X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Fsimple.ml;h=b1b05eca5c43f8f81429836ccda109d10f5c317b;hb=refs%2Fheads%2Fstrong_simple_measure;hp=d9bc38917910db68afe1c226d3ae153e85a4e4b4;hpb=276d4f75cbe40801f2d9faa82ac82d1c82204e55;p=fireball-separation.git

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index d9bc389..b1b05ec 100644
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -6,40 +6,49 @@ let print_hline = Console.print_hline;;
 
 open Pure
 
+type var_flag = [
+ `Inherit | `Some of bool ref
+ (* bool:
+     true if original application and may determine a distinction
+  *)
+  | `Duplicate
+] ;;
+
 type var = int;;
 type t =
  | V of var
- | A of t * t
+ | A of var_flag * t * t
  | L of t
- | B (* bottom *)
- | C of int
 ;;
 
-let delta = L(A(V 0, V 0));;
-
-let eta_eq' =
- let rec aux l1 l2 t1 t2 = match t1, t2 with
-  | L t1, L t2 -> aux l1 l2 t1 t2
-  | L t1, t2 -> aux l1 (l2+1) t1 t2
-  | t1, L t2 -> aux (l1+1) l2 t1 t2
-  | V a, V b -> a + l1 = b + l2
-  | C a, C b -> a = b
-  | A(t1,t2), A(u1,u2) -> aux l1 l2 t1 u1 && aux l1 l2 t2 u2
-  | _, _ -> false
- in aux ;;
-let eta_eq = eta_eq' 0 0;;
+let index_of x =
+ let rec aux n =
+  function
+    [] -> None
+  | x'::_ when x == x' -> Some n
+  | _::xs -> aux (n+1) xs
+ in aux 1
+;;
 
-(* is arg1 eta-subterm of arg2 ? *)
-let eta_subterm u =
- let rec aux lev t = eta_eq' lev 0 u t || match t with
- | L t -> aux (lev+1) t
- | A(t1, t2) -> aux lev t1 || aux lev t2
- | _ -> false
- in aux 0
+let sep_of_app =
+ let apps = ref [] in
+ function
+    r when not !r -> " "
+  | r ->
+    let i =
+     match index_of r !apps with
+        Some i -> i
+      | None ->
+         apps := !apps @ [r];
+         List.length !apps
+    in " " ^ string_of_int i ^ ":"
 ;;
+let string_of_var_flag = function
+ | `Some b -> sep_of_app b
+ | `Inherit -> " ?"
+ | `Duplicate -> " !"
+ ;;
 
-(* does NOT lift t *)
-let mk_lams = fold_nat (fun x _ -> L x) ;;
 
 let string_of_t =
   let string_of_bvar =
@@ -49,12 +58,10 @@ let string_of_t =
   let rec string_of_term_w_pars level = function
     | V v -> if v >= level then "`" ^ string_of_int (v-level) else
        string_of_bvar (level - v-1)
-    | C n -> "c" ^ string_of_int n
     | A _
     | L _ as t -> "(" ^ string_of_term_no_pars level t ^ ")"
-    | B -> "BOT"
   and string_of_term_no_pars_app level = function
-    | A(t1,t2) -> string_of_term_no_pars_app level t1 ^ " " ^ string_of_term_w_pars level t2
+    | A(b,t1,t2) -> string_of_term_no_pars_app level t1 ^ string_of_var_flag b ^ string_of_term_w_pars level t2
     | _ as t -> string_of_term_w_pars level t
   and string_of_term_no_pars level = function
     | L t -> "λ" ^ string_of_bvar level ^ ". " ^ string_of_term_no_pars (level+1) t
@@ -62,25 +69,44 @@ let string_of_t =
   in string_of_term_no_pars 0
 ;;
 
+
+let delta = L(A(`Some (ref true),V 0, V 0));;
+
+(* does NOT lift the argument *)
+let mk_lams = fold_nat (fun x _ -> L x) ;;
+
+let measure_of_t =
+ let rec aux acc = function
+ | V _ -> acc, 0
+ | A(b,t1,t2) ->
+   let acc, m1 = aux acc t1 in
+   let acc, m2 = aux acc t2 in
+   (match b with
+   | `Some b when !b && not (List.memq b acc) -> b::acc, 1 + m1 + m2
+   | _ -> acc, m1 + m2)
+ | L t -> aux acc t
+ in snd ++ (aux [])
+;;
+
 type problem = {
    orig_freshno: int
  ; freshno : int
  ; div : t
  ; conv : t
  ; sigma : (var * t) list (* substitutions *)
- ; stepped : var list
  ; phase : [`One | `Two] (* :'( *)
 }
 
 let string_of_problem p =
  let lines = [
-  "[stepped] " ^ String.concat " " (List.map string_of_int p.stepped);
+  "[measure] " ^ string_of_int (measure_of_t p.div);
   "[DV] " ^ string_of_t p.div;
   "[CV] " ^ string_of_t p.conv;
  ] in
  String.concat "\n" lines
 ;;
 
+exception B;;
 exception Done of (var * t) list (* substitution *);;
 exception Fail of int * string;;
 
@@ -96,71 +122,110 @@ let freshvar ({freshno} as p) =
 
 let rec is_inert =
  function
- | A(t,_) -> is_inert t
+ | A(_,t,_) -> is_inert t
  | V _ -> true
- | C _
- | L _ | B -> false
+ | L _ -> false
 ;;
 
 let is_var = function V _ -> true | _ -> false;;
 let is_lambda = function L _ -> true | _ -> false;;
 
-let rec no_leading_lambdas = function
- | L t -> 1 + no_leading_lambdas t
- | _ -> 0
-;;
-
 let rec get_inert = function
  | V n -> (n,0)
- | A(t, _) -> let hd,args = get_inert t in hd,args+1
+ | A(_,t,_) -> let hd,args = get_inert t in hd,args+1
  | _ -> assert false
 ;;
 
-let rec subst level delift sub =
+(* precomputes the number of leading lambdas in a term,
+   after replacing _v_ w/ a term starting with n lambdas *)
+let rec no_leading_lambdas v n = function
+ | L t -> 1 + no_leading_lambdas (v+1) n t
+ | A _ as t -> let v', m = get_inert t in if v = v' then max 0 (n - m) else 0
+ | V v' -> if v = v' then n else 0
+;;
+
+let rec erase = function
+ | L t -> L (erase t)
+ | A(_,t1,t2) -> A(`Some(ref false), erase t1, erase t2)
+ | V _ as t -> t
+;;
+
+let rec subst top level delift ((flag, var, tm) as sub) =
  function
- | V v -> if v = level + fst sub then lift level (snd sub) else V (if delift && v > level then v-1 else v)
- | L t -> let t = subst (level + 1) delift sub t in if t = B then B else L t
- | A (t1,t2) ->
-  let t1 = subst level delift sub t1 in
-  let t2 = subst level delift sub t2 in
-  mk_app t1 t2
- | C _ as t -> t
- | B -> B
-and mk_app t1 t2 = if t2 = B || (t1 = delta && t2 = delta) then B
+ | V v -> if v = level + var then lift level tm else V (if delift && v > level then v-1 else v)
+ | L t -> L (subst top (level + 1) delift sub t)
+ | A(b,t1,t2) ->
+    let special = b = `Duplicate && top && t2 = V (level + var) in
+    let t1' = subst (if special then false else top) level delift sub t1 in
+    let t2' = subst false level delift sub t2 in
+    match b with
+    | `Duplicate when special ->
+        assert (match t1' with L _ -> false | _ -> true) ;
+        (match flag with
+          | `Some b when !b -> b := false
+          | `Some b -> ()
+            (*print_string "WARNING! Stepping on a useless argument!";
+            ignore(read_line())*)
+          | `Inherit | `Duplicate -> assert false);
+        A(flag, t1', erase t2')
+    | `Inherit | `Duplicate ->
+       let b' = if t2 = V (level + var)
+        then (assert (flag <> `Inherit); flag)
+        else b in
+       assert (match t1' with L _ -> false | _ -> true) ;
+       A(b', t1', t2')
+    | `Some b' -> mk_app top b' t1' t2'
+and mk_app top flag t1 t2 = if t1 = delta && t2 = delta then raise B
  else match t1 with
- | C _ as t -> t
- | B -> B
- | L t1 -> subst 0 true (0, t2) t1
- | _ -> A (t1, t2)
+ | L t1 -> subst top 0 true (`Some flag, 0, t2) t1
+ | _ -> A (`Some flag, t1, t2)
 and lift n =
  let rec aux lev =
   function
   | V m -> V (if m >= lev then m + n else m)
-  | L t -> L (aux (lev+1) t)
-  | A (t1, t2) -> A (aux lev t1, aux lev t2)
-  | C _ as t -> t
-  | B -> B
+  | L t -> L(aux (lev+1) t)
+  | A (b,t1, t2) -> A (b,aux lev t1, aux lev t2)
  in aux 0
 ;;
-let subst = subst 0 false;;
-
-let subst_in_problem (sub: var * t) (p: problem) =
-print_endline ("-- SUBST " ^ string_of_t (V (fst sub)) ^ " |-> " ^ string_of_t (snd sub));
- {p with
-  div=subst sub p.div;
-  conv=subst sub p.conv;
-  stepped=(fst sub)::p.stepped;
-  sigma=sub::p.sigma}
+let subst top = subst top 0 false;;
+let mk_app = mk_app true;;
+
+let eta_eq =
+ let rec aux t1 t2 = match t1, t2 with
+  | L t1, L t2 -> aux t1 t2
+  | L t1, t2 -> aux t1 (A(`Some (ref true),lift 1 t2,V 0))
+  | t1, L t2 -> aux (A(`Some (ref true),lift 1 t1,V 0)) t2
+  | V a, V b -> a = b
+  | A(_,t1,t2), A(_,u1,u2) -> aux t1 u1 && aux t2 u2
+  | _, _ -> false
+ in aux ;;
+
+(* is arg1 eta-subterm of arg2 ? *)
+let eta_subterm u =
+ let rec aux lev t = eta_eq u (lift lev t) || match t with
+ | L t -> aux (lev+1) t
+ | A(_, t1, t2) -> aux lev t1 || aux lev t2
+ | _ -> false
+ in aux 0
+;;
+
+let subst_in_problem ?(top=true) ((v, t) as sub) p =
+print_endline ("-- SUBST " ^ string_of_t (V v) ^ " |-> " ^ string_of_t t);
+ let sigma = sub::p.sigma in
+ let sub = (`Inherit, v, t) in
+ let div = try subst top sub p.div with B -> raise (Done sigma) in
+ let conv = try subst false sub p.conv with B -> raise (Fail(-1,"p.conv diverged")) in
+ {p with div; conv; sigma}
 ;;
 
 let get_subterm_with_head_and_args hd_var n_args =
  let rec aux lev = function
- | C _
- | V _ | B -> None
+ | V _ -> None
  | L t -> aux (lev+1) t
- | A(t1,t2) as t ->
+ | A(_,t1,t2) as t ->
    let hd_var', n_args' = get_inert t1 in
    if hd_var' = hd_var + lev && n_args <= 1 + n_args'
+    (* the `+1` above is because of t2 *)
     then Some (lift ~-lev t)
     else match aux lev t2 with
     | None -> aux lev t1
@@ -170,10 +235,8 @@ let get_subterm_with_head_and_args hd_var n_args =
 
 let rec purify = function
  | L t -> Pure.L (purify t)
- | A (t1,t2) -> Pure.A (purify t1, purify t2)
+ | A(_,t1,t2) -> Pure.A (purify t1, purify t2)
  | V n -> Pure.V n
- | C _ -> Pure.V max_int (* FIXME *)
- | B -> Pure.B
 ;;
 
 let check p sigma =
@@ -181,7 +244,7 @@ let check p sigma =
  let div = purify p.div in
  let conv = purify p.conv in
  let sigma = List.map (fun (v,t) -> v, purify t) sigma in
- let freshno = List.fold_right (fun (x,_) -> max x) sigma 0 in
+ let freshno = List.fold_right (max ++ fst) sigma 0 in
  let env = Pure.env_of_sigma freshno sigma in
  assert (Pure.diverged (Pure.mwhd (env,div,[])));
  print_endline " D diverged.";
@@ -192,19 +255,19 @@ let check p sigma =
 
 let sanity p =
  print_endline (string_of_problem p); (* non cancellare *)
- if p.conv = B then problem_fail p "p.conv diverged";
- if p.div = B then raise (Done p.sigma);
  if p.phase = `Two && p.div = delta then raise (Done p.sigma);
  if not (is_inert p.div) then problem_fail p "p.div converged";
  p
 ;;
 
 (* drops the arguments of t after the n-th *)
+(* FIXME! E' usato in modo improprio contando sul fatto
+   errato che ritorna un inerte lungo esattamente n *)
 let inert_cut_at n t =
  let rec aux t =
   match t with
   | V _ as t -> 0, t
-  | A(t1,_) as t ->
+  | A(_,t1,_) as t ->
     let k', t' = aux t1 in
      if k' = n then n, t'
       else k'+1, t
@@ -212,110 +275,103 @@ let inert_cut_at n t =
  in snd (aux t)
 ;;
 
-let find_eta_difference p t n_args =
- let t = inert_cut_at n_args t in
+(* return the index of the first argument with a difference
+   (the first argument is 0)
+   precondition: p.div and t have n+1 arguments
+   *)
+let find_eta_difference p t argsno =
+ let t = inert_cut_at argsno t in
  let rec aux t u k = match t, u with
- | V _, V _ -> assert false (* div subterm of conv *)
- | A(t1,t2), A(u1,u2) ->
-    if not (eta_eq t2 u2) then (print_endline((string_of_t t2) ^ " <> " ^ (string_of_t u2)); k)
-    else aux t1 u1 (k-1)
+ | V _, V _ -> None
+ | A(b1,t1,t2), A(b2,u1,u2) ->
+    (match aux t1 u1 (k-1) with
+    | None ->
+      if not (eta_eq t2 u2) then begin
+        let is_relevant = function `Some b -> !b | _ -> false in
+        if not (is_relevant b1 || is_relevant b2) then begin
+         print_string "WARNING! Stepping on a useless argument!";
+print_string (string_of_t  t ^ " <==> " ^ string_of_t u);
+         ignore(read_line())
+        end ;
+        Some (k-1)
+       end
+      else None
+    | Some j -> Some j)
  | _, _ -> assert false
- in aux p.div t n_args
+ in match aux p.div t argsno with
+ | None -> problem_fail p "no eta difference found (div subterm of conv?)"
+ | Some j -> j
 ;;
 
 let compute_max_lambdas_at hd_var j =
  let rec aux hd = function
- | A(t1,t2) ->
+ | A(_,t1,t2) ->
     (if get_inert t1 = (hd, j)
       then max ( (*FIXME*)
        if is_inert t2 && let hd', j' = get_inert t2 in hd' = hd
         then let hd', j' = get_inert t2 in j - j'
-        else no_leading_lambdas t2)
+        else no_leading_lambdas hd_var j t2)
       else id) (max (aux hd t1) (aux hd t2))
  | L t -> aux (hd+1) t
  | V _ -> 0
- | _ -> assert false
  in aux hd_var
 ;;
 
 let print_cmd s1 s2 = print_endline (">> " ^ s1 ^ " " ^ s2);;
 
-(* eat the arguments of the divergent and explode.
- It does NOT perform any check, may fail if done unsafely *)
-let eat p =
-print_cmd "EAT" "";
- let var, k = get_inert p.div in
- let phase = p.phase in
- let p, t =
-  match phase with
-  | `One ->
-      let n = 1 + max
-       (compute_max_lambdas_at var k p.div)
-       (compute_max_lambdas_at var k p.conv) in
-      (* apply fresh vars *)
-      let p, t = fold_nat (fun (p, t) _ ->
-        let p, v = freshvar p in
-        p, A(t, V (v + k))
-      ) (p, V 0) n in
-      let p = {p with phase=`Two} in p, A(t, delta)
-  | `Two -> p, delta in
- let subst = var, mk_lams t k in
- let p = subst_in_problem subst p in
- sanity p;
- let p = if phase = `One then {p with div = (match p.div with A(t,_) -> t | _ -> assert false)} else p in
- sanity p
-;;
-
 (* step on the head of div, on the k-th argument, with n fresh vars *)
-let step k n p =
+let step ?(isfinish=false) k n p =
  let var, _ = get_inert p.div in
 print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (of:" ^ string_of_int n ^ ")");
  let p, t = (* apply fresh vars *)
   fold_nat (fun (p, t) _ ->
     let p, v = freshvar p in
-    p, A(t, V (v + k + 1))
+    p, A(`Some (ref false), t, V (v + k + 1))
   ) (p, V 0) n in
- let t = (* apply unused bound variables V_{k-1}..V_1 *)
-  fold_nat (fun t m -> A(t, V (k-m+1))) t k in
+ let t = (* apply bound variables V_k..V_0 *)
+  fold_nat (fun t m -> A((if m = k+1 then `Duplicate else `Inherit), t, V (k-m+1))) t (k+1) in
  let t = mk_lams t (k+1) in (* make leading lambdas *)
  let subst = var, t in
- let p = subst_in_problem subst p in
+ let p = subst_in_problem ~top:(not isfinish) subst p in
  sanity p
 ;;
-;;
-
-let parse strs =
-  let rec aux level = function
-  | Parser_andrea.Lam t -> L (aux (level + 1) t)
-  | Parser_andrea.App (t1, t2) ->
-   if level = 0 then mk_app (aux level t1) (aux level t2)
-    else A(aux level t1, aux level t2)
-  | Parser_andrea.Var v -> V v in
-  let (tms, free) = Parser_andrea.parse_many strs in
-  (List.map (aux 0) tms, free)
-;;
 
-let problem_of div conv =
- print_hline ();
- let [@warning "-8"] [div; conv], var_names = parse ([div; conv]) in
- let varno = List.length var_names in
- let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; stepped=[]; phase=`One} in
- (* initial sanity check *)
+let finish p =
+ let compute_max_arity =
+   let rec aux n = function
+   | A(_,t1,t2) -> max (aux (n+1) t1) (aux 0 t2)
+   | L t -> max n (aux 0 t)
+   | V _ -> n
+ in aux 0 in
+print_cmd "FINISH" "";
+ let div_hd, div_nargs = get_inert p.div in
+ let j = div_nargs - 1 in
+ let arity = compute_max_arity p.conv in
+ let n = 1 + arity + max
+  (compute_max_lambdas_at div_hd j p.div)
+  (compute_max_lambdas_at div_hd j p.conv) in
+ let p = step ~isfinish:true j n p in
+ let div_hd, div_nargs = get_inert p.div in
+ let rec aux m = function
+  A(_,t1,t2) -> if is_var t2 then
+   (let delta_var, _ = get_inert t2 in
+     if delta_var <> div_hd && get_subterm_with_head_and_args delta_var 1 p.conv = None
+      then m, delta_var
+      else aux (m-1) t1) else aux (m-1) t1
+  | _ -> assert false in
+ let m, delta_var = aux div_nargs p.div in
+ let p = subst_in_problem (delta_var, delta) p in
+ let p = subst_in_problem (div_hd, mk_lams delta (m-1)) p in
  sanity p
 ;;
 
-let exec div conv cmds =
- let p = problem_of div conv in
- try
-  problem_fail (List.fold_left (|>) p cmds) "Problem not completed"
- with
- | Done _ -> ()
-;;
-
 let rec auto p =
  let hd_var, n_args = get_inert p.div in
  match get_subterm_with_head_and_args hd_var n_args p.conv with
  | None ->
+   (try problem_fail (finish p) "Auto.2 did not complete the problem"
+   with Done sigma -> sigma)
+   (*
    (try
     let phase = p.phase in
      let p = eat p in
@@ -323,16 +379,55 @@ let rec auto p =
       then problem_fail p "Auto.2 did not complete the problem"
       else auto p
     with Done sigma -> sigma)
+    *)
  | Some t ->
-  let j = find_eta_difference p t n_args - 1 in
+  let j = find_eta_difference p t n_args in
   let k = 1 + max
    (compute_max_lambdas_at hd_var j p.div)
     (compute_max_lambdas_at hd_var j p.conv) in
+  let m1 = measure_of_t p.div in
   let p = step j k p in
+  let m2 = measure_of_t p.div in
+  (if m2 >= m1 then
+    (print_string ("WARNING! Measure did not decrease : " ^ string_of_int m2 ^ " >= " ^ string_of_int m1 ^ " (press <Enter>)");
+    ignore(read_line())));
   auto p
 ;;
 
-let interactive div conv cmds =
+let problem_of (label, div, convs, ps, var_names) =
+ print_hline ();
+ let rec aux = function
+ | `Lam(_,t) -> L (aux t)
+ | `I ((v,_), args) -> Listx.fold_left (fun x y -> mk_app (ref true) x (aux y)) (V v) args
+ | `Var(v,_) -> V v
+ | `N _ | `Match _ -> assert false in
+ assert (List.length ps = 0);
+ let convs = (List.rev convs :> Num.nf list) in
+ let conv = aux
+  (if List.length convs = 1
+   then List.hd convs
+   else `I((List.length var_names, min_int), Listx.from_list convs)) in
+ let var_names = "@" :: var_names in
+ let div = match div with
+ | Some div -> aux (div :> Num.nf)
+ | None -> assert false in
+ let varno = List.length var_names in
+ let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; phase=`One} in
+ (* initial sanity check *)
+ sanity p
+;;
+
+let solve p =
+ if eta_subterm p.div p.conv
+  then print_endline "!!! div is subterm of conv. Problem was not run !!!"
+  else check p (auto p)
+;;
+
+Problems.main (solve ++ problem_of);
+
+(* Example usage of interactive: *)
+
+(* let interactive div conv cmds =
  let p = problem_of div conv in
  try (
  let p = List.fold_left (|>) p cmds in
@@ -354,59 +449,8 @@ let interactive div conv cmds =
   | Done _ -> print_endline "Done! Commands history: "; List.iter print_endline (List.rev cmds)
  in f p []
  ) with Done _ -> ()
-;;
-
-let rec conv_join = function
- | [] -> "@"
- | x::xs -> conv_join xs ^ " ("^ x ^")"
-;;
-
-let auto' a b =
- let p = problem_of a (conv_join b) in
- let sigma = auto p in
- check p sigma
-;;
-
-(* Example usage of exec, interactive:
-
-exec
- "x x"
- (conv_join["x y"; "y y"; "y x"])
- [ step 0 1; eat ]
-;;
+;; *)
 
-interactive "x y"
+(* interactive "x y"
  "@ (x x) (y x) (y z)" [step 0 1; step 0 2; eat]
-;;
-
-*)
-
-auto' "x x" ["x y"; "y y"; "y x"] ;;
-auto' "x y" ["x (_. x)"; "y z"; "y x"] ;;
-auto' "a (x. x b) (x. x c)" ["a (x. b b) @"; "a @ c"; "a (x. x x) a"; "a (a a a) (a c c)"] ;;
-
-auto' "x (y. x y y)" ["x (y. x y x)"] ;;
-
-auto' "x a a a a" [
- "x b a a a";
- "x a b a a";
- "x a a b a";
- "x a a a b";
-] ;;
-
-(* Controesempio ad usare un conto dei lambda che non considere le permutazioni *)
-auto' "x a a a a (x (x. x x) @ @ (_._.x. x x) x) b b b" [
- "x a a a a (_. a) b b b";
- "x a a a a (_. _. _. _. x. y. x y)";
-] ;;
-
-
-print_hline();
-print_endline "ALL DONE. "
-
-let solve div convs =
- let p = problem_of div (conv_join convs) in
- if eta_subterm p.div p.conv
-  then print_endline "!!! div is subterm of conv. Problem was not run !!!"
-  else check p (auto p)
-;;
+;; *)