X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Fsimple.ml;h=bac3ddf98a532784a587fa90cd9cbd67ca1f1e0a;hb=2b941d27823cb7d06bbf83353c21779c866f3161;hp=8e4f61946e453827b4024dccca02d6ce8ac2f19b;hpb=5664c5924f59c805c6e658698cc2fa535cab27f6;p=fireball-separation.git

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index 8e4f619..bac3ddf 100644
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -12,18 +12,24 @@ type t =
  | A of t * t
  | L of t
  | B (* bottom *)
- | C of int
+ | C (* constant *)
 ;;
 
 let delta = L(A(V 0, V 0));;
 
+let rec is_stuck = function
+ | C -> true
+ | A(t,_) -> is_stuck t
+ | _ -> false
+;;
+
 let eta_eq' =
  let rec aux l1 l2 t1 t2 = match t1, t2 with
+  | _, _ when is_stuck t1 || is_stuck t2 -> true
   | 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 ;;
@@ -31,11 +37,11 @@ let eta_eq = eta_eq' 0 0;;
 
 (* is arg1 eta-subterm of arg2 ? *)
 let eta_subterm u =
- let rec aux lev t = eta_eq' lev 0 u t || match t with
+ let rec aux lev t = if t = C then false else (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
+ | _ -> false) in
+ aux 0
 ;;
 
 (* does NOT lift the argument *)
@@ -49,7 +55,7 @@ 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
+    | C -> "C"
     | A _
     | L _ as t -> "(" ^ string_of_term_no_pars level t ^ ")"
     | B -> "BOT"
@@ -98,24 +104,23 @@ let rec is_inert =
  function
  | A(t,_) -> is_inert t
  | V _ -> true
- | C _
+ | C
  | L _ | B -> false
 ;;
 
-let is_var = function V _ -> true | _ -> false;;
-let is_lambda = function L _ -> true | _ -> false;;
-
 let rec get_inert = function
- | V n -> (n,0)
+ | V _ | C as t -> (t,0)
  | A(t, _) -> let hd,args = get_inert t in hd,args+1
  | _ -> assert false
 ;;
 
-let rec no_leading_lambdas hd_var j = function
- | L t -> 1 + no_leading_lambdas (hd_var+1) j t
- | A _ as t -> let hd_var', n = get_inert t in if hd_var = hd_var' then max 0 (j - n) else 0
- | V n -> if n = hd_var then j else 0
- | B | C _ -> 0
+(* 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 = v' then max 0 (n - m) else 0
+ | V v' -> if v = v' then n else 0
+ | B | C -> 0
 ;;
 
 let rec subst level delift sub =
@@ -126,8 +131,7 @@ let rec subst level delift sub =
   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
+ | C | B as t -> t
 and mk_app t1 t2 = if t2 = B || (t1 = delta && t2 = delta) then B
  else match t1 with
  | B -> B
@@ -139,41 +143,37 @@ and lift n =
   | 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
+  | C  | B as t -> t
  in aux 0
 ;;
 let subst = subst 0 false;;
 
-let subst_in_problem sub p =
-print_endline ("-- SUBST " ^ string_of_t (V (fst sub)) ^ " |-> " ^ string_of_t (snd sub));
+let subst_in_problem ((v, t) as sub) p =
+print_endline ("-- SUBST " ^ string_of_t (V v) ^ " |-> " ^ string_of_t t);
  {p with
   div=subst sub p.div;
   conv=subst sub p.conv;
-  stepped=(fst sub)::p.stepped;
+  stepped=v::p.stepped;
   sigma=sub::p.sigma}
 ;;
 
-let get_subterm_with_head_and_args hd_var n_args =
- let rec aux lev = function
- | C _
- | V _ | B -> None
- | L t -> aux (lev+1) t
+let get_subterms_with_head hd_var =
+ let rec aux lev inert_done = function
+ | C | V _ | B -> []
+ | L t -> aux (lev+1) false 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'
-    then Some (lift ~-lev t)
-    else match aux lev t2 with
-    | None -> aux lev t1
-    | Some _ as res -> res
- in aux 0
+   if not inert_done && hd_var' = V (hd_var + lev)
+    then lift ~-lev t :: aux lev true t1 @ aux lev false t2
+    else aux lev true t1 @ aux lev false t2
+ in aux 0 false
 ;;
 
 let rec purify = function
  | L t -> Pure.L (purify t)
  | A (t1,t2) -> Pure.A (purify t1, purify t2)
  | V n -> Pure.V n
- | C _ -> Pure.V max_int (* FIXME *)
+ | C -> Pure.V (min_int/2)
  | B -> Pure.B
 ;;
 
@@ -182,7 +182,7 @@ 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.";
@@ -201,6 +201,8 @@ let sanity 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
@@ -213,28 +215,33 @@ 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 *)
+ | V _, V _ -> []
  | A(t1,t2), A(u1,u2) ->
-    if not (eta_eq t2 u2) then ((*print_endline((string_of_t t2) ^ " <> " ^ (string_of_t u2));*) k)
+    print_endline (string_of_t t2 ^ " vs " ^ string_of_t u2);
+    if not (eta_eq t2 u2) then (k-1)::aux t1 u1 (k-1)
     else aux t1 u1 (k-1)
  | _, _ -> assert false
- in aux p.div t n_args
+ in aux p.div t argsno
 ;;
 
 let compute_max_lambdas_at hd_var j =
  let rec aux hd = function
  | A(t1,t2) ->
-    (if get_inert t1 = (hd, j)
+    (if get_inert t1 = (V hd, j)
       then max ( (*FIXME*)
-       if is_inert t2 && let hd', j' = get_inert t2 in hd' = hd
+       if is_inert t2 && let hd', j' = get_inert t2 in hd' = V hd
         then let hd', j' = get_inert t2 in j - j'
         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
+ | V _ | C -> 0
  | _ -> assert false
  in aux hd_var
 ;;
@@ -246,6 +253,9 @@ let print_cmd s1 s2 = print_endline (">> " ^ s1 ^ " " ^ s2);;
 let eat p =
 print_cmd "EAT" "";
  let var, k = get_inert p.div in
+ match var with
+ | C | L _ | B | A _ -> assert false
+ | V var ->
  let phase = p.phase in
  let p =
   match phase with
@@ -273,8 +283,11 @@ print_cmd "EAT" "";
 
 (* step on the head of div, on the k-th argument, with n fresh vars *)
 let step 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 hd, _ = get_inert p.div in
+ match hd with
+ | C | L _ | B | A _  -> assert false
+ | V var ->
+print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (on " ^ string_of_int (k+1) ^ "th)");
  let p, t = (* apply fresh vars *)
   fold_nat (fun (p, t) _ ->
     let p, v = freshvar p in
@@ -288,39 +301,60 @@ print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (of:" ^ string_of_int n ^ ")")
  sanity p
 ;;
 
-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
-    let phase = p.phase in
+let auto p =
+ let rec aux p =
+ let hd, n_args = get_inert p.div in
+ match hd with
+ | C | L _ | B | A _  -> assert false
+ | V hd_var ->
+ let tms = get_subterms_with_head hd_var p.conv in
+ if List.exists (fun t -> snd (get_inert t) >= n_args) tms
+  then (
+    (* let tms = List.sort (fun t1 t2 -> - compare (snd (get_inert t1)) (snd (get_inert t2))) tms in *)
+    List.iter (fun t -> try
+      let js = find_eta_difference p t n_args in
+      (* print_endline (String.concat ", " (List.map string_of_int js)); *)
+      if js = [] then problem_fail p "no eta difference found (div subterm of conv?)";
+      let js = List.rev js in
+       List.iter
+        (fun j ->
+         try
+          let k = 1 + max
+           (compute_max_lambdas_at hd_var j p.div)
+            (compute_max_lambdas_at hd_var j p.conv) in
+          ignore (aux (step j k p))
+         with Fail(_, s) ->
+          print_endline ("Backtracking (eta_diff) because: " ^ s)) js;
+       raise (Fail(-1, "no eta difference"))
+      with Fail(_, s) ->
+       print_endline ("Backtracking (get_subterms) because: " ^ s)) tms;
+     raise (Fail(-1, "no similar terms"))
+   )
+  else
+    (let phase = p.phase in
      let p = eat p in
      if phase = `Two
       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 k = 1 + max
-   (compute_max_lambdas_at hd_var j p.div)
-    (compute_max_lambdas_at hd_var j p.conv) in
-  let p = step j k p in
-  auto p
+      else aux p)
+  in
+  try
+   aux p
+  with Done sigma -> sigma
 ;;
 
 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 x (aux y)) (V v) args
- | `Var(v,_) -> V v
+ let rec aux lev = function
+ | `Lam(_, t) -> L (aux (lev+1) t)
+ | `I (v, args) -> Listx.fold_left (fun x y -> mk_app x (aux lev y)) (aux lev (`Var v)) args
+ | `Var(v,_) -> if v >= lev && List.nth var_names (v-lev) = "C" then C else V v
  | `N _ | `Match _ -> assert false in
  assert (List.length ps = 0);
  let convs = List.rev convs in
- let conv = List.fold_left (fun x y -> mk_app x (aux (y :> Num.nf))) (V (List.length var_names)) convs in
+ let conv = List.fold_left (fun x y -> mk_app x (aux 0 (y :> Num.nf))) (V (List.length var_names)) convs in
  let var_names = "@" :: var_names in
  let div = match div with
- | Some div -> aux (div :> Num.nf)
+ | Some div -> aux 0 (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=[]; stepped=[]; phase=`One} in
@@ -329,7 +363,8 @@ let problem_of (label, div, convs, ps, var_names) =
 ;;
 
 let solve p =
- if eta_subterm p.div p.conv
+ if is_stuck p.div then print_endline "!!! div is stuck. Problem was not run !!!"
+ else if eta_subterm p.div p.conv
   then print_endline "!!! div is subterm of conv. Problem was not run !!!"
   else check p (auto p)
 ;;