left
-        (fun q (_, id, _) ->
+      (* calculate cycle variables and forget variables *)
+      let cycle = List.fold_left
+        (fun q (_, id, ty) ->
             if id.[0] = 'N' then
-              (String.sub id 1 (String.length id - 1), id)::q
-            else
-              q)
-        [] vars
+              (String.sub id 1 (String.length id - 1), id, ty)::q
+            else q)
+        [] rp.all_vars
       in
-      let e = E.assign e tr_assigns in
-
-      let forget_vars = List.map (fun (_, id, _) -> id)
+      let forget = List.map (fun (_, id, ty) -> (id, ty))
           (List.filter
-              (fun (_, id, _) ->
-                 not (List.exists (fun (_, id2, _) -> id2 = "N"^id) vars))
-              vars) in
-      let e = List.fold_left E.forgetvar e forget_vars in
-      e
+            (fun (_, id, _) ->
+              not (List.exists (fun (_, id2, _) -> id2 = "N"^id) rp.all_vars))
+            rp.all_vars)
+      in
+
+      (* calculate disjunction variables *)
+      (* first approximation : use all enum variables appearing in init formula *)
+      let rec calculate_dvars (ec, _, r) =
+          let a = List.map (fun (_, id, _) -> id) ec in
+          let rec aux = function
+          | CLTrue | CLFalse -> []
+          | CLAnd(u, v) ->
+              aux u @ aux v
+          | CLOr(u, v) ->
+              calculate_dvars u @ calculate_dvars v
+          in a @ aux r
+      in
+      let d_vars_0 = calculate_dvars init_cl in
+      let d_vars_1 = List.filter
+          (fun id -> disj id && not (List.mem id d_vars_0) && id.[0] <> 'N')
+          (List.map (fun (id, _) -> id) enum_vars) in
+      let d_vars = d_vars_0 @ d_vars_1 in
+
+      (* setup abstract data *)
+      let top = ED.top enum_vars, ND.top num_vars in
+      let delta = [] in
+      let widen = Hashtbl.create 12 in
 
+      (* calculate initial state and environment *)
+      let init_s = dd_bot d_vars in
+
+      let init_ec, _, _ = init_cl in
+      let init_ed = List.fold_left
+          (fun ed cons ->
+            List.flatten (List.map (fun x -> ED.apply_cons x cons) ed))
+          [ED.top enum_vars] (init_ec) in
+      List.iter (fun ed -> dd_add_case init_s (ed, ND.top num_vars)) init_ed;
+      let env_dd = apply_cl init_s init_cl in
+      let env = env_dd.data in
+      
+      let st = 
+      { rp; widen_delay; enum_vars; num_vars;
+        f; cl; f_g; cl_g; guarantees;
+        cycle; forget; d_vars; top;
+        env; delta; widen } in
+
+      Hashtbl.iter (fun case _ -> st.delta <- case::st.delta) st.env;
+
+      st
 
-    (* cycle : st -> cl -> env -> env *)
-    let cycle st cl i =
-      (pass_cycle st.rp.all_vars (E.apply_cl i cl)) 
 
     (*
-      loop : st -> env -> env -> env
+      pass_cycle : st -> case_v -> case_v
     *)
-    let loop st acc0 =
+    let pass_cycle st (enum, num) =
+        let assign_e = 
+          List.map (fun (a, b, _) -> a, b)
+          (List.filter
+            (fun (_, _, t) -> match t with TEnum _ -> true | _ -> false)
+            st.cycle) in
+        let assign_n = 
+          List.map (fun (a, b, _) -> a, NIdent b)
+          (List.filter
+            (fun (_, _, t) -> match t with TInt | TReal -> true | _ -> false)
+            st.cycle) in
 
-      Format.printf "Loop @[<hv>%a@]@.@."
-        Formula_printer.print_conslist st.cl;
+        let enum = ED.assign enum assign_e in
+        let num = ND.assign num assign_n in
 
-      let fsharp cl i = 
-        Format.printf "Acc @[<hv>%a@]@." E.print_all i;
-        let j = cycle st cl i in
-        E.join acc0 j
-      in
+        List.fold_left
+            (fun (enum, num) (var, t) -> match t with
+              | TEnum _ -> ED.forgetvar enum var, num
+              | TReal | TInt -> enum, ND.forgetvar num var)
+            (enum, num) st.forget
 
-      let rec iter n i =
-        let i' =
-          if n < st.widen_delay
-            then E.join i (fsharp st.cl i)
-            else E.widen i (fsharp st.cl_g i)
-        in
-        if E.eq i i' then i else iter (n+1) i'
-      in
+    let dd_pass_cycle st (v : dd_v) =
+      let vv = dd_bot v.d_vars in
+      Hashtbl.iter (fun _ x -> dd_add_case vv (pass_cycle st x)) v.data;
+      vv
+
+    (*
+      cycle : st -> cl -> dd_v -> dd_v
+    *)
+    let cycle st cl env =
+      let env_f = apply_cl env cl in
+      (* Format.printf "{{ %a ->@.%a }}@." print_dd env print_dd env_f; *)
+      dd_pass_cycle st env_f
 
-      let x = iter 0 acc0 in
-      let y = fix E.eq (fsharp st.cl) x in    (* decreasing iteration *)
-      let z = E.apply_cl y st.cl in             (* no more guarantee *)
-      y, z
+
+    (*
+      set_target_case : st -> dd_v -> case -> dd_v
+    *)
+    let set_target_case st env case =
+      List.fold_left2
+        (fun env id v ->
+          if List.exists (fun (id2, _) -> id2 = "N"^id) st.enum_vars then
+            dd_apply_econs env (E_EQ, "N"^id, EItem v)
+          else env)
+        env st.d_vars case
 
     (*
       do_prog : rooted_prog -> unit
     *)
-    let do_prog widen_delay rp =
-      let st = init_state widen_delay rp in
+    let do_prog widen_delay disj rp =
+      let st = init_state widen_delay disj rp in
+
+      Format.printf "Init: %a@." print_st st;
+
+      let n_ch_iter = ref 0 in
 
-      let final_nc, final = loop st st.env in
+      (* chaotic iteration loop *)
+      while st.delta <> [] do
+        let case = List.hd st.delta in
+
+        incr n_ch_iter;
+        Format.printf "Chaotic iteration %d: @[<hov>[%a]@]@."
+            !n_ch_iter
+            (Ast_printer.print_list Formula_printer.print_id ", ") case;
+        
+        let start = try Hashtbl.find st.env case with Not_found -> assert false in
+        let start_dd = dd_singleton st.d_vars start in
+        let f i =
+          let i = dd_singleton st.d_vars i in
+          let i' = set_target_case st i case in
+          let q = dd_join start_dd (cycle st st.cl i') in
+          try Hashtbl.find q.data case with Not_found -> assert false
+        in
+
+        let rec iter n (i_enum, i_num) =
+          let fi_enum, fi_num = f (i_enum, i_num) in
+          let j_enum, j_num =
+            if n < st.widen_delay then
+              ED.join i_enum fi_enum, ND.join i_num fi_num
+            else
+              ED.join i_enum fi_enum, ND.widen i_num fi_num
+          in
+          if ED.eq j_enum i_enum && ND.eq j_num i_num
+            then (i_enum, i_num)
+            else iter (n+1) (j_enum, j_num)
+        in
+        let y = iter 0 start in
+        let z = fix (fun (a, b) (c, d) -> ED.eq a c && ND.eq b d) f y in
+
+        let i = dd_singleton st.d_vars z in
+        let j = cycle st st.cl i in
+        let cases = ref [] in
+        Hashtbl.iter (fun case _ -> cases := case::(!cases)) j.data;
+        List.iter
+            (fun case ->
+              let i' = set_target_case st i case in
+              let j = cycle st st.cl i' in
+              Hashtbl.iter (fun _ q -> add_case st q) j.data)
+            !cases;
+
+        st.delta <- List.filter ((<>) case) st.delta;
+
+        (* Format.printf "Final: %a@." print_st st; *)
+
+      done;
+
+      let final = apply_cl { d_vars = st.d_vars; data = st.env } st.cl in
+      Format.printf "Accessible: %a@." print_dd final;
 
-      Format.printf "@[<hov>F %a@]@.@."
-        E.print_all final_nc;
-      Format.printf "@[<hov>F' %a@]@.@."
-        E.print_all final;
 
       let check_guarantee (id, f) =
         let cl = Formula.conslist_of_f f in
         Format.printf "@[<hv 4>%s:@ %a ⇒ ⊥  @ "
           id Formula_printer.print_conslist cl;
-        let z = E.apply_cl final cl in
-        if E.is_bot z then
+        let z = apply_cl final cl in
+        if Hashtbl.length z.data = 0 then
           Format.printf "OK@]@ "
         else
           Format.printf "FAIL@]@ "
@@ -153,12 +451,26 @@ end = struct
 
       if List.exists (fun (p, _, _) -> p) st.rp.all_vars then begin
         Format.printf "Probes: @[<v 0>";
-        List.iter (fun (p, id, _) ->
-          if p then Format.printf "%a ∊ %a@ "
-                Formula_printer.print_id id
-                E.print_itv (E.var_itv final id))
+        List.iter (fun (p, id, ty) ->
+          if p then begin
+            Format.printf "%a ∊ @[<v>" Formula_printer.print_id id;
+            Hashtbl.iter (fun case (enum, num) ->
+              begin match ty with
+              | TInt | TReal ->
+                Format.printf "%a" ND.print_itv (ND.project num id)
+              | TEnum _ ->
+                Format.printf "@[<hov>{ %a }@]"
+                  (Ast_printer.print_list Formula_printer.print_id ", ")
+                  (ED.project enum id)
+              end;
+              Format.printf " when @[<hov>[%a]@]@ "
+                (Ast_printer.print_list Formula_printer.print_id ", ") case)
+              final.data;
+            Format.printf "@]@ "
+          end)
           st.rp.all_vars;
         Format.printf "@]@."
       end
 
 end
+