;;\r
\r
let eta_eq' =\r
- let rec aux l1 l2 t1 t2 = match t1, t2 with\r
- | _, _ when is_stuck t1 || is_stuck t2 -> true\r
+ let rec aux l1 l2 t1 t2 =\r
+ let stuck1, stuck2 = is_stuck t1, is_stuck t2 in\r
+ match t1, t2 with\r
+ | _, _ when not stuck1 && stuck2 -> false\r
+ | _, _ when stuck1 -> true\r
| L t1, L t2 -> aux l1 l2 (fst t1) (fst t2)\r
| L t1, t2 -> aux l1 (l2+1) (fst t1) t2\r
| t1, L t2 -> aux (l1+1) l2 t1 (fst t2)\r
| C -> C\r
in aux 0\r
;;\r
-let subst = subst 0 false;;\r
+let subst' = subst;;\r
+let subst = subst' 0 false;;\r
+\r
+let rec mk_apps t = function\r
+ | u::us -> mk_apps (A(t,u)) us\r
+ | [] -> t\r
+;;\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
let sigma = sub :: p.sigma in\r
let div, g = try subst sub p.div with B -> raise (Done sigma) in\r
- assert (g = []);\r
- let conv, f = try subst sub p.conv with B -> raise (Backtrack "p.conv diverged") in\r
- assert (g = []);\r
- {p with div; conv; sigma}\r
+ let divs = div :: g in\r
+ let conv, g = try subst sub p.conv with B -> raise (Backtrack "p.conv diverged") in\r
+ let conv = if g = [] then conv else mk_apps C (conv::g) in\r
+ divs, {p with div; conv; sigma}\r
;;\r
\r
let get_subterms_with_head hd_var =\r
\r
let sanity p =\r
print_endline (string_of_problem p); (* non cancellare *)\r
- if not (is_inert p.div) then raise (Backtrack "p.div converged");\r
(* Trailing constant args can be removed because do not contribute to eta-diff *)\r
let rec remove_trailing_constant_args = function\r
| A(t1, t2) when is_constant t2 -> remove_trailing_constant_args t1\r
let divargs = args_of_inert p.div in\r
let conargs = args_of_inert t in\r
let rec range i j =\r
- if j = -1 then [] else i :: range (i+1) (j-1) in\r
+ if j = 0 then [] else i :: range (i+1) (j-1) in\r
let rec aux k divargs conargs =\r
match divargs,conargs with\r
[],conargs -> range k (List.length conargs)\r
fold_nat (fun t m -> A(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
- sanity p\r
+ let divs, p = subst_in_problem subst p in\r
+ divs, sanity p\r
;;\r
\r
let finish p =\r
let n = 1 + arity + max\r
(compute_max_lambdas_at div_hd j p.div)\r
(compute_max_lambdas_at div_hd j p.conv) in\r
- let p = step j n p in\r
+ let _, p = step j n p in\r
(* Now, find first argument of div that is a variable never applied anywhere.\r
It must exist because of some invariant, since we just did a step,\r
and because of the arity of the divergent *)\r
| A(t,_) -> aux (m-1) t\r
| _ -> assert false in\r
let m, delta_var = aux div_nargs p.div in\r
- let p = subst_in_problem (delta_var, delta) p in\r
- let p = subst_in_problem (div_hd, mk_lams delta (m-1)) p in\r
+ let _, p = subst_in_problem (delta_var, delta) p in\r
+ let _, p = subst_in_problem (div_hd, mk_lams delta (m-1)) p in\r
sanity p\r
;;\r
\r
let auto p =\r
let rec aux p =\r
- let hd, n_args = get_inert p.div in\r
- match hd with\r
- | C | L _ | A _ -> assert false\r
- | V hd_var ->\r
- let tms = get_subterms_with_head hd_var p.conv in\r
- if List.exists (fun t -> snd (get_inert t) >= n_args) tms\r
- then (\r
- (* let tms = List.sort (fun t1 t2 -> - compare (snd (get_inert t1)) (snd (get_inert t2))) tms in *)\r
- try_all "no similar terms" (fun t ->\r
+ match p.div with\r
+ | L(div,g) -> (* case p.div is an abstraction *)\r
+ let f l t = fst (subst' 0 true (0, C) t) :: l in\r
+ (* the `fst' above is because we can ignore the\r
+ garbage generated by the subst, because substituting\r
+ C does not create redexes and thus no new garbage is activated *)\r
+ let tms = List.fold_left f [] (div::g) in\r
+ try_all "auto.L"\r
+ (fun div -> aux {p with div}) tms\r
+ | _ -> (\r
+ if is_constant p.div (* case p.div is rigid inert *)\r
+ then try_all "auto.C"\r
+ (fun div -> aux {p with div}) (args_of_inert p.div)\r
+ else (* case p.div is flexible inert *)\r
+ let hd, n_args = get_inert p.div in\r
+ match hd with\r
+ | C | L _ | A _ -> assert false\r
+ | V hd_var ->\r
+ let tms = get_subterms_with_head hd_var p.conv in\r
+ if List.exists (fun t -> snd (get_inert t) >= n_args) tms\r
+ then (\r
+ (* let tms = List.sort (fun t1 t2 -> - compare (snd (get_inert t1)) (snd (get_inert t2))) tms in *)\r
+ try_all "no similar terms" (fun t ->\r
let js = find_eta_difference p t in\r
(* print_endline (String.concat ", " (List.map string_of_int js)); *)\r
let js = List.rev js in\r
- try_all "no eta difference"\r
- (fun j ->\r
- let k = 1 + max\r
- (compute_max_lambdas_at hd_var j p.div)\r
- (compute_max_lambdas_at hd_var j p.conv) in\r
- aux (step j k p)) js) tms\r
- )\r
- else\r
- problem_fail (finish p) "Finish did not complete the problem"\r
- in\r
- try\r
- aux p\r
- with Done sigma -> sigma\r
+ try_all "no eta difference"\r
+ (fun j ->\r
+ let k = 1 + max\r
+ (compute_max_lambdas_at hd_var j p.div)\r
+ (compute_max_lambdas_at hd_var j p.conv) in\r
+ let divs, p = step j k p in\r
+ try_all "p.div" (fun div -> aux (sanity {p with div})) divs\r
+ ) js) tms)\r
+ else\r
+ problem_fail (finish p) "Finish did not complete the problem"\r
+ ) in try\r
+ aux p\r
+ with Done sigma -> sigma\r
;;\r
\r
let problem_of (label, div, convs, ps, var_names) =\r
| `N _ | `Match _ -> assert false in\r
assert (List.length ps = 0);\r
let convs = List.rev convs in\r
- let conv = List.fold_left (fun x y -> fst (mk_app x (aux 0 (y :> Num.nf)))) (V (List.length var_names)) convs in\r
- let var_names = "@" :: var_names in\r
+ let conv = List.fold_left (fun x y -> fst (mk_app x (aux 0 (y :> Num.nf)))) C convs in\r
let div = match div with\r
| Some div -> aux 0 (div :> Num.nf)\r
| None -> assert false in\r