From 9b714951d57db4789d60552a1185287343bd3b74 Mon Sep 17 00:00:00 2001
From: acondolu <andrea.condoluci@unibo.it>
Date: Sat, 2 Jun 2018 19:32:12 +0200
Subject: [PATCH] Added flag to lam and app, their propagation during subst,
 and a measure

The measure seems correct :O
---
 ocaml/simple.ml | 96 +++++++++++++++++++++++++++----------------------
 1 file changed, 54 insertions(+), 42 deletions(-)

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index c8daad1..36d1b13 100644
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -9,19 +9,19 @@ open Pure
 type var = int;;
 type t =
  | V of var
- | A of t * t
- | L of t
+ | A of bool * t * t
+ | L of (bool * t)
 ;;
 
-let delta = L(A(V 0, V 0));;
+let delta = L(true,A(true,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
-  | L t1, t2 -> aux l1 (l2+1) t1 t2
-  | t1, L t2 -> aux (l1+1) l2 t1 t2
+  | L t1, L t2 -> aux l1 l2 (snd t1) (snd t2)
+  | L t1, t2 -> aux l1 (l2+1) (snd t1) t2
+  | t1, L t2 -> aux (l1+1) l2 t1 (snd t2)
   | V a, V b -> a + l1 = b + l2
-  | A(t1,t2), A(u1,u2) -> aux l1 l2 t1 u1 && aux l1 l2 t2 u2
+  | A(_,t1,t2), A(_,u1,u2) -> aux l1 l2 t1 u1 && aux l1 l2 t2 u2
   | _, _ -> false
  in aux ;;
 let eta_eq = eta_eq' 0 0;;
@@ -29,14 +29,20 @@ 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
- | L t -> aux (lev+1) t
- | A(t1, t2) -> aux lev t1 || aux lev t2
+ | L(_,t) -> aux (lev+1) t
+ | A(_, t1, t2) -> aux lev t1 || aux lev t2
  | _ -> false
  in aux 0
 ;;
 
 (* does NOT lift the argument *)
-let mk_lams = fold_nat (fun x _ -> L x) ;;
+let mk_lams = fold_nat (fun x _ -> L(false,x)) ;;
+
+let rec measure_of_t = function
+ | V _ -> 0
+ | A(b,t1,t2) -> (if b then 1 else 0) + measure_of_t t1 + measure_of_t t2
+ | L(b,t) -> if b then measure_of_t t else 0
+;;
 
 let string_of_t =
   let string_of_bvar =
@@ -49,10 +55,10 @@ let string_of_t =
     | A _
     | L _ as t -> "(" ^ string_of_term_no_pars level t ^ ")"
   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
+    | A(b,t1,t2) -> string_of_term_no_pars_app level t1 ^ (if b then "," else " ") ^ string_of_term_w_pars level t2
     | _ as t -> string_of_term_w_pars level t
   and string_of_term_no_pars level = function
-    | L t -> "λ" ^ string_of_bvar level ^ ". " ^ string_of_term_no_pars (level+1) t
+    | L(_,t) -> "λ" ^ string_of_bvar level ^ ". " ^ string_of_term_no_pars (level+1) t
     | _ as t -> string_of_term_no_pars_app level t
   in string_of_term_no_pars 0
 ;;
@@ -67,6 +73,7 @@ type problem = {
 
 let string_of_problem p =
  let lines = [
+  "[measure] " ^ string_of_int (measure_of_t p.div);
   "[DV] " ^ string_of_t p.div;
   "[CV] " ^ string_of_t p.conv;
   "";
@@ -90,7 +97,7 @@ let freshvar ({freshno} as p) =
 
 let rec is_inert =
  function
- | A(t,_) -> is_inert t
+ | A(_,t,_) -> is_inert t
  | V _ -> true
  | L _ -> false
 ;;
@@ -100,39 +107,41 @@ let is_lambda = function L _ -> true | _ -> false;;
 
 let rec get_inert = function
  | V n -> (n,0)
- | A(t, _) -> let hd,args = get_inert t in hd,args+1
+ | A(_,t,_) -> let hd,args = get_inert t in hd,args+1
  | _ -> assert false
 ;;
 
 (* 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
+ | 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
  | V v' -> if v = v' then n else 0
 ;;
 
-let rec subst level delift sub =
+(* b' defaults to false *)
+let rec subst b' 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)
- | L t -> L (subst (level + 1) delift sub t)
- | A (t1,t2) ->
-  let t1 = subst level delift sub t1 in
-  let t2 = subst level delift sub t2 in
-  mk_app t1 t2
-and mk_app t1 t2 = if t1 = delta && t2 = delta then raise B
+ | L(b,t) -> L(b, subst b' (level + 1) delift sub t)
+ | A(_,t1,(V v as t2)) when b' && v = level + fst sub ->
+    mk_app b' (subst b' level delift sub t1) (subst b' level delift sub t2)
+ | A(b,t1,t2) ->
+    mk_app b (subst b' level delift sub t1) (subst b' level delift sub t2)
+and mk_app b' t1 t2 = if t1 = delta && t2 = delta then raise B
  else match t1 with
- | L t1 -> subst 0 true (0, t2) t1
- | _ -> A (t1, t2)
+ | L(b,t1) -> subst (b' && not b) 0 true (0, t2) t1
+ | _ -> A (b', t1, t2)
 and lift n =
  let rec aux lev =
   function
   | 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)
+  | L(b,t) -> L(b,aux (lev+1) t)
+  | A (b,t1, t2) -> A (b,aux lev t1, aux lev t2)
  in aux 0
 ;;
-let subst = subst 0 false;;
+let subst = subst false 0 false;;
+let mk_app = mk_app true;;
 
 let subst_in_problem ((v, t) as sub) p =
 print_endline ("-- SUBST " ^ string_of_t (V v) ^ " |-> " ^ string_of_t t);
@@ -145,8 +154,8 @@ print_endline ("-- SUBST " ^ string_of_t (V v) ^ " |-> " ^ string_of_t t);
 let get_subterm_with_head_and_args hd_var n_args =
  let rec aux lev = function
  | V _ -> None
- | L t -> aux (lev+1) t
- | A(t1,t2) as t ->
+ | 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'
     (* the `+1` above is because of t2 *)
@@ -158,8 +167,8 @@ let get_subterm_with_head_and_args hd_var n_args =
 ;;
 
 let rec purify = function
- | L t -> Pure.L (purify t)
- | A (t1,t2) -> Pure.A (purify t1, purify t2)
+ | L(_,t) -> Pure.L (purify t)
+ | A(_,t1,t2) -> Pure.A (purify t1, purify t2)
  | V n -> Pure.V n
 ;;
 
@@ -191,7 +200,7 @@ let inert_cut_at n t =
  let rec aux t =
   match t with
   | V _ as t -> 0, t
-  | A(t1,_) as t ->
+  | A(_,t1,_) as t ->
     let k', t' = aux t1 in
      if k' = n then n, t'
       else k'+1, t
@@ -207,7 +216,7 @@ 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?)"
- | A(t1,t2), A(u1,u2) ->
+ | A(_,t1,t2), A(_,u1,u2) ->
     if not (eta_eq t2 u2) then (k-1)
     else aux t1 u1 (k-1)
  | _, _ -> assert false
@@ -216,22 +225,22 @@ let find_eta_difference p t argsno =
 
 let compute_max_lambdas_at hd_var j =
  let rec aux hd = function
- | A(t1,t2) ->
+ | 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 hd_var j t2)
       else id) (max (aux hd t1) (aux hd t2))
- | L t -> aux (hd+1) t
+ | L(_,t) -> aux (hd+1) t
  | V _ -> 0
  in aux hd_var
 ;;
 
 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)
+ | A(_,t1, t2) -> max (aux (n+1) t1) (aux 0 t2)
+ | L(_,t) -> max n (aux 0 t)
  | V _ -> n
  in aux 0
 ;;
@@ -249,10 +258,10 @@ 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, A(false, 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
+  fold_nat (fun t m -> A(false, 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
@@ -266,7 +275,7 @@ print_cmd "FINISH" "";
  let p = step j p true in
  let div_hd, div_nargs = get_inert p.div in
  let rec aux m = function
-  A(t1,t2) -> if is_var t2 then
+  A(_,t1,t2) -> if is_var t2 then
    (let delta_var, _ = get_inert t2 in
      if delta_var <> div_hd && get_subterm_with_head_and_args delta_var 1 p.conv = None
       then m, delta_var
@@ -284,18 +293,21 @@ let rec auto p =
  match get_subterm_with_head_and_args hd_var n_args p.conv with
  | None ->
    (try
-     problem_fail (finish p) "Auto did not complete the problem"
+     problem_fail (finish p) "finish() did not complete the problem"
     with Done sigma -> sigma)
  | Some t ->
   let j = find_eta_difference p t n_args in
+  let m1 = measure_of_t p.div in
   let p = step j p false in
+  let m2 = measure_of_t p.div in
+  (if m2 >= m1 then problem_fail p "Measure did not decrease");
   auto p
 ;;
 
 let problem_of (label, div, convs, ps, var_names) =
  print_hline ();
  let rec aux = function
- | `Lam(_, t) -> L (aux t)
+ | `Lam(_, t) -> L (true,aux t)
  | `I ((v,_), args) -> Listx.fold_left (fun x y -> mk_app x (aux y)) (V v) args
  | `Var(v,_) -> V v
  | `N _ | `Match _ -> assert false in
-- 
2.39.2