X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Fnum.ml;h=c1a84b0e35dc57197d8a365a6d1cdf1aa7fbb65a;hb=b0ecd3e4062bb9012ea9623237d0b379bd7646f2;hp=2cb9b731a1dda17d50f9211a694548e7153b89bf;hpb=0e005c102417c907b7dd0ec48a45739fafe54f59;p=fireball-separation.git

diff --git a/ocaml/num.ml b/ocaml/num.ml
index 2cb9b73..c1a84b0 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*)
@@ -22,7 +25,7 @@ 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 nf_ = [ `Lam of (* was_unpacked *) bool * 'nf nf_ | 'nf i_num_var_ ]
+type 'nf nf_ = [ `Lam of (* was_unpacked *) bool * 'nf nf_ * ('nf nf_) list | 'nf i_num_var_ ]
 type nf = nf nf_
 type i_var = nf i_var_;;
 type i_n_var = nf i_n_var_;;
@@ -58,7 +61,7 @@ let lift m (t : nf) =
  and aux l =
   function
      #i_num_var as x -> (aux_i_num_var l x :> nf)
-   | `Lam(b,nf) -> `Lam (b, aux (l+1) nf)
+   | `Lam(b,nf,g) -> `Lam (b, aux (l+1) nf, List.map (aux (l+1)) g)
  in
   (aux 0 t : nf)
 ;;
@@ -67,68 +70,90 @@ let lift m (t : nf) =
 let rec make_lams t =
  function
    0 -> t
- | n when n > 0 -> `Lam (false, lift 1 (make_lams t (n-1)))
+ | 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]) @
+  | `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))
-  | `Lam(_,t) -> aux (n+1) t
+  | `Lam(_,t,g) -> List.concat (List.map (aux (n+1)) (t::g))
   | `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)
   in aux 0
 ;;
+let free_vars = (List.map fst) ++ free_vars';;
 
 module ToScott =
 struct
 
+let delta = let open Pure in L(A(V 0, V 0))
+
+let bomb = ref(`Var(-1, -666));;
+
 let rec t_of_i_num_var =
  function
   | `N n -> Scott.mk_n n
-  | `Var(v,_) -> Pure.V v
+  | `Var(v,_) as x -> assert (x <> !bomb); 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 bs = List.map (
+        function (n,t) -> n,
+         (if t = !bomb then delta
+          else Pure.L (t_of_nf (lift (liftno+1) t)))
+        ) !bs in
       let t = t_of_i_num_var t in
       let m = Scott.mk_match t bs in
+      let m = Pure.A(m,delta) 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)
+  | `Lam(b,f,g) ->
+    let t = t_of_nf (lift (List.length g) f) in
+    let t = List.fold_left (fun t g -> Pure.A(Pure.L t, t_of_nf g)) t g in
+    Pure.L t
 
 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 string_of_term =
+ let boundvar x = "v" ^ string_of_int x in
+ let varname lev l n =
+  if n < lev then boundvar (lev-n-1)
+   else if n - lev < List.length l then List.nth l (n-lev)
+    else "`" ^ string_of_int (n-lev) in
+ let rec string_of_term_w_pars lev l  = function
+  | `Var(n,ar) -> varname lev 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) ^ ")"
-  | `Lam _ as t -> "(" ^ string_of_term_no_pars_lam l t ^ ")"
-  | `Match(t,_,bs_lift,bs,args) ->
-     "(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)) !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))
-  | #nf as t -> string_of_term_w_pars l t
- and string_of_term_no_pars_lam l  = function
-  | `Lam(_,t) -> let name = string_of_var (List.length l) in
-   "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
-  | `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
+  | `I _ as t -> "(" ^ string_of_term_no_pars_app lev l t ^ ")"
+  | `Lam _ as t -> "(" ^ string_of_term_no_pars_lam lev l t ^ ")"
+  | `Match(t,(v,ar),bs_lift,bs,args) ->
+      (* assert (bs_lift = lev); *)
+     "(["^ varname 0 l v ^ (if debug_display_arities then ":"^ string_of_int ar else "") ^",match " ^ string_of_term_no_pars lev l (t :> nf) ^
+     " with " ^ String.concat " | " (List.map (fun (n,t) -> string_of_int n ^ " => " ^ string_of_term l (t :> nf)) !bs) ^ "] " ^
+     String.concat " " (List.map (string_of_term l) (args :> nf list)) ^ ")"
+ and string_of_term_no_pars_app lev l  = function
+  | `I((n,ar), args) -> varname lev l n ^ (if debug_display_arities then ":" ^ string_of_int ar else "") ^ " " ^ String.concat " " (List.map (string_of_term_w_pars lev l) (Listx.to_list args :> nf list))
+  | #nf as t -> string_of_term_w_pars lev l t
+ and string_of_term_no_pars_lam lev l  = function
+  | `Lam(_,t,g) -> "λ" ^ boundvar lev ^ ". " ^ (string_of_term_no_pars_lam (lev+1) l t)
+     ^ (if g = [] then "" else String.concat ", " ("" :: List.map (string_of_term_no_pars (lev+1) l) g))
+  | _ as t -> string_of_term_no_pars lev l t
+ and string_of_term_no_pars lev l = function
+  | `Lam _ as t -> string_of_term_no_pars_lam lev l t
+  | #nf as t -> string_of_term_no_pars_app lev l t
+ and string_of_term t = string_of_term_no_pars 0 t in
+ string_of_term
 ;;
 
 let print ?(l=[]) = string_of_term l;;
@@ -157,12 +182,13 @@ 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
+(* FIXME because onlt variables should be in branches of matches, one day *)
 | `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 _ 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;;
 
@@ -171,7 +197,7 @@ let rec mk_app (h : nf) (arg : nf) =
  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 *)
+  | `Lam(truelam,nf,g) -> assert (g = []); 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 *)
 (*in let l = ["v0";"v1";"v2"] in
@@ -197,10 +223,11 @@ and mk_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'))
- | `Var(i,oldar) -> `Var(i, if truelam && oldar = min_int then ar else oldar)
+ let rec aux_propagate_arity ar = function
+ | `Lam(false,t,g) when not delift_by_one -> assert (g = []); `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
@@ -217,37 +244,27 @@ and subst truelam delift_by_one what (with_what : nf) (where : nf) =
    | `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
+       (* Warning! It now applies again the substitution in branches of matches.
+          But careful, it does it many times, for every occurrence of
+          the match. This is okay because what does not occur in with_what. *)
        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 = cast_to_i_num_var (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)
+   | `Lam(b, nf, g) -> `Lam(b, aux (l+1) nf, List.map (aux (l+1)) g)
 (*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
   aux 0 where
 ;;
 
-(************ Parsing ************************************)
-
-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
-  let (tms, free) = Parser.parse_many strs in
-  List.map aux tms, free
-;;
-
 (************** Algorithm(s) ************************)
 
 let eta_compare x y =
@@ -266,9 +283,9 @@ let eta_compare x y =
     clex compare (lex aux) (n1, Listx.to_list l1) (n2, Listx.to_list l2)
   | `Lam _, `N _ -> -1
   | `N _, `Lam _ -> 1
-  | `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)))
+  | `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)))
   | `N n1, `N n2 -> compare n1 n2
   | `Match(u,_,bs_lift,bs,args), `Match(u',_,bs_lift',bs',args') ->
     let bs = List.sort (fun (n,_) (m,_) -> compare n m) !bs in
@@ -288,14 +305,14 @@ let eta_eq (#nf as x) (#nf as y) = 0 = eta_compare x y ;;
 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'
+  | `Lam(_,t,g) -> List.exists (eta_subterm (lift 1 sub)) (t::g)
   | `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
-   | `Var v' -> v = v'
-   | `I(v', args') -> v = v'
+     || 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'))
    | _ -> false
@@ -316,17 +333,17 @@ let max_arity_tms n =
  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))
-  | `Lam(_,t) -> aux (l+1) t
+  | `Lam(_,t, g) -> List.fold_left (fun n t -> max n (aux (l+1) t)) None (t::g)
   | `Match(u,_,_,bs,args) -> max (max (aux l (u :> nf)) (aux_tms l args)) (aux_tms l (List.map snd !bs))
   | `N _ -> 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
+| `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 _
@@ -339,7 +356,7 @@ let compute_arities m =
   if n = 0
    then []
    else
-    let tms = Util.filter_map (function `Lam(_,t) -> Some t | _ -> None ) tms in
+    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)