X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=ocaml%2Fsimple.ml;h=897d6b68a4b736952774d4127e109020f2fb7618;hb=69f44e4fb3d56f89adcc952514707914886fdd79;hp=534100d4f0787961fb688461dd34f52d82314bed;hpb=1e41340acff1c4e4439b44ce5437542c905c352f;p=fireball-separation.git

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index 534100d..897d6b6 100644
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -11,25 +11,39 @@ type t =
  | V of var
  | A of t * t
  | L of t
- | B (* bottom *)
- | C of int
+ | C (* constant *)
 ;;
 
 let delta = L(A(V 0, V 0));;
 
-let eta_eq =
+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 0 0
+ in aux ;;
+let eta_eq = eta_eq' 0 0;;
+
+(* is arg1 eta-subterm of arg2 ? *)
+let eta_subterm u =
+ 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
 ;;
 
-(* does NOT lift t *)
+(* does NOT lift the argument *)
 let mk_lams = fold_nat (fun x _ -> L x) ;;
 
 let string_of_t =
@@ -40,10 +54,9 @@ 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"
   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
     | _ as t -> string_of_term_w_pars level t
@@ -59,19 +72,17 @@ type problem = {
  ; 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);
   "[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;;
 
@@ -85,28 +96,49 @@ let freshvar ({freshno} as p) =
  {p with freshno=freshno+1}, freshno+1
 ;;
 
+(* CSC: rename? is an applied C an inert?
+   is_inert and get_inert work inconsistently *)
 let rec is_inert =
  function
  | A(t,_) -> is_inert t
  | V _ -> true
- | C _
- | L _ | B -> false
+ | C
+ | 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 is_constant =
+ function
+    C -> true
+  | V _ -> false
+  | A(t,_)
+  | L t -> is_constant t
 ;;
 
 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 args_of_inert =
+ let rec aux acc =
+  function
+   | V _ | C -> acc
+   | A(t, a) -> aux (a::acc) t
+   | _ -> assert false
+ in
+  aux []
+;;
+
+(* 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
+ | C -> 0
+;;
+
 let rec subst level delift 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)
@@ -115,12 +147,9 @@ 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
-and mk_app t1 t2 = if t2 = B || (t1 = delta && t2 = delta) then B
+ | C -> C
+and mk_app 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)
 and lift n =
@@ -129,42 +158,36 @@ 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 -> C
  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));
+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;
   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
+ | L t -> aux (lev+1) false t
+ | C | V _ -> []
  | 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 *)
- | B -> Pure.B
+ | C -> Pure.V (min_int/2)
 ;;
 
 let check p sigma =
@@ -172,7 +195,7 @@ 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.";
@@ -183,10 +206,13 @@ 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"
+ 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
 ;;
 
 (* drops the arguments of t after the n-th *)
@@ -202,64 +228,56 @@ 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
- 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)
- | _, _ -> assert false
- in aux p.div t n_args
+(* return the index of the first argument with a difference
+   (the first argument is 0) *)
+let find_eta_difference p t =
+ let divargs = args_of_inert p.div in
+ let conargs = args_of_inert t in
+ let rec aux k divargs conargs =
+  match divargs,conargs with
+     [],_ -> []
+   | _::_,[] -> [k]
+   | t1::divargs,t2::conargs ->
+      (if not (eta_eq t1 t2) then [k] else []) @ aux (k+1) divargs conargs
+ in
+  aux 0 divargs conargs
 ;;
 
 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 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
+ | V _ | C -> 0
  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; p
+(* returns Some i if i is the smallest integer s.t. p holds for the i-th
+   element of the list in input *)
+let smallest_such_that p =
+ let rec aux i =
+  function
+     [] -> None
+   | hd::_ when (print_endline (string_of_t hd) ; p hd) -> Some i
+   | _::tl -> aux (i+1) tl
+ in
+  aux 0
 ;;
 
 (* 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 _ | 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
@@ -270,58 +288,114 @@ print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (of:" ^ string_of_int n ^ ")")
  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; p
+ 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 finish p =
+ (* one-step version of eat *)
+ 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)
+   | _ -> 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 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
+ (* 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 *)
+ let div_hd, div_nargs = get_inert p.div in
+ let div_hd = match div_hd with V n -> n | _ -> assert false in
+ let rec aux m = function
+ | A(t, V delta_var) ->
+   if delta_var <> div_hd && get_subterms_with_head delta_var p.conv = []
+   then m, delta_var
+   else aux (m-1) t
+ | 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 problem_of div conv =
+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
+;;
+
+let problem_of (label, div, convs, ps, var_names) =
  print_hline ();
- let [@warning "-8"] [div; conv], var_names = parse ([div; conv]) in
+ let rec aux lev = function
+ | `Lam(_, t) -> L (aux (lev+1) t, [])
+ | `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 div = match div with
+ | 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
- (* initial sanity check *)
- sanity p; p
+ {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]}
 ;;
 
-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 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 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 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
-;;
+Problems.main (solve ++ problem_of);
+
+(* Example usage of interactive: *)
 
-let interactive div conv cmds =
+(* let interactive div conv cmds =
  let p = problem_of div conv in
  try (
  let p = List.fold_left (|>) p cmds in
@@ -343,54 +417,8 @@ 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 = auto';;
+;; *)