From 587d5b28d74a035b6038d4105a379a6fe4fac37b Mon Sep 17 00:00:00 2001
From: acondolu <andrea.condoluci@unibo.it>
Date: Fri, 1 Jun 2018 17:12:42 +0200
Subject: [PATCH] Implementing constants

auto now iterates the eta differences and backtracks if no more available
---
 ocaml/simple.ml | 73 +++++++++++++++++++++++++++++++++----------------
 1 file changed, 49 insertions(+), 24 deletions(-)

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index a633149..4a69c6e 100644
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -17,8 +17,15 @@ type t =
 
 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
@@ -30,11 +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 *)
@@ -102,7 +109,7 @@ let rec is_inert =
 ;;
 
 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
 ;;
@@ -111,7 +118,7 @@ let rec get_inert = function
    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
+ | 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
 ;;
@@ -156,7 +163,7 @@ let get_subterm_with_head_and_args hd_var n_args =
  | L t -> aux (lev+1) 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'
+   if hd_var' = V (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
@@ -218,9 +225,10 @@ let inert_cut_at n t =
 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 _ -> problem_fail p "no eta difference found (div subterm of conv?)"
+ | V _, V _ -> []
  | A(t1,t2), A(u1,u2) ->
-    if not (eta_eq t2 u2) then (k-1)
+    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 argsno
@@ -229,9 +237,9 @@ let find_eta_difference p 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))
@@ -278,8 +286,11 @@ 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
@@ -293,24 +304,37 @@ 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
+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 ->
  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)
+      else aux p
  | Some t ->
-  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 p = step j k p in
-  auto p
+  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 because: " ^ s)) js;
+   raise (Fail(-1, "no eta difference")) in
+  try
+   aux p
+  with Done sigma -> sigma
 ;;
 
 let problem_of (label, div, convs, ps, var_names) =
@@ -334,7 +358,8 @@ 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)
 ;;
-- 
2.39.2