X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Fnum.ml;h=71f493545df93edce3e4a9b844b838b3b54e2c66;hb=a104858f2dd754e5d086c3884823f3f39d716691;hp=d00398532ae4495d6379a2fca1cc3e7f1adbf002;hpb=5c065c453e7d3f1e35d9f23fb4b6345d88d0f083;p=fireball-separation.git

diff --git a/ocaml/num.ml b/ocaml/num.ml
index d003985..71f4935 100644
--- a/ocaml/num.ml
+++ b/ocaml/num.ml
@@ -2,6 +2,9 @@ open Util
 open Util.Vars
 open Pure
 
+(* debug options *)
+let debug_display_arities = false;;
+
 (************ Syntax ************************************)
 
 (* Normal forms*)
@@ -16,17 +19,18 @@ and i =
   | I of int * nf listx
 ;;*)
 type var = int * (* arity of variable*) int;;
-type 'nf i_var_ = [ `I of var * 'nf Listx.listx | `Var of var ]
-type 'nf i_n_var_ = [ `N of int | 'nf i_var_ ]
-type 'nf i_num_var_ = [
-  | 'nf i_n_var_
-  | `Match of 'nf i_num_var_ * (* originating var *) var * (*lift*) int * (*branches*)(int * 'nf) list ref * (*args*)'nf list
+type 'nf_nob i_var_ = [ `I of var * 'nf_nob Listx.listx | `Var of var ]
+type 'nf_nob i_n_var_ = [ `N of int | 'nf_nob i_var_ ]
+type ('nf_nob,'nf) i_num_var_ = [
+  | 'nf_nob i_n_var_
+  | `Match of ('nf_nob,'nf) i_num_var_ * (* originating var *) var * (*lift*) int * (*branches*)(int * 'nf) list ref * (*args*)'nf_nob list
 ]
-type 'nf nf_ = [ `Lam of (* was_unpacked *) bool * 'nf nf_ | 'nf i_num_var_ ]
-type nf = nf nf_
-type i_var = nf i_var_;;
-type i_n_var = nf i_n_var_;;
-type i_num_var = nf i_num_var_;;
+type 'nf nf_nob_ = [ `Lam of (* was_unpacked *) bool * 'nf | `Pacman | ('nf nf_nob_,'nf) i_num_var_ ]
+type nf = [ nf nf_nob_ | `Bottom  ]
+type nf_nob = nf nf_nob_
+type i_var = nf_nob i_var_;;
+type i_n_var = nf_nob i_n_var_;;
+type i_num_var = (nf_nob,nf) i_num_var_;;
 
 let hd_of_i_var =
  function
@@ -50,15 +54,20 @@ let lift m (t : nf) =
  let aux_var l (n, ar) = (if n < l then n else n+m), ar in
  let rec aux_i_num_var l =
   function
-    `I(v,args) -> `I(aux_var l v, Listx.map (aux l) args)
+    `I(v,args) -> `I(aux_var l v, Listx.map (aux_nob l) args)
    | `Var v -> `Var(aux_var l v)
    | `N _ as x -> x
    | `Match(t,v,lift,bs,args) ->
-      `Match(aux_i_num_var l t, v, lift + m, bs, List.map (aux l) args)
- and aux l =
+      `Match(aux_i_num_var l t, v, lift + m, bs, List.map (aux_nob l) args)
+ and aux_nob l =
   function
-     #i_num_var as x -> (aux_i_num_var l x :> nf)
+     #i_num_var as x -> (aux_i_num_var l x :> nf_nob)
    | `Lam(b,nf) -> `Lam (b, aux (l+1) nf)
+   | `Pacman -> `Pacman
+ and aux l =
+  function
+     #nf_nob as x -> (aux_nob l x :> nf)
+   | `Bottom -> `Bottom
  in
   (aux 0 t : nf)
 ;;
@@ -70,69 +79,74 @@ let rec make_lams t =
  | n when n > 0 -> `Lam (false, lift 1 (make_lams t (n-1)))
  | _ -> assert false
 
-let free_vars =
+let free_vars' =
  let rec aux n = function
     `N _ -> []
-  | `Var(x,_) -> if x < n then [] else [x-n]
-  | `I((x,_),args) ->
-      (if x < n then [] else [x-n]) @
-      List.concat (List.map (aux n) (Listx.to_list args))
+  | `Var(x,ar) -> if x < n then [] else [(x-n,ar)]
+  | `I((x,ar),args) ->
+      (if x < n then [] else [(x-n,ar)]) @
+      List.concat (List.map (aux n) (Listx.to_list args :> nf list))
   | `Lam(_,t) -> aux (n+1) t
   | `Match(t,_,liftno,bs,args) ->
       aux n (t :> nf) @
       List.concat (List.map (fun (_,t) -> aux (n-liftno) t) !bs) @
-      List.concat (List.map (aux n) args)
+      List.concat (List.map (aux n) (args :> nf list))
+  | `Bottom | `Pacman -> []
   in aux 0
 ;;
+let free_vars = (List.map fst) ++ free_vars';;
 
 module ToScott =
 struct
 
-let rec t_of_i_num_var =
- function
-  | `N n -> Scott.mk_n n
-  | `Var(v,_) -> Pure.V v
-  | `Match(t,_,liftno,bs,args) ->
-      let bs = List.map (fun (n,t) -> n, t_of_nf (lift liftno t)) !bs in
-      let t = t_of_i_num_var t in
-      let m = Scott.mk_match t bs in
-      List.fold_left (fun acc t -> Pure.A(acc,t_of_nf t)) m args
-  | `I((v,_), args) -> Listx.fold_left (fun acc t -> Pure.A(acc,t_of_nf t)) (Pure.V v) args
-and t_of_nf =
- function
-  | #i_num_var as x -> t_of_i_num_var x
-  | `Lam(b,f) -> Pure.L (t_of_nf f)
-
+let rec scott_of_nf = function
+ | `N n -> Scott.mk_n n
+ | `Var(v,_) -> Pure.V v
+ | `Match(t,_,liftno,bs,args) ->
+ let bs = List.map (fun (n,t) -> n, scott_of_nf (lift liftno (t :> nf))) !bs in
+     let t = scott_of_nf (t :> nf) in
+     let m = Scott.mk_match t bs in
+     List.fold_left (fun acc t -> Pure.A(acc,scott_of_nf t)) m (args :> nf list)
+ | `I((v,_), args) -> Listx.fold_left (fun acc t -> Pure.A(acc,scott_of_nf t)) (Pure.V v) (args :> nf Listx.listx)
+ | `Lam(_,t) -> Pure.L (scott_of_nf t)
+ | `Bottom -> Pure.B
+ | `Pacman -> let f x = Pure.A (x,x) in f (Pure.L (Pure.L (f (Pure.V 0))))
 end
 
 
 (************ Pretty-printing ************************************)
 
-let rec string_of_term l =
- let rec string_of_term_w_pars l = function
-  | `Var(n,ar) -> print_name l n ^ ":" ^ string_of_int ar
+(* let rec string_of_term l  = fun _ -> "";; *)
+
+let rec string_of_term l  =
+ let rec string_of_term_w_pars l  = function
+  | `Var(n,ar) -> print_name l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "")
   | `N n -> string_of_int n
-  | `I _ as t -> "(" ^ string_of_term_no_pars_app l (t :> nf) ^ ")"
+  | `I _ as t -> "(" ^ string_of_term_no_pars_app l t ^ ")"
+  | `Lam(_,`Bottom) -> "BOMB"
   | `Lam _ as t -> "(" ^ string_of_term_no_pars_lam l t ^ ")"
   | `Match(t,(v,ar),bs_lift,bs,args) ->
-     "[match("^print_name l v ^ ":" ^ string_of_int ar^") " ^ string_of_term_no_pars l (t :> nf) ^
-     " with " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ string_of_term l (lift bs_lift t)) !bs) ^ "] " ^
-     String.concat " " (List.map (string_of_term l) args) ^ ")"
- and string_of_term_no_pars_app l = function
-  | `I((n,ar), args) -> print_name l n  ^ ":" ^ string_of_int ar ^ " " ^ String.concat " " (List.map (string_of_term_w_pars l) (Listx.to_list args))
+     "["^ string_of_var v ^ (if debug_display_arities then ":"^ string_of_int ar else "") ^",match " ^ string_of_term_no_pars l (t :> nf) ^
+     " with " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ string_of_term l (lift bs_lift (t :> nf))) !bs) ^ "] " ^
+     String.concat " " (List.map (string_of_term l) (args :> nf list)) ^ ")"
+  | `Bottom -> "BOT"
+  | `Pacman -> "PAC"
+ and string_of_term_no_pars_app l  = function
+  | `I((n,ar), args) -> print_name l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "") ^ " " ^ String.concat " " (List.map (string_of_term_w_pars l) (Listx.to_list args :> nf list))
   | #nf as t -> string_of_term_w_pars l t
  and string_of_term_no_pars_lam l  = function
+  | `Lam(_,`Bottom) -> "BOMB"
   | `Lam(_,t) -> let name = string_of_var (List.length l) in
-   "λ" ^ name ^ ". " ^ (string_of_term_no_pars_lam (name::l) t)
+     "λ" ^ name ^ ". " ^ (string_of_term_no_pars_lam (name::l) t)
   | _ as t -> string_of_term_no_pars l t
- and string_of_term_no_pars l : nf -> string = function
+ and string_of_term_no_pars l  = function
   | `Lam _ as t -> string_of_term_no_pars_lam l t
   | #nf as t -> string_of_term_no_pars_app l t
  in string_of_term_no_pars l
 ;;
 
 let print ?(l=[]) = string_of_term l;;
-let string_of_nf t = string_of_term [] (t:>nf);;
+let string_of_nf t = string_of_term [] (t :> nf);;
 
 (************ Hereditary substitutions ************************************)
 
@@ -157,23 +171,26 @@ let cast_to_i_num_var =
     prerr_endline (print (t :> nf));
     assert false (* algorithm failed *)
 
-let set_arity arity = function
+let rec set_arity arity = function
 | `Var(n,_) -> `Var(n,arity)
-| `Lam(false, `N _)
-| `Lam(false, `Lam _) as t -> t
-| `Lam(false, `Match(t,(n,_),bs_lift,bs,args)) -> `Lam(false, `Match(t,(n,arity),bs_lift,bs,args))
-| _ -> assert false
+| `N _ | `Bottom | `Pacman as t -> t
+| `Lam(false, t) -> `Lam(false, set_arity arity t)
+| `Match(t,(n,_),bs_lift,bs,args) -> `Match(t,(n,arity),bs_lift,bs,args)
+| `I _ | `Lam _ -> assert false
 
 let minus1 n = if n = min_int then n else n - 1;;
 
 let rec mk_app (h : nf) (arg : nf) =
-(*let res =*)
- match h with
-    `I(v,args) -> `I(v,Listx.append (Listx.Nil arg) args)
-  | `Var v -> `I(v, Listx.Nil arg)
-  | `Lam(truelam,nf) -> subst truelam true 0 arg (nf : nf) (* AC FIXME sanity check on arity *)
-  | `Match(t,v,lift,bs,args) -> `Match(t,v,lift,bs,List.append args [arg])
-  | `N _ -> assert false (* Numbers cannot be applied *)
+ match arg with
+  | `Bottom -> `Bottom
+  | #nf_nob as arg ->
+    match h with
+     | `I(v,args) -> `I(v,Listx.append (Listx.Nil arg) args)
+     | `Var v -> `I(v, Listx.Nil arg)
+     | `Lam(truelam,nf) -> subst truelam true 0 arg (nf : nf) (* AC FIXME sanity check on arity *)
+     | `Match(t,v,lift,bs,args) -> `Match(t,v,lift,bs,List.append args [arg])
+     | `Bottom | `Pacman as t -> t
+     | `N _ -> assert false (* Numbers cannot be applied *)
 (*in let l = ["v0";"v1";"v2"] in
 prerr_endline ("mk_app h:" ^ print ~l h ^ " arg:" ^ print ~l:l arg ^ " res:" ^ print ~l:l res); res*)
 
@@ -185,49 +202,62 @@ and mk_appx h args = Listx.fold_left mk_app h args
 
 and mk_match t (n,ar) bs_lift bs args =
  (*prerr_endline ("MK_MATCH: ([" ^ print t ^ "] " ^ String.concat " " (Listx.to_list (Listx.map (fun (n,t) -> string_of_int n ^ " => " ^ print t) bs)) ^ ") " ^ String.concat " " (List.map print args));*)
- match t with
-    `N m ->
+ let m =
+  match t with
+    `N m as t ->
       (try
         let h = List.assoc m !bs in
         let h = set_arity (minus1 ar) h in
         let h = lift bs_lift h in
-        mk_appl h args
+         h
        with Not_found ->
-        `Match (t,(n,ar),bs_lift,bs,args))
-  | `I _ | `Var _ | `Match _ -> `Match(t,(n,ar),bs_lift,bs,args)
-
-and subst truelam delift_by_one what (with_what : nf) (where : nf) =
- let aux_propagate_arity ar = function
- | `Lam(false,`Match(`I(v,args),(x,_),liftno,bs,args')) when not delift_by_one ->
-    `Lam(false,`Match(`I(v,args),(x,ar),liftno,bs,args'))
+        `Match (t,(n,ar),bs_lift,bs,[]))
+   (* We are assuming that the econding of matches is s.t.:
+      - match PAC.. --> PAC
+      - match BOT.. --> BOT *)
+   | `Bottom -> `Bottom
+   | `Pacman -> `Pacman
+   | `Lam _ -> assert false
+   | `I _ | `Var _ | `Match _ as t -> `Match(t,(n,ar),bs_lift,bs,[]) in
+ mk_appl m args
+
+and subst truelam delift_by_one what (with_what : nf(*_nob*)) (where : nf) =
+ let rec aux_propagate_arity ar = function
+ | `Lam(false, t) when not delift_by_one -> `Lam(false, aux_propagate_arity ar t)
+ | `Match(`I(v,args),(x,_),liftno,bs,args') when not delift_by_one ->
+    `Match(`I(v,args),(x,ar),liftno,bs,args')
  | `Var(i,oldar) -> `Var(i, if truelam then (assert (oldar = min_int); ar) else oldar)
  | _ as t -> t in
  let rec aux_i_num_var l =
   function
      `I((n,ar),args) ->
        if n = what + l then
-        mk_appx (lift l (aux_propagate_arity ar with_what)) (Listx.map (aux l) args)
+       let args = Listx.map (aux l) (args :> nf Listx.listx) in
+        mk_appx (lift l (aux_propagate_arity ar (with_what :> nf))) args
        else
-        `I (((if delift_by_one && n >= l then n-1 else n), ar), Listx.map (aux l) args)
+        mk_appl (`Var ((if delift_by_one && n >= l then n-1 else n), ar)) (List.map (aux l) (Listx.to_list (args :> nf Listx.listx)))
    | `Var(n,ar) ->
        if n = what + l then
-        lift l (aux_propagate_arity ar with_what)
+        lift l (aux_propagate_arity ar (with_what :> nf))
        else
         `Var((if delift_by_one && n >= l then n-1 else n), ar)
    | `N _ as x -> x
    | `Match(t,v,bs_lift,bs,args) ->
        let bs_lift = bs_lift + if delift_by_one then -1 else 0 in
        let l' = l - bs_lift  in
-       let with_what' = lift l' with_what in
+       let with_what' = lift l' (with_what :> nf) in
        (* The following line should be the identity when delift_by_one = true because we
           are assuming the ts to not contain lambda-bound variables. *)
        bs := List.map (fun (n,t) -> n,subst truelam false what with_what' t) !bs ;
-       mk_match (cast_to_i_num_var (aux_i_num_var l t)) v bs_lift bs (List.map (aux l) args)
+       let body = aux_i_num_var l t in
+       mk_match body v bs_lift bs (List.map (aux l) (args :> nf list))
  and aux l(*lift*) =
 (*function iii -> let res = match iii with*)
   function
    | #i_num_var as x -> aux_i_num_var l x
    | `Lam(b, nf) -> `Lam(b, aux (l+1) nf)
+   | `Bottom -> `Bottom
+   | `Pacman -> `Pacman
 (*in let ll = ["v0";"v1";"v2"] in
 prerr_endline ("subst l:" ^ string_of_int l ^ " delift_by_one:" ^ string_of_bool delift_by_one ^ " what:" ^ (List.nth ll what) ^ " with_what:" ^ print ~l:ll with_what ^ " where:" ^ print ~l:ll iii ^ " res:" ^ print ~l:ll res); res*)
  in
@@ -238,14 +268,24 @@ prerr_endline ("subst l:" ^ string_of_int l ^ " delift_by_one:" ^ string_of_bool
 
 let parse' strs =
   let fix_arity = function
-  | `I((n,_),args) -> `I((n,1+Listx.length args),args)
-  | _ -> assert false in
-  let rec aux = function
-  | Parser.Lam t -> `Lam (true, aux t)
-  | Parser.App (t1, t2) -> fix_arity (mk_app (aux t1) (aux t2))
-  | Parser.Var v -> `Var(v,1) in
+   | `I((n,_),args) -> `I((n,1+Listx.length args),args)
+   | _ -> assert false in
   let (tms, free) = Parser.parse_many strs in
-  List.map aux tms, free
+  (* Replace pacmans and bottoms *)
+  let n_bot = try Util.index_of "BOT" free with Not_found -> min_int in
+  let n_pac = try Util.index_of "PAC" free with Not_found -> min_int in
+  let n_bomb = try Util.index_of "BOMB" free with Not_found -> min_int in
+  let fix lev v =
+   if v = lev + n_bot then `Bottom
+    else if v = lev + n_pac then `Pacman
+     else if v = lev + n_bomb then `Lam(true, `Bottom)
+      else `Var(v,1) in (* 1 by default when variable not applied *)
+  (* Fix arity *)
+  let rec aux lev = function
+   | Parser.Lam t -> `Lam (true, aux (lev+1) t)
+   | Parser.App (t1, t2) -> fix_arity (mk_app (aux lev t1) (aux lev t2))
+   | Parser.Var v -> fix lev v in
+  List.map (aux 0) tms, free
 ;;
 
 (************** Algorithm(s) ************************)
@@ -263,9 +303,13 @@ let eta_compare x y =
  let rec aux t1 t2 = match t1, t2 with
   | `Var(n,_) , `Var(m,_) -> compare n m
   | `I((n1,_), l1), `I((n2,_), l2) ->
-    clex compare (lex aux) (n1, Listx.to_list l1) (n2, Listx.to_list l2)
+    clex compare (lex aux) (n1, (Listx.to_list l1 :> nf list)) (n2, (Listx.to_list l2 :> nf list))
+  | `Bottom, `Bottom
+  | `Pacman, `Pacman -> 0
   | `Lam _, `N _ -> -1
   | `N _, `Lam _ -> 1
+  | `Bottom, `Lam _
+  | `Lam _, `Bottom -> assert false (* TO BE UNDERSTOOD *)
   | `Lam(_,t1), `Lam(_,t2) -> aux t1 t2
   | `Lam(_,t1), t2 -> - aux t1 (mk_app (lift 1 t2) (`Var(0,-666)))
   | t2, `Lam(_,t1) ->   aux t1 (mk_app (lift 1 t2) (`Var(0,-666)))
@@ -273,13 +317,17 @@ let eta_compare x y =
   | `Match(u,_,bs_lift,bs,args), `Match(u',_,bs_lift',bs',args') ->
     let bs = List.sort (fun (n,_) (m,_) -> compare n m) !bs in
     let bs' = List.sort (fun (n,_) (m,_) -> compare n m) !bs' in
-    clex aux (clex (lex (clex compare aux)) (lex aux)) ((u :> nf), (bs, args)) ((u' :> nf), (bs', args'))
+    clex aux (clex (lex (clex compare aux)) (lex aux)) ((u :> nf), (bs, (args :> nf list))) ((u' :> nf), (bs', (args' :> nf list)))
   | `Match _, _ -> -1
   | _, `Match _ -> 1
   | `N _, _ -> -1
   | _, `N _ -> 1
   | `I _, _ -> -1
   | _, `I _ -> 1
+  | `Bottom, _ -> -1
+  | _, `Bottom -> 1
+  | `Pacman, _ -> -1
+  | _, `Pacman -> 1
   in aux x y
 ;;
 
@@ -289,15 +337,17 @@ let rec eta_subterm sub t =
  if eta_eq sub t then true else
   match t with
   | `Lam(_,t') -> eta_subterm (lift 1 sub) t'
+  | `Bottom
+  | `Pacman  -> false
   | `Match(u,ar,liftno,bs,args) ->
      eta_subterm sub (u :> nf)
      || List.exists (fun (_, t) -> eta_subterm sub (lift liftno t)) !bs
-     || List.exists (eta_subterm sub) args
-  | `I(v, args) -> List.exists (eta_subterm sub) (Listx.to_list args) || (match sub with
+     || List.exists (eta_subterm sub) (args :> nf list)
+  | `I(v, args) -> List.exists (eta_subterm sub) ((Listx.to_list args) :> nf list) || (match sub with
    | `Var v' -> v = v'
    | `I(v', args') -> v = v'
     && Listx.length args' < Listx.length args
-    && List.for_all (fun (x,y) -> eta_eq x y) (List.combine (Util.take (Listx.length args') (Listx.to_list args)) (Listx.to_list args'))
+    && List.for_all (fun (x,y) -> eta_eq x y) (List.combine (Util.take (Listx.length args') (Listx.to_list args :> nf list)) (Listx.to_list args' :> nf list))
    | _ -> false
    )
   | `N _ | `Var _ -> false
@@ -305,7 +355,6 @@ let rec eta_subterm sub t =
 
 let eta_subterm (#nf as x) (#nf as y) = eta_subterm x y;;
 
-
 let max_arity_tms n =
  let max a b = match a, b with
   | None, None -> None
@@ -315,37 +364,11 @@ let max_arity_tms n =
  let aux_var l (m,a) = if n + l = m then Some a else None in
  let rec aux l = function
   | `Var v -> aux_var l v
-  | `I(v,tms) -> max (aux_var l v) (aux_tms l (Listx.to_list tms))
+  | `I(v,tms) -> max (aux_var l v) (aux_tms l (Listx.to_list tms :> nf list))
   | `Lam(_,t) -> aux (l+1) t
-  | `Match(u,_,_,bs,args) -> max (max (aux l (u :> nf)) (aux_tms l args)) (aux_tms l (List.map snd !bs))
-  | `N _ -> None
+  | `Match(u,_,_,bs,args) -> max (max (aux l (u :> nf)) (aux_tms l (args :> nf list))) (aux_tms l (List.map snd !bs))
+  | `N _ | `Bottom | `Pacman -> None
  and aux_tms l =
-  List.fold_left (fun acc t -> Pervasives.max acc (aux l t)) None in
+  List.fold_left (fun acc t -> max acc (aux l t)) None in
  fun tms -> aux_tms 0 (tms :> nf list)
 ;;
-
-let get_first_args var =
-let rec aux l = function
-| `Lam(_,t) -> aux (l+1) t
-| `Match(u,orig,liftno,bs,args) -> Util.concat_map (aux l) args
-| `I((n,_), args) -> if n = var + l then [Listx.last args] else []
-| `N _
-| `Var _ -> []
-in aux 0
-;;
-
-let compute_arities m =
- let rec aux n tms =
-  if n = 0
-   then []
-   else
-    let tms = Util.filter_map (function `Lam(_,t) -> Some t | _ -> None ) tms in
-    let arity = match max_arity_tms (m-n) tms with None -> -666 | Some x -> x in
-     arity :: (aux (n-1) tms)
- in fun tms -> List.rev (aux m tms)
-;;
-
-let compute_arities var special_k all_tms =
- let tms = List.fold_left (fun acc t -> acc @ (get_first_args var t)) [] all_tms in
- compute_arities special_k tms
-;;