From 11ba0158d9b6947f5d5b9033955b98a6adfe7959 Mon Sep 17 00:00:00 2001
From: acondolu <andrea.condoluci@unibo.it>
Date: Wed, 30 May 2018 13:49:13 +0200
Subject: [PATCH] Clean-up step function; move code

---
 ocaml/andrea.ml | 62 ++++++++++++++++++++++---------------------------
 1 file changed, 28 insertions(+), 34 deletions(-)

diff --git a/ocaml/andrea.ml b/ocaml/andrea.ml
index 93d69a8..bd2ad09 100644
--- a/ocaml/andrea.ml
+++ b/ocaml/andrea.ml
@@ -1,5 +1,6 @@
 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;;
 
@@ -22,17 +23,8 @@ let eta_eq =
  in aux 0 0
 ;;
 
-type problem = {
-   orig_freshno: int
- ; freshno : int
- ; div : t
- ; conv : t
- ; sigma : (var * t) list (* substitutions *)
- ; stepped : var list
-}
-
-exception Done of (var * t) list (* substitution *);;
-exception Fail of int * string;;
+(* does NOT lift t *)
+let mk_lams = fold_nat (fun x _ -> L x) ;;
 
 let string_of_t =
   let string_of_bvar =
@@ -54,6 +46,15 @@ let string_of_t =
   in string_of_term_no_pars 0
 ;;
 
+type problem = {
+   orig_freshno: int
+ ; freshno : int
+ ; div : t
+ ; conv : t
+ ; sigma : (var * t) list (* substitutions *)
+ ; stepped : var list
+}
+
 let string_of_problem p =
  let lines = [
   "[stepped] " ^ String.concat " " (List.map string_of_int p.stepped);
@@ -63,6 +64,9 @@ let string_of_problem p =
  String.concat "\n" lines
 ;;
 
+exception Done of (var * t) list (* substitution *);;
+exception Fail of int * string;;
+
 let problem_fail p reason =
  print_endline "!!!!!!!!!!!!!!! FAIL !!!!!!!!!!!!!!!";
  print_endline (string_of_problem p);
@@ -150,11 +154,7 @@ let print_cmd s1 s2 = print_endline (">> " ^ s1 ^ " " ^ s2);;
 let eat p =
 print_cmd "EAT" "";
  let var, n = get_inert p.div in
- let rec aux m t =
-  if m = 0
-   then lift n t
-   else L (aux (m-1) t) in
- let subst = var, aux n B in
+ let subst = var, mk_lams B n in
  let p = subst_in_problem subst p in
  sanity p; p
 ;;
@@ -162,21 +162,15 @@ 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 rec aux' p m t =
-  if m < 0
-   then p, t
-    else
-     let p, v = freshvar p in
-     let p, t = aux' p (m-1) t in
-      p, A(t, V (v + k + 1)) in
- let p, t = aux' p n (V 0) in
- let rec aux' m t = if m < 0 then t else A(aux' (m-1) t, V (k-m)) in
- let rec aux m t =
-  if m < 0
-   then aux' (k-1) t
-   else L (aux (m-1) t) in
- let t = aux k t in
+print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (of:" ^ string_of_int n ^ ")");
+ let p, t = (* apply fresh vars *)
+  fold_nat (fun (p, t) _ ->
+    let p, v = freshvar p in
+    p, A(t, V (v + k + 1))
+  ) (p, V 0) n in
+ let t = (* apply unused bound variables V_{k-1}..V_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; p
@@ -266,7 +260,7 @@ let rec auto p =
     (try problem_fail (eat p) "Auto did not complete the problem"  with Done _ -> ())
  | Some t ->
   let j = find_eta_difference p t n_args - 1 in
-  let k = max
+  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
@@ -309,11 +303,11 @@ let auto' a b = auto (problem_of a (conv_join b));;
 exec
  "x x"
  (conv_join["x y"; "y y"; "y x"])
- [ step 0 0; eat ]
+ [ step 0 1; eat ]
 ;;
 
 interactive "x y"
- "@ (x x) (y x) (y z)" [step 0 0; step 0 1; eat]
+ "@ (x x) (y x) (y z)" [step 0 1; step 0 2; eat]
 ;;
 
 *)
-- 
2.39.2