let (++) f g x = f (g x);;\r
let id x = x;;\r
+let rec fold_nat f x n = if n = 0 then x else f (fold_nat f x (n-1)) n ;;\r
\r
let print_hline = Console.print_hline;;\r
\r
+open Pure\r
+\r
type var = int;;\r
type t =\r
| V of var\r
| B (* bottom *)\r
;;\r
\r
+let delta = L(A(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
in aux 0 0\r
;;\r
\r
-type problem = {\r
- orig_freshno: int\r
- ; freshno : int\r
- ; div : t\r
- ; conv : t\r
- ; sigma : (var * t) list (* substitutions *)\r
- ; stepped : var list\r
-}\r
-\r
-exception Done of (var * t) list (* substitution *);;\r
-exception Fail of int * string;;\r
+(* does NOT lift t *)\r
+let mk_lams = fold_nat (fun x _ -> L x) ;;\r
\r
let string_of_t =\r
let string_of_bvar =\r
in string_of_term_no_pars 0\r
;;\r
\r
+type problem = {\r
+ orig_freshno: int\r
+ ; freshno : int\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
String.concat "\n" lines\r
;;\r
\r
+exception Done of (var * t) list (* substitution *);;\r
+exception Fail of int * string;;\r
+\r
let problem_fail p reason =\r
print_endline "!!!!!!!!!!!!!!! FAIL !!!!!!!!!!!!!!!";\r
print_endline (string_of_problem p);\r
let is_var = function V _ -> true | _ -> false;;\r
let is_lambda = function L _ -> true | _ -> false;;\r
\r
+let rec no_leading_lambdas = function\r
+ | L t -> 1 + no_leading_lambdas t\r
+ | _ -> 0\r
+;;\r
+\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
let rec subst 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
+ | L t -> let t = subst (level + 1) delift sub t in if t = B then B else L 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
| B -> B\r
-and mk_app t1 t2 = match t1 with\r
- | B | _ when t2 = B -> B\r
+and mk_app t1 t2 = if t2 = B || (t1 = delta && t2 = delta) then B\r
+ else match t1 with\r
+ | B -> B\r
| L t1 -> subst 0 true (0, t2) t1\r
- | t1 -> A (t1, t2)\r
+ | _ -> A (t1, t2)\r
and lift n =\r
let rec aux lev =\r
function\r
in aux 0\r
;;\r
\r
+let rec purify = function\r
+ | L t -> Pure.L (purify t)\r
+ | A (t1,t2) -> Pure.A (purify t1, purify t2)\r
+ | V n -> Pure.V n\r
+ | B -> Pure.B\r
+;;\r
+\r
+let check p sigma =\r
+ print_endline "Checking...";\r
+ let div = purify p.div in\r
+ let conv = purify p.conv in\r
+ let sigma = List.map (fun (v,t) -> v, purify t) sigma in\r
+ let freshno = List.fold_right (fun (x,_) -> max x) sigma 0 in\r
+ let env = Pure.env_of_sigma freshno sigma in\r
+ assert (Pure.diverged (Pure.mwhd (env,div,[])));\r
+ assert (not (Pure.diverged (Pure.mwhd (env,conv,[]))));\r
+ ()\r
+;;\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
;;\r
\r
+(* drops the arguments of t after the n-th *)\r
+let inert_cut_at n t =\r
+ let rec aux t =\r
+ match t with\r
+ | V _ as t -> 0, 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
+ | _ -> assert false\r
+ in snd (aux t)\r
+;;\r
+\r
+let find_eta_difference p t n_args =\r
+ let t = inert_cut_at n_args t in\r
+ let rec aux t u k = match t, u with\r
+ | V _, V _ -> assert false (* div subterm of conv *)\r
+ | A(t1,t2), A(u1,u2) ->\r
+ if not (eta_eq t2 u2) then (print_endline((string_of_t t2) ^ " <> " ^ (string_of_t u2)); k)\r
+ else aux t1 u1 (k-1)\r
+ | _, _ -> assert false\r
+ in aux p.div t n_args\r
+;;\r
+\r
+let compute_max_lambdas_at hd_var j =\r
+ let rec aux hd = function\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 t2)\r
+ else id) (max (aux hd t1) (aux hd t2))\r
+ | L t -> aux (hd+1) t\r
+ | V _ -> 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, n = get_inert p.div in\r
- let rec aux m t =\r
- if m = 0\r
- then lift n t\r
- else L (aux (m-1) t) in\r
- let subst = var, aux n B in\r
+ let var, k = get_inert p.div in\r
+ let phase = p.phase in\r
+ let p, t =\r
+ match phase with\r
+ | `One ->\r
+ let n = 1 + max\r
+ (compute_max_lambdas_at var k p.div)\r
+ (compute_max_lambdas_at var k 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 p, A(t, delta)\r
+ | `Two -> p, delta in\r
+ let subst = var, mk_lams t k in\r
let p = subst_in_problem subst p in\r
+ let p = if phase = `One then {p with div = (match p.div with A(t,_) -> t | _ -> assert false)} else p in\r
sanity p; p\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 var, _ = get_inert p.div in\r
- print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (of:" ^ string_of_int n ^ ")");\r
- let rec aux' p m t =\r
- if m < 0\r
- then p, t\r
- else\r
- let p, v = freshvar p in\r
- let p, t = aux' p (m-1) t in\r
- p, A(t, V (v + k + 1)) in\r
- let p, t = aux' p n (V 0) in\r
- let rec aux' m t = if m < 0 then t else A(aux' (m-1) t, V (k-m)) in\r
- let rec aux m t =\r
- if m < 0\r
- then aux' (k-1) t\r
- else L (aux (m-1) t) in\r
- let t = aux k t in\r
+print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (of:" ^ string_of_int n ^ ")");\r
+ 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, 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
+ 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; p\r
| Parser_andrea.App (t1, t2) ->\r
if level = 0 then mk_app (aux level t1) (aux level t2)\r
else A(aux level t1, aux level t2)\r
- | Parser_andrea.Var v -> V v\r
- in let (tms, free) = Parser_andrea.parse_many strs\r
- in (List.map (aux 0) tms, free)\r
+ | Parser_andrea.Var v -> V v in\r
+ let (tms, free) = Parser_andrea.parse_many strs in\r
+ (List.map (aux 0) tms, free)\r
;;\r
\r
let problem_of div conv =\r
print_hline ();\r
- let all_tms, var_names = parse ([div; conv]) in\r
- let div, conv = List.hd all_tms, List.hd (List.tl all_tms) in\r
+ let [@warning "-8"] [div; conv], var_names = parse ([div; conv]) in\r
let varno = List.length var_names in\r
- let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; stepped=[]} in\r
- (* activate bombs *)\r
- let p = try\r
- let subst = Util.index_of "BOMB" var_names, L B in\r
- subst_in_problem subst p\r
- with Not_found -> p in\r
+ let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; stepped=[]; phase=`One} in\r
(* initial sanity check *)\r
sanity p; p\r
;;\r
| Done _ -> ()\r
;;\r
\r
-let inert_cut_at n t =\r
- let rec aux t =\r
- match t with\r
- | V _ as t -> 0, 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
- | _ -> assert false\r
- in snd (aux t)\r
-;;\r
-\r
-let find_eta_difference p t n_args =\r
- let t = inert_cut_at n_args t in\r
- let rec aux t u k = match t, u with\r
- | V _, V _ -> assert false (* div subterm of conv *)\r
- | A(t1,t2), A(u1,u2) ->\r
- if not (eta_eq t2 u2) then (print_endline((string_of_t t2) ^ " <> " ^ (string_of_t u2)); k)\r
- else aux t1 u1 (k-1)\r
- | _, _ -> assert false\r
- in aux p.div t n_args\r
-;;\r
-\r
-let rec no_leading_lambdas = function\r
- | L t -> 1 + no_leading_lambdas t\r
- | _ -> 0\r
-;;\r
-\r
-let compute_max_lambdas_at hd_var j =\r
- let rec aux hd = function\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 t2)\r
- else id) (max (aux hd t1) (aux hd t2))\r
- | L t -> aux (hd+1) t\r
- | V _ -> 0\r
- | _ -> assert false\r
- in aux hd_var\r
-;;\r
-\r
let rec auto p =\r
let hd_var, n_args = get_inert p.div in\r
match get_subterm_with_head_and_args hd_var n_args p.conv with\r
| None ->\r
- (try problem_fail (eat p) "Auto did not complete the problem" with Done _ -> ())\r
+ (try\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 auto p\r
+ with Done sigma -> sigma)\r
| Some t ->\r
let j = find_eta_difference p t n_args - 1 in\r
- let k = max\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 p = step j k p in\r
| x::xs -> conv_join xs ^ " ("^ x ^")"\r
;;\r
\r
-let auto' a b = auto (problem_of a (conv_join b));;\r
+let auto' a b =\r
+ let p = problem_of a (conv_join b) in\r
+ let sigma = auto p in\r
+ check p sigma\r
+;;\r
\r
(* Example usage of exec, interactive:\r
\r
exec\r
"x x"\r
(conv_join["x y"; "y y"; "y x"])\r
- [ step 0 0; eat ]\r
+ [ step 0 1; eat ]\r
;;\r
\r
interactive "x y"\r
- "@ (x x) (y x) (y z)" [step 0 0; step 0 1; eat]\r
+ "@ (x x) (y x) (y z)" [step 0 1; step 0 2; eat]\r
;;\r
\r
*)\r
projects / fireball-separation.git / blobdiff