X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Fsimple.ml;h=185c54ef2f025afeea14d38d6bfa74d2423722de;hb=47a9f6a73ecea5a2e60932ce324e21f4a90315c2;hp=a028b1f269015752f08833999edad20386d1cf52;hpb=b532f22eeae82f364dbc533926ea657df765d1e8;p=fireball-separation.git

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index a028b1f..185c54e 100644
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -1,5 +1,4 @@
 let (++) f g x = f (g x);;
-let id x = x;;
 let rec fold_nat f x n = if n = 0 then x else f (fold_nat f x (n-1)) n ;;
 
 let print_hline = Console.print_hline;;
@@ -23,8 +22,11 @@ let rec is_stuck = function
 ;;
 
 let eta_eq' =
- let rec aux l1 l2 t1 t2 = match t1, t2 with
-  | _, _ when is_stuck t1 || is_stuck t2 -> true
+ let rec aux l1 l2 t1 t2 =
+  let stuck1, stuck2 = is_stuck t1, is_stuck t2 in
+  match t1, t2 with
+  | _, _ when not stuck1 && stuck2 -> false
+  | _, _ when stuck1 -> true
   | L t1, L t2 -> aux l1 l2 (fst t1) (fst t2)
   | L t1, t2 -> aux l1 (l2+1) (fst t1) t2
   | t1, L t2 -> aux (l1+1) l2 t1 (fst t2)
@@ -62,7 +64,7 @@ let string_of_t =
     | _ as t -> string_of_term_w_pars level t
   and string_of_term_no_pars level = function
     | L(t,g) -> "λ" ^ string_of_bvar level ^ ". " ^ string_of_term_no_pars (level+1) t
-       ^ (if g = [] then "" else String.concat ", " ("" :: List.map (string_of_term_w_pars level) g))
+       ^ (if g = [] then "" else String.concat ", " ("" :: List.map (string_of_term_w_pars (level+1)) g))
     | _ as t -> string_of_term_no_pars_app level t
   in string_of_term_no_pars 0
 ;;
@@ -70,6 +72,7 @@ let string_of_t =
 type problem = {
    orig_freshno: int
  ; freshno : int
+ ; label : string
  ; div : t
  ; conv : t
  ; sigma : (var * t) list (* substitutions *)
@@ -85,12 +88,21 @@ let string_of_problem p =
 
 exception B;;
 exception Done of (var * t) list (* substitution *);;
-exception Fail of int * string;;
+exception Unseparable of string;;
+exception Backtrack of string;;
+
+let rec try_all label f = function
+ | x::xs -> (try f x with Backtrack s -> (if s <> "" then print_endline ("\n<< BACKTRACK: "^s)); try_all label f xs)
+ | [] -> raise (Backtrack label)
+;;
+let try_both label f x g y =
+ try_all label (function `L x -> f x | `R y -> g y) [`L x ; `R y]
+;;
 
 let problem_fail p reason =
  print_endline "!!!!!!!!!!!!!!! FAIL !!!!!!!!!!!!!!!";
  print_endline (string_of_problem p);
- raise (Fail (-1, reason))
+ failwith reason
 ;;
 
 let freshvar ({freshno} as p) =
@@ -169,16 +181,22 @@ and lift n =
   | C -> C
  in aux 0
 ;;
-let subst = subst 0 false;;
+let subst' = subst;;
+let subst = subst' 0 false;;
+
+let rec mk_apps t = function
+ | u::us -> mk_apps (A(t,u)) us
+ | [] -> t
+;;
 
 let subst_in_problem ((v, t) as sub) p =
 print_endline ("-- SUBST " ^ string_of_t (V v) ^ " |-> " ^ string_of_t t);
  let sigma = sub :: p.sigma in
  let div, g = try subst sub p.div with B -> raise (Done sigma) in
- assert (g = []);
- let conv, f = try subst sub p.conv with B -> raise (Fail(-1, "p.conv diverged")) in
- assert (g = []);
- {p with div; conv; sigma}
+ let divs = div :: g in
+ let conv, g = try subst sub p.conv with B -> raise (Backtrack "p.conv diverged") in
+ let conv = if g = [] then conv else mk_apps C (conv::g) in
+ divs, {p with div; conv; sigma}
 ;;
 
 let get_subterms_with_head hd_var =
@@ -206,28 +224,23 @@ let purify =
 ;;
 
 let check p sigma =
- print_endline "Checking...";
+ print_endline "\nChecking...";
  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 (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.";
- assert (not (Pure.diverged (Pure.mwhd (env,conv,[]))));
- print_endline " C converged.";
+ (if not (Pure.diverged (Pure.mwhd (env,div,[])))
+  then failwith "D converged in Pure");
+ print_endline "- D diverged.";
+ (if Pure.diverged (Pure.mwhd (env,conv,[]))
+  then failwith "C diverged in Pure");
+ print_endline "- C converged.";
  ()
 ;;
 
 let sanity p =
- print_endline (string_of_problem p); (* non cancellare *)
- if not (is_inert p.div) then problem_fail p "p.div converged";
- (* Trailing constant args can be removed because do not contribute to eta-diff *)
- let rec remove_trailing_constant_args = function
- | A(t1, t2) when is_constant t2 -> remove_trailing_constant_args t1
- | _ as t -> t in
- let p = {p with div=remove_trailing_constant_args p.div} in
- p
+ print_endline (string_of_problem p) (* non cancellare *); p
 ;;
 
 (* drops the arguments of t after the n-th *)
@@ -248,9 +261,11 @@ let inert_cut_at n t =
 let find_eta_difference p t =
  let divargs = args_of_inert p.div in
  let conargs = args_of_inert t in
+ let rec range i j =
+  if j = 0 then [] else i :: range (i+1) (j-1) in
  let rec aux k divargs conargs =
   match divargs,conargs with
-     [],_ -> []
+     [],conargs -> range k (List.length conargs)
    | _::_,[] -> [k]
    | t1::divargs,t2::conargs ->
       (if not (eta_eq t1 t2) then [k] else []) @ aux (k+1) divargs conargs
@@ -260,19 +275,17 @@ let find_eta_difference p t =
 
 let compute_max_lambdas_at hd_var j =
  let rec aux hd = function
- | A(t1,t2) ->
+ | A(t1,t2) -> max (max (aux hd t1) (aux hd t2))
     (if get_inert t1 = (V hd, j)
-      then max ( (*FIXME*)
-       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))
+      then no_leading_lambdas hd (j+1) t2
+      else 0)
  | L(t,_) -> aux (hd+1) t
- | V _ | C -> 0
+ | V _
+ | C -> 0
  in aux hd_var
 ;;
 
-let print_cmd s1 s2 = print_endline (">> " ^ s1 ^ " " ^ s2);;
+let print_cmd s1 s2 = print_endline ("\n>> " ^ s1 ^ " " ^ s2);;
 
 (* returns Some i if i is the smallest integer s.t. p holds for the i-th
    element of the list in input *)
@@ -280,7 +293,7 @@ let smallest_such_that p =
  let rec aux i =
   function
      [] -> None
-   | hd::_ when (print_endline (string_of_t hd) ; p hd) -> Some i
+   | hd::_ when p i hd -> Some i
    | _::tl -> aux (i+1) tl
  in
   aux 0
@@ -302,11 +315,11 @@ print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (on " ^ string_of_int (k+1) ^
   fold_nat (fun t m -> A(t, V (k-m+1))) t k 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
- sanity p
+ let divs, p = subst_in_problem subst p in
+ divs, p
 ;;
 
-let finish p =
+let finish p arity =
  (* one-step version of eat *)
  let compute_max_arity =
    let rec aux n = function
@@ -314,17 +327,19 @@ let finish p =
    | L(t,g) -> List.fold_right (max ++ (aux 0)) (t::g) 0
    | _ -> n
  in aux 0 in
-print_cmd "FINISH" "";
  (* First, a step on the last argument of the divergent.
     Because of the sanity check, it will never be a constant term. *)
  let div_hd, div_nargs = get_inert p.div in
- let div_hd = match div_hd with V n -> n | _ -> assert false in
- let j = div_nargs - 1 in
+ let div_hd = match div_hd with V n -> n | _ -> raise (Backtrack "Cannot finish on constant tm") in
+ let j = match
+  smallest_such_that (fun i t -> i >= arity && not (is_constant t)) (args_of_inert p.div)
+  with Some j -> j | None -> raise (Backtrack "") in
+ print_endline "\n>> FINISHING";
  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 j n p in
+ let _, p = step j n p in
  (* Now, find first argument of div that is a variable never applied anywhere.
  It must exist because of some invariant, since we just did a step,
  and because of the arity of the divergent *)
@@ -338,102 +353,87 @@ print_cmd "FINISH" "";
  | A(t,_) -> aux (m-1) t
  | _ -> 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 _, p = subst_in_problem (delta_var, delta) p in
+ ignore (subst_in_problem (div_hd, mk_lams delta (m-1)) p);
+ assert false
 ;;
 
 let auto p =
  let rec aux p =
- let hd, n_args = get_inert p.div in
- match hd with
- | C | L _ | 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 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
-    problem_fail (finish p) "Finish did not complete the problem"
-  in
-  try
-   aux p
-  with Done sigma -> sigma
+ if eta_subterm p.div p.conv
+ then raise (Backtrack "div is subterm of conv");
+ match p.div with
+ | L _ as t -> (* case p.div is an abstraction *)
+    print_endline "\nSOTTO UN LAMBDA";
+    let t, g = mk_app t C in
+    aux ({p with div=mk_apps C (t::g)})
+ | V _ | C -> raise (Backtrack "V | C")
+ | A _ -> (
+   if is_constant p.div (* case p.div is rigid inert *)
+   then (print_endline "\nSOTTO UN C"; try_all "auto.C"
+    (fun div -> aux (sanity {p with div})) (args_of_inert p.div))
+   else (* case p.div is flexible inert *)
+    let hd, n_args = get_inert p.div in
+   match hd with
+   | C | L _ | A _  -> assert false
+   | V hd_var ->
+   let tms = get_subterms_with_head hd_var p.conv in
+   let arity = List.fold_right (max ++ (snd ++ get_inert)) tms 0 in
+   try_both "???" (finish p) arity
+    (fun _ ->
+      let jss = List.concat (List.map (find_eta_difference p) tms) in
+      let jss = List.sort_uniq compare jss in
+      let f = try_all "no differences"
+       (fun j ->
+         let k = 1 + max
+          (compute_max_lambdas_at hd_var j p.div)
+           (compute_max_lambdas_at hd_var j p.conv) in
+         let divs, p = step j k p in
+         try_all "p.div" (fun div -> aux (sanity {p with div})) divs
+         ) in
+       try_both "step, then diverge arguments"
+        f jss
+        (try_all "tried p.div arguments" (fun div -> aux {p with div})) (args_of_inert p.div)
+      ) ()
+ ) in try
+  aux p
+ with Done sigma -> sigma
 ;;
 
 let problem_of (label, div, convs, ps, var_names) =
  print_hline ();
  let rec aux lev = function
- | `Lam(_, t) -> L (aux (lev+1) t, [])
+ | `Lam(_, t, g) -> L (aux (lev+1) t, List.map (aux (lev+1)) g)
  | `I (v, args) -> Listx.fold_left (fun x y -> fst (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 -> fst (mk_app x (aux 0 (y :> Num.nf)))) (V (List.length var_names)) convs in
- let var_names = "@" :: var_names in
+ let conv = List.fold_left (fun x y -> fst (mk_app x (aux 0 (y :> Num.nf)))) C convs in
  let div = match div with
  | Some div -> aux 0 (div :> Num.nf)
  | None -> assert false in
  let varno = List.length var_names in
- {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]}
+ {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; label}
 ;;
 
 let solve p =
- if is_constant 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 let p = sanity p (* initial sanity check *) in check p (auto p)
+ let c = if String.length p.label > 0 then String.sub (p.label) 0 1 else "" in
+ let module M = struct exception Okay end in
+ try
+  if eta_subterm p.div p.conv
+  then raise (Unseparable "div is subterm of conv")
+  else
+   let p = sanity p (* initial sanity check *) in
+   check p (auto p);
+   raise M.Okay
+ with
+  | M.Okay -> if c = "?" then
+    failwith "The problem succeeded, but was supposed to be unseparable"
+  | e when c = "!" ->
+    failwith ("The problem was supposed to be separable, but: "^Printexc.to_string e)
+  | e ->
+    print_endline ("The problem failed, as expected ("^Printexc.to_string e^")")
 ;;
 
 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
- let rec f p cmds =
-  let nth spl n = int_of_string (List.nth spl n) in
-  let read_cmd () =
-   let s = read_line () in
-   let spl = Str.split (Str.regexp " +") s in
-   s, let uno = List.hd spl in
-    try if uno = "eat" then eat
-    else if uno = "step" then step (nth spl 1) (nth spl 2)
-    else failwith "Wrong input."
-    with Failure s -> print_endline s; (fun x -> x) in
-  let str, cmd = read_cmd () in
-  let cmds = (" " ^ str ^ ";")::cmds in
-  try
-   let p = cmd p in f p cmds
-  with
-  | Done _ -> print_endline "Done! Commands history: "; List.iter print_endline (List.rev cmds)
- in f p []
- ) with Done _ -> ()
-;; *)
-
-(* interactive "x y"
- "@ (x x) (y x) (y z)" [step 0 1; step 0 2; eat]
-;; *)