From 7c60aa45d5f4486768b6338e2e5aa411dbec8ad9 Mon Sep 17 00:00:00 2001
From: acondolu <andrea.condoluci@unibo.it>
Date: Wed, 30 May 2018 16:31:24 +0200
Subject: [PATCH] Simple strong separation implemented!

- Two phases for eat
- Moved code
- Reduction does not diverge (replaces DD with B)
---
 ocaml/andrea.ml | 115 +++++++++++++++++++++++++++++-------------------
 1 file changed, 70 insertions(+), 45 deletions(-)

diff --git a/ocaml/andrea.ml b/ocaml/andrea.ml
index 7493905..dcc954e 100644
--- a/ocaml/andrea.ml
+++ b/ocaml/andrea.ml
@@ -14,6 +14,8 @@ type t =
  | B (* bottom *)
 ;;
 
+let delta = L(A(V 0, V 0));;
+
 let eta_eq =
  let rec aux l1 l2 t1 t2 = match t1, t2 with
   | L t1, L t2 -> aux l1 l2 t1 t2
@@ -55,6 +57,7 @@ type problem = {
  ; conv : t
  ; sigma : (var * t) list (* substitutions *)
  ; stepped : var list
+ ; phase : [`One | `Two] (* :'( *)
 }
 
 let string_of_problem p =
@@ -109,7 +112,7 @@ let rec subst level delift sub =
   let t2 = subst level delift sub t2 in
   mk_app t1 t2
  | B -> B
-and mk_app t1 t2 = match t1 with
+and mk_app t1 t2 = if t1 = delta && t2 = delta then B else match t1 with
  | B | _ when t2 = B -> B
  | L t1 -> subst 0 true (0, t2) t1
  | t1 -> A (t1, t2)
@@ -168,19 +171,74 @@ 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.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"
 ;;
 
+(* drops the arguments of t after the n-th *)
+let inert_cut_at n t =
+ let rec aux t =
+  match t with
+  | V _ as t -> 0, t
+  | A(t1,_) as t ->
+    let k', t' = aux t1 in
+     if k' = n then n, t'
+      else k'+1, t
+  | _ -> assert false
+ 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
+;;
+
+let compute_max_lambdas_at hd_var j =
+ let rec aux hd = function
+ | A(t1,t2) ->
+    (if get_inert t1 = (hd, j)
+      then max ( (*FIXME*)
+       if is_inert t2 && let hd', j' = get_inert t2 in hd' = hd
+        then let hd', j' = get_inert t2 in j - j'
+        else no_leading_lambdas t2)
+      else id) (max (aux hd t1) (aux hd t2))
+ | L t -> aux (hd+1) t
+ | V _ -> 0
+ | _ -> assert false
+ 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, n = get_inert p.div in
- let subst = var, mk_lams B n in
+ 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
+ let p = if phase = `One then {p with div = (match p.div with A(t,_) -> t | _ -> assert false)} else p in
  sanity p; p
 ;;
 
@@ -216,7 +274,7 @@ let problem_of div conv =
  print_hline ();
  let [@warning "-8"] [div; conv], var_names = parse ([div; conv]) in
  let varno = List.length var_names in
- let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; stepped=[]} in
+ let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; stepped=[]; phase=`One} in
  (* initial sanity check *)
  sanity p; p
 ;;
@@ -229,50 +287,17 @@ let exec div conv cmds =
  | Done _ -> ()
 ;;
 
-(* drops the arguments of t after the n-th *)
-let inert_cut_at n t =
- let rec aux t =
-  match t with
-  | V _ as t -> 0, t
-  | A(t1,_) as t ->
-    let k', t' = aux t1 in
-     if k' = n then n, t'
-      else k'+1, t
-  | _ -> assert false
- 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
-;;
-
-let compute_max_lambdas_at hd_var j =
- let rec aux hd = function
- | A(t1,t2) ->
-    (if get_inert t1 = (hd, j)
-      then max ( (*FIXME*)
-       if is_inert t2 && let hd', j' = get_inert t2 in hd' = hd
-        then let hd', j' = get_inert t2 in j - j'
-        else no_leading_lambdas t2)
-      else id) (max (aux hd t1) (aux hd t2))
- | L t -> aux (hd+1) t
- | V _ -> 0
- | _ -> assert false
- in aux hd_var
-;;
-
 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 problem_fail (eat p) "Auto did not complete the problem"  with Done sigma -> sigma)
+   (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
-- 
2.39.2