Implementing constants

auto now iterates the eta differences and backtracks if no more available

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index a63314959984a88c3407ec8d20f89a60a9c1efd1..4a69c6e84b5ba2f046deac6281630a5b866f9897 100644 (file)
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -17,8 +17,15 @@ type t =
 \r
 let delta = L(A(V 0, V 0));;\r
 \r
+let rec is_stuck = function\r
+ | C -> true\r
+ | A(t,_) -> is_stuck t\r
+ | _ -> false\r
+;;\r
+\r
 let eta_eq' =\r
  let rec aux l1 l2 t1 t2 = match t1, t2 with\r
+  | _, _ when is_stuck t1 || is_stuck t2 -> true\r
   | L t1, L t2 -> aux l1 l2 t1 t2\r
   | L t1, t2 -> aux l1 (l2+1) t1 t2\r
   | t1, L t2 -> aux (l1+1) l2 t1 t2\r
@@ -30,11 +37,11 @@ let eta_eq = eta_eq' 0 0;;
 \r
 (* is arg1 eta-subterm of arg2 ? *)\r
 let eta_subterm u =\r
- let rec aux lev t = eta_eq' lev 0 u t || match t with\r
+ let rec aux lev t = if t = C then false else (eta_eq' lev 0 u t || match t with\r
  | L t -> aux (lev+1) t\r
  | A(t1, t2) -> aux lev t1 || aux lev t2\r
- | _ -> false\r
- in aux 0\r
+ | _ -> false) in\r
+ aux 0\r
 ;;\r
 \r
 (* does NOT lift the argument *)\r
@@ -102,7 +109,7 @@ let rec is_inert =
 ;;\r
 \r
 let rec get_inert = function\r
- | V n -> (n,0)\r
+ | V _ | C as t -> (t,0)\r
  | A(t, _) -> let hd,args = get_inert t in hd,args+1\r
  | _ -> assert false\r
 ;;\r
@@ -111,7 +118,7 @@ let rec get_inert = function
    after replacing _v_ w/ a term starting with n lambdas *)\r
 let rec no_leading_lambdas v n = function\r
  | L t -> 1 + no_leading_lambdas (v+1) n t\r
- | A _ as t -> let v', m = get_inert t in if v = v' then max 0 (n - m) else 0\r
+ | A _ as t -> let v', m = get_inert t in if V v = v' then max 0 (n - m) else 0\r
  | V v' -> if v = v' then n else 0\r
  | B | C -> 0\r
 ;;\r
@@ -156,7 +163,7 @@ let get_subterm_with_head_and_args hd_var n_args =
  | L t -> aux (lev+1) t\r
  | A(t1,t2) as t ->\r
    let hd_var', n_args' = get_inert t1 in\r
-   if hd_var' = hd_var + lev && n_args <= 1 + n_args'\r
+   if hd_var' = V (hd_var + lev) && n_args <= 1 + n_args'\r
     (* the `+1` above is because of t2 *)\r
     then Some (lift ~-lev t)\r
     else match aux lev t2 with\r
@@ -218,9 +225,10 @@ let inert_cut_at n t =
 let find_eta_difference p t argsno =\r
  let t = inert_cut_at argsno t in\r
  let rec aux t u k = match t, u with\r
- | V _, V _ -> problem_fail p "no eta difference found (div subterm of conv?)"\r
+ | V _, V _ -> []\r
  | A(t1,t2), A(u1,u2) ->\r
-    if not (eta_eq t2 u2) then (k-1)\r
+    print_endline (string_of_t t2 ^ " vs " ^ string_of_t u2);\r
+    if not (eta_eq t2 u2) then (k-1)::aux t1 u1 (k-1)\r
     else aux t1 u1 (k-1)\r
  | _, _ -> assert false\r
  in aux p.div t argsno\r
@@ -229,9 +237,9 @@ let find_eta_difference p t argsno =
 let compute_max_lambdas_at hd_var j =\r
  let rec aux hd = function\r
  | A(t1,t2) ->\r
-    (if get_inert t1 = (hd, j)\r
+    (if get_inert t1 = (V hd, j)\r
       then max ( (*FIXME*)\r
-       if is_inert t2 && let hd', j' = get_inert t2 in hd' = hd\r
+       if is_inert t2 && let hd', j' = get_inert t2 in hd' = V hd\r
         then let hd', j' = get_inert t2 in j - j'\r
         else no_leading_lambdas hd_var j t2)\r
       else id) (max (aux hd t1) (aux hd t2))\r
@@ -278,8 +286,11 @@ print_cmd "EAT" "";
 \r
 (* step on the head of div, on the k-th argument, with n fresh vars *)\r
 let step k n p =\r
- let var, _ = get_inert p.div in\r
-print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (of:" ^ string_of_int n ^ ")");\r
+ let hd, _ = get_inert p.div in\r
+ match hd with\r
+ | C | L _ | B | A _  -> assert false\r
+ | V var ->\r
+print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (on " ^ string_of_int (k+1) ^ "th)");\r
  let p, t = (* apply fresh vars *)\r
   fold_nat (fun (p, t) _ ->\r
     let p, v = freshvar p in\r
@@ -293,24 +304,37 @@ print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (of:" ^ string_of_int n ^ ")")
  sanity p\r
 ;;\r
 \r
-let rec auto p =\r
- let hd_var, n_args = get_inert p.div in\r
+let auto p =\r
+ let rec aux p =\r
+ let hd, n_args = get_inert p.div in\r
+ match hd with\r
+ | C | L _ | B | A _  -> assert false\r
+ | V hd_var ->\r
  match get_subterm_with_head_and_args hd_var n_args p.conv with\r
  | None ->\r
-   (try\r
     let phase = p.phase in\r
      let p = eat p in\r
      if phase = `Two\r
       then problem_fail p "Auto.2 did not complete the problem"\r
-      else auto p\r
-    with Done sigma -> sigma)\r
+      else aux p\r
  | Some t ->\r
-  let j = find_eta_difference p t n_args in\r
-  let k = 1 + max\r
-   (compute_max_lambdas_at hd_var j p.div)\r
-    (compute_max_lambdas_at hd_var j p.conv) in\r
-  let p = step j k p in\r
-  auto p\r
+  let js = find_eta_difference p t n_args in\r
+  (* print_endline (String.concat ", " (List.map string_of_int js)); *)\r
+  if js = [] then problem_fail p "no eta difference found (div subterm of conv?)";\r
+  let js = List.rev js in\r
+   List.iter\r
+    (fun j ->\r
+     try\r
+      let k = 1 + max\r
+       (compute_max_lambdas_at hd_var j p.div)\r
+        (compute_max_lambdas_at hd_var j p.conv) in\r
+      ignore (aux (step j k p))\r
+     with Fail(_, s) ->\r
+      print_endline ("Backtracking because: " ^ s)) js;\r
+   raise (Fail(-1, "no eta difference")) in\r
+  try\r
+   aux p\r
+  with Done sigma -> sigma\r
 ;;\r
 \r
 let problem_of (label, div, convs, ps, var_names) =\r
@@ -334,7 +358,8 @@ let problem_of (label, div, convs, ps, var_names) =
 ;;\r
 \r
 let solve p =\r
- if eta_subterm p.div p.conv\r
+ if is_stuck p.div then print_endline "!!! div is stuck. Problem was not run !!!"\r
+ else if eta_subterm p.div p.conv\r
   then print_endline "!!! div is subterm of conv. Problem was not run !!!"\r
   else check p (auto p)\r
 ;;\r