| V of var\r
| A of t * t\r
| L of t\r
- | B (* bottom *)\r
| C (* constant *)\r
;;\r
\r
| C -> "C"\r
| A _\r
| L _ as t -> "(" ^ string_of_term_no_pars level t ^ ")"\r
- | B -> "BOT"\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
| _ as t -> string_of_term_w_pars level t\r
; div : t\r
; conv : t\r
; sigma : (var * t) list (* substitutions *)\r
- ; stepped : var list\r
- ; phase : [`One | `Two] (* :'( *)\r
}\r
\r
let string_of_problem p =\r
let lines = [\r
- "[stepped] " ^ String.concat " " (List.map string_of_int p.stepped);\r
"[DV] " ^ string_of_t p.div;\r
"[CV] " ^ string_of_t p.conv;\r
] in\r
String.concat "\n" lines\r
;;\r
\r
+exception B;;\r
exception Done of (var * t) list (* substitution *);;\r
exception Fail of int * string;;\r
\r
{p with freshno=freshno+1}, freshno+1\r
;;\r
\r
+(* CSC: rename? is an applied C an inert?\r
+ is_inert and get_inert work inconsistently *)\r
let rec is_inert =\r
function\r
| A(t,_) -> is_inert t\r
| V _ -> true\r
| C\r
- | L _ | B -> false\r
+ | L _ -> false\r
+;;\r
+\r
+let rec is_constant =\r
+ function\r
+ C -> true\r
+ | V _ -> false\r
+ | A(t,_)\r
+ | L t -> is_constant t\r
;;\r
\r
let rec get_inert = function\r
| _ -> assert false\r
;;\r
\r
+let args_of_inert =\r
+ let rec aux acc =\r
+ function\r
+ | V _ | C -> acc\r
+ | A(t, a) -> aux (a::acc) t\r
+ | _ -> assert false\r
+ in\r
+ aux []\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
| A _ as t -> let v', m = get_inert t in if V v = v' then max 0 (n - m) else 0\r
| V v' -> if v = v' then n else 0\r
- | B | C -> 0\r
+ | C -> 0\r
;;\r
\r
let rec subst level delift sub =\r
let t1 = subst level delift sub t1 in\r
let t2 = subst level delift sub t2 in\r
mk_app t1 t2\r
- | C | B as t -> t\r
-and mk_app t1 t2 = if t2 = B || (t1 = delta && t2 = delta) then B\r
+ | C -> C\r
+and mk_app t1 t2 = if t1 = delta && t2 = delta then raise B\r
else match t1 with\r
- | B -> B\r
| L t1 -> subst 0 true (0, t2) t1\r
| _ -> A (t1, t2)\r
and lift n =\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
- | C | B as t -> t\r
+ | C -> C\r
in aux 0\r
;;\r
let subst = subst 0 false;;\r
{p with\r
div=subst sub p.div;\r
conv=subst sub p.conv;\r
- stepped=v::p.stepped;\r
sigma=sub::p.sigma}\r
;;\r
\r
let get_subterms_with_head hd_var =\r
let rec aux lev inert_done = function\r
- | C | V _ | B -> []\r
| L t -> aux (lev+1) false t\r
+ | C | V _ -> []\r
| A(t1,t2) as t ->\r
let hd_var', n_args' = get_inert t1 in\r
if not inert_done && hd_var' = V (hd_var + lev)\r
| A (t1,t2) -> Pure.A (purify t1, purify t2)\r
| V n -> Pure.V n\r
| C -> Pure.V (min_int/2)\r
- | B -> Pure.B\r
;;\r
\r
let check p sigma =\r
\r
let sanity p =\r
print_endline (string_of_problem p); (* non cancellare *)\r
- if p.conv = B then problem_fail p "p.conv diverged";\r
- if p.div = B then raise (Done p.sigma);\r
- if p.phase = `Two && p.div = delta then raise (Done p.sigma);\r
if not (is_inert p.div) then problem_fail p "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
+ | _ as t -> t in\r
+ let p = {p with div=remove_trailing_constant_args p.div} in\r
p\r
;;\r
\r
(* drops the arguments of t after the n-th *)\r
-(* FIXME! E' usato in modo improprio contando sul fatto\r
- errato che ritorna un inerte lungo esattamente n *)\r
let inert_cut_at n t =\r
let rec aux t =\r
match t with\r
;;\r
\r
(* return the index of the first argument with a difference\r
- (the first argument is 0)\r
- precondition: p.div and t have n+1 arguments\r
- *)\r
-let find_eta_difference p t argsno =\r
- let t = inert_cut_at argsno t in\r
- let rec aux t u k = match t, u with\r
- | V _, V _ -> []\r
- | A(t1,t2), A(u1,u2) ->\r
- print_endline (string_of_t t2 ^ " vs " ^ string_of_t u2);\r
- if not (eta_eq t2 u2) then (k-1)::aux t1 u1 (k-1)\r
- else aux t1 u1 (k-1)\r
- | _, _ -> assert false\r
- in aux p.div t argsno\r
+ (the first argument is 0) *)\r
+let find_eta_difference p t =\r
+ let divargs = args_of_inert p.div in\r
+ let conargs = args_of_inert t in\r
+ let rec aux k divargs conargs =\r
+ match divargs,conargs with\r
+ [],_ -> []\r
+ | _::_,[] -> [k]\r
+ | t1::divargs,t2::conargs ->\r
+ (if not (eta_eq t1 t2) then [k] else []) @ aux (k+1) divargs conargs\r
+ in\r
+ aux 0 divargs conargs\r
;;\r
\r
let compute_max_lambdas_at hd_var j =\r
else id) (max (aux hd t1) (aux hd t2))\r
| L t -> aux (hd+1) t\r
| V _ | C -> 0\r
- | _ -> assert false\r
in aux hd_var\r
;;\r
\r
let print_cmd s1 s2 = print_endline (">> " ^ s1 ^ " " ^ s2);;\r
\r
-(* eat the arguments of the divergent and explode.\r
- It does NOT perform any check, may fail if done unsafely *)\r
-let eat p =\r
-print_cmd "EAT" "";\r
- let var, k = get_inert p.div in\r
- match var with\r
- | C | L _ | B | A _ -> assert false\r
- | V var ->\r
- let phase = p.phase in\r
- let p =\r
- match phase with\r
- | `One ->\r
- let n = 1 + max\r
- (compute_max_lambdas_at var (k-1) p.div)\r
- (compute_max_lambdas_at var (k-1) p.conv) in\r
- (* apply fresh vars *)\r
- let p, t = fold_nat (fun (p, t) _ ->\r
- let p, v = freshvar p in\r
- p, A(t, V (v + k))\r
- ) (p, V 0) n in\r
- let p = {p with phase=`Two} in\r
- let t = A(t, delta) in\r
- let t = fold_nat (fun t m -> A(t, V (k-m))) t (k-1) in\r
- let subst = var, mk_lams t k in\r
- let p = subst_in_problem subst p in\r
- let _, args = get_inert p.div in\r
- {p with div = inert_cut_at (args-k) p.div}\r
- | `Two ->\r
- let subst = var, mk_lams delta k in\r
- subst_in_problem subst p in\r
- sanity p\r
+(* returns Some i if i is the smallest integer s.t. p holds for the i-th\r
+ element of the list in input *)\r
+let smallest_such_that p =\r
+ let rec aux i =\r
+ function\r
+ [] -> None\r
+ | hd::_ when (print_endline (string_of_t hd) ; p hd) -> Some i\r
+ | _::tl -> aux (i+1) tl\r
+ in\r
+ aux 0\r
;;\r
\r
(* step on the head of div, on the k-th argument, with n fresh vars *)\r
let step k n p =\r
let hd, _ = get_inert p.div in\r
match hd with\r
- | C | L _ | B | A _ -> assert false\r
+ | C | L _ | A _ -> assert false\r
| V var ->\r
print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (on " ^ string_of_int (k+1) ^ "th)");\r
let p, t = (* apply fresh vars *)\r
sanity p\r
;;\r
\r
+let finish p =\r
+ (* one-step version of eat *)\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
+ | _ -> n\r
+ in aux 0 in\r
+print_cmd "FINISH" "";\r
+ (* First, a step on the last argument of the divergent.\r
+ Because of the sanity check, it will never be a constant term. *)\r
+ let div_hd, div_nargs = get_inert p.div in\r
+ let div_hd = match div_hd with V n -> n | _ -> assert false in\r
+ let j = div_nargs - 1 in\r
+ let arity = compute_max_arity p.conv in\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
+ (* 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
+ let div_hd, div_nargs = get_inert p.div in\r
+ let div_hd = match div_hd with V n -> n | _ -> assert false in\r
+ let rec aux m = function\r
+ | A(t, V delta_var) ->\r
+ if delta_var <> div_hd && get_subterms_with_head delta_var p.conv = []\r
+ then m, delta_var\r
+ else aux (m-1) t\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
+ 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 _ | B | A _ -> assert false\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
List.iter (fun t -> try\r
- let js = find_eta_difference p t n_args in\r
+ let js = find_eta_difference p t in\r
(* print_endline (String.concat ", " (List.map string_of_int js)); *)\r
if js = [] then problem_fail p "no eta difference found (div subterm of conv?)";\r
let js = List.rev js in\r
raise (Fail(-1, "no similar terms"))\r
)\r
else\r
- (let phase = p.phase in\r
- let p = eat p in\r
- if phase = `Two\r
- then problem_fail p "Auto.2 did not complete the problem"\r
- else aux p)\r
+ problem_fail (finish p) "Finish did not complete the problem"\r
in\r
try\r
aux p\r
let problem_of (label, div, convs, ps, var_names) =\r
print_hline ();\r
let rec aux lev = function\r
- | `Lam(_, t) -> L (aux (lev+1) t)\r
- | `I (v, args) -> Listx.fold_left (fun x y -> mk_app x (aux lev y)) (aux lev (`Var v)) args\r
+ | `Lam(_, t) -> L (aux (lev+1) t, [])\r
+ | `I (v, args) -> Listx.fold_left (fun x y -> fst (mk_app x (aux lev y))) (aux lev (`Var v)) args\r
| `Var(v,_) -> if v >= lev && List.nth var_names (v-lev) = "C" then C else V v\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 -> mk_app x (aux 0 (y :> Num.nf))) (V (List.length var_names)) 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 div = match div with\r
| Some div -> aux 0 (div :> Num.nf)\r
| None -> assert false in\r
let varno = List.length var_names in\r
- let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; stepped=[]; phase=`One} in\r
- (* initial sanity check *)\r
- sanity p\r
+ {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]}\r
;;\r
\r
let solve p =\r
- if is_stuck p.div then print_endline "!!! div is stuck. Problem was not run !!!"\r
+ if is_constant p.div\r
+ then print_endline "!!! div is stuck. Problem was not run !!!"\r
else if eta_subterm p.div p.conv\r
then print_endline "!!! div is subterm of conv. Problem was not run !!!"\r
- else check p (auto p)\r
+ else let p = sanity p (* initial sanity check *) in check p (auto p)\r
;;\r
\r
Problems.main (solve ++ problem_of);\r
projects / fireball-separation.git / blobdiff