Added flag to lam and app, their propagation during subst, and a measure

The measure seems correct :O

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index c8daad1e4394936ca29eec4e7cf8f78bc6004731..36d1b1396ee8b24cccf8770120881a3149aa42bd 100644 (file)
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -9,19 +9,19 @@ open Pure
 type var = int;;\r
 type t =\r
  | V of var\r
- | A of t * t\r
- | L of t\r
+ | A of bool * t * t\r
+ | L of (bool * t)\r
 ;;\r
 \r
-let delta = L(A(V 0, V 0));;\r
+let delta = L(true,A(true,V 0, V 0));;\r
 \r
 let eta_eq' =\r
  let rec aux l1 l2 t1 t2 = match t1, t2 with\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
+  | L t1, L t2 -> aux l1 l2 (snd t1) (snd t2)\r
+  | L t1, t2 -> aux l1 (l2+1) (snd t1) t2\r
+  | t1, L t2 -> aux (l1+1) l2 t1 (snd t2)\r
   | V a, V b -> a + l1 = b + l2\r
-  | A(t1,t2), A(u1,u2) -> aux l1 l2 t1 u1 && aux l1 l2 t2 u2\r
+  | A(_,t1,t2), A(_,u1,u2) -> aux l1 l2 t1 u1 && aux l1 l2 t2 u2\r
   | _, _ -> false\r
  in aux ;;\r
 let eta_eq = eta_eq' 0 0;;\r
@@ -29,14 +29,20 @@ let eta_eq = eta_eq' 0 0;;
 (* 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
- | L t -> aux (lev+1) t\r
- | A(t1, t2) -> aux lev t1 || aux lev t2\r
+ | L(_,t) -> aux (lev+1) t\r
+ | A(_, t1, t2) -> aux lev t1 || aux lev t2\r
  | _ -> false\r
  in aux 0\r
 ;;\r
 \r
 (* does NOT lift the argument *)\r
-let mk_lams = fold_nat (fun x _ -> L x) ;;\r
+let mk_lams = fold_nat (fun x _ -> L(false,x)) ;;\r
+\r
+let rec measure_of_t = function\r
+ | V _ -> 0\r
+ | A(b,t1,t2) -> (if b then 1 else 0) + measure_of_t t1 + measure_of_t t2\r
+ | L(b,t) -> if b then measure_of_t t else 0\r
+;;\r
 \r
 let string_of_t =\r
   let string_of_bvar =\r
@@ -49,10 +55,10 @@ let string_of_t =
     | A _\r
     | L _ as t -> "(" ^ string_of_term_no_pars level t ^ ")"\r
   and string_of_term_no_pars_app level = function\r
-    | A(t1,t2) -> string_of_term_no_pars_app level t1 ^ " " ^ string_of_term_w_pars level t2\r
+    | A(b,t1,t2) -> string_of_term_no_pars_app level t1 ^ (if b then "," else " ") ^ string_of_term_w_pars level t2\r
     | _ as t -> string_of_term_w_pars level t\r
   and string_of_term_no_pars level = function\r
-    | L t -> "λ" ^ string_of_bvar level ^ ". " ^ string_of_term_no_pars (level+1) t\r
+    | L(_,t) -> "λ" ^ string_of_bvar level ^ ". " ^ string_of_term_no_pars (level+1) t\r
     | _ as t -> string_of_term_no_pars_app level t\r
   in string_of_term_no_pars 0\r
 ;;\r
@@ -67,6 +73,7 @@ type problem = {
 \r
 let string_of_problem p =\r
  let lines = [\r
+  "[measure] " ^ string_of_int (measure_of_t p.div);\r
   "[DV] " ^ string_of_t p.div;\r
   "[CV] " ^ string_of_t p.conv;\r
   "";\r
@@ -90,7 +97,7 @@ let freshvar ({freshno} as p) =
 \r
 let rec is_inert =\r
  function\r
- | A(t,_) -> is_inert t\r
+ | A(_,t,_) -> is_inert t\r
  | V _ -> true\r
  | L _ -> false\r
 ;;\r
@@ -100,39 +107,41 @@ let is_lambda = function L _ -> true | _ -> false;;
 \r
 let rec get_inert = function\r
  | V n -> (n,0)\r
- | A(t, _) -> let hd,args = get_inert t in hd,args+1\r
+ | A(_,t,_) -> let hd,args = get_inert t in hd,args+1\r
  | _ -> assert false\r
 ;;\r
 \r
 (* precomputes the number of leading lambdas in a term,\r
    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
+ | 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
  | V v' -> if v = v' then n else 0\r
 ;;\r
 \r
-let rec subst level delift sub =\r
+(* b' defaults to false *)\r
+let rec subst b' level delift sub =\r
  function\r
  | V v -> if v = level + fst sub then lift level (snd sub) else V (if delift && v > level then v-1 else v)\r
- | L t -> L (subst (level + 1) delift sub t)\r
- | A (t1,t2) ->\r
-  let t1 = subst level delift sub t1 in\r
-  let t2 = subst level delift sub t2 in\r
-  mk_app t1 t2\r
-and mk_app t1 t2 = if t1 = delta && t2 = delta then raise B\r
+ | L(b,t) -> L(b, subst b' (level + 1) delift sub t)\r
+ | A(_,t1,(V v as t2)) when b' && v = level + fst sub ->\r
+    mk_app b' (subst b' level delift sub t1) (subst b' level delift sub t2)\r
+ | A(b,t1,t2) ->\r
+    mk_app b (subst b' level delift sub t1) (subst b' level delift sub t2)\r
+and mk_app b' t1 t2 = if t1 = delta && t2 = delta then raise B\r
  else match t1 with\r
- | L t1 -> subst 0 true (0, t2) t1\r
- | _ -> A (t1, t2)\r
+ | L(b,t1) -> subst (b' && not b) 0 true (0, t2) t1\r
+ | _ -> A (b', t1, t2)\r
 and lift n =\r
  let rec aux lev =\r
   function\r
   | V m -> V (if m >= lev then m + n else m)\r
-  | L t -> L (aux (lev+1) t)\r
-  | A (t1, t2) -> A (aux lev t1, aux lev t2)\r
+  | L(b,t) -> L(b,aux (lev+1) t)\r
+  | A (b,t1, t2) -> A (b,aux lev t1, aux lev t2)\r
  in aux 0\r
 ;;\r
-let subst = subst 0 false;;\r
+let subst = subst false 0 false;;\r
+let mk_app = mk_app true;;\r
 \r
 let subst_in_problem ((v, t) as sub) p =\r
 print_endline ("-- SUBST " ^ string_of_t (V v) ^ " |-> " ^ string_of_t t);\r
@@ -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 =\r
  let rec aux lev = function\r
  | V _ -> None\r
- | L t -> aux (lev+1) t\r
- | A(t1,t2) as t ->\r
+ | 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
     (* the `+1` above is because of t2 *)\r
@@ -158,8 +167,8 @@ let get_subterm_with_head_and_args hd_var n_args =
 ;;\r
 \r
 let rec purify = function\r
- | L t -> Pure.L (purify t)\r
- | A (t1,t2) -> Pure.A (purify t1, purify t2)\r
+ | L(_,t) -> Pure.L (purify t)\r
+ | A(_,t1,t2) -> Pure.A (purify t1, purify t2)\r
  | V n -> Pure.V n\r
 ;;\r
 \r
@@ -191,7 +200,7 @@ let inert_cut_at n t =
  let rec aux t =\r
   match t with\r
   | V _ as t -> 0, t\r
-  | A(t1,_) as t ->\r
+  | A(_,t1,_) as t ->\r
     let k', t' = aux t1 in\r
      if k' = n then n, t'\r
       else k'+1, t\r
@@ -207,7 +216,7 @@ let find_eta_difference p t argsno =
  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
- | A(t1,t2), A(u1,u2) ->\r
+ | A(_,t1,t2), A(_,u1,u2) ->\r
     if not (eta_eq t2 u2) then (k-1)\r
     else aux t1 u1 (k-1)\r
  | _, _ -> assert false\r
@@ -216,22 +225,22 @@ let find_eta_difference p t argsno =
 \r
 let compute_max_lambdas_at hd_var j =\r
  let rec aux hd = function\r
- | A(t1,t2) ->\r
+ | A(_,t1,t2) ->\r
     (if get_inert t1 = (hd, j)\r
       then max ( (*FIXME*)\r
        if is_inert t2 && let hd', j' = get_inert t2 in hd' = 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
- | L t -> aux (hd+1) t\r
+ | L(_,t) -> aux (hd+1) t\r
  | V _ -> 0\r
  in aux hd_var\r
 ;;\r
 \r
 let compute_max_arity =\r
  let rec aux n = function\r
- | A(t1, t2) -> max (aux (n+1) t1) (aux 0 t2)\r
- | L t -> max n (aux 0 t)\r
+ | A(_,t1, t2) -> max (aux (n+1) t1) (aux 0 t2)\r
+ | L(_,t) -> max n (aux 0 t)\r
  | V _ -> n\r
  in aux 0\r
 ;;\r
@@ -249,10 +258,10 @@ print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (of:" ^ string_of_int n ^ ")")
  let p, t = (* apply fresh vars *)\r
   fold_nat (fun (p, t) _ ->\r
     let p, v = freshvar p in\r
-    p, A(t, V (v + k + 1))\r
+    p, A(false, t, V (v + k + 1))\r
   ) (p, V 0) n in\r
  let t = (* apply unused bound variables V_{k-1}..V_1 *)\r
-  fold_nat (fun t m -> A(t, V (k-m+1))) t k in\r
+  fold_nat (fun t m -> A(false, t, V (k-m+1))) t k in\r
  let t = mk_lams t (k+1) in (* make leading lambdas *)\r
  let subst = var, t in\r
  let p = subst_in_problem subst p in\r
@@ -266,7 +275,7 @@ print_cmd "FINISH" "";
  let p = step j p true in\r
  let div_hd, div_nargs = get_inert p.div in\r
  let rec aux m = function\r
-  A(t1,t2) -> if is_var t2 then\r
+  A(_,t1,t2) -> if is_var t2 then\r
    (let delta_var, _ = get_inert t2 in\r
      if delta_var <> div_hd && get_subterm_with_head_and_args delta_var 1 p.conv = None\r
       then m, delta_var\r
@@ -284,18 +293,21 @@ let rec auto p =
  match get_subterm_with_head_and_args hd_var n_args p.conv with\r
  | None ->\r
    (try\r
-     problem_fail (finish p) "Auto did not complete the problem"\r
+     problem_fail (finish p) "finish() did not complete the problem"\r
     with Done sigma -> sigma)\r
  | Some t ->\r
   let j = find_eta_difference p t n_args in\r
+  let m1 = measure_of_t p.div in\r
   let p = step j p false in\r
+  let m2 = measure_of_t p.div in\r
+  (if m2 >= m1 then problem_fail p "Measure did not decrease");\r
   auto p\r
 ;;\r
 \r
 let problem_of (label, div, convs, ps, var_names) =\r
  print_hline ();\r
  let rec aux = function\r
- | `Lam(_, t) -> L (aux t)\r
+ | `Lam(_, t) -> L (true,aux t)\r
  | `I ((v,_), args) -> Listx.fold_left (fun x y -> mk_app x (aux y)) (V v) args\r
  | `Var(v,_) -> V v\r
  | `N _ | `Match _ -> assert false in\r