LIB = unix.cmxa str.cmxa
UTILS = parser.cmx console.cmx listx.cmx util.cmx pure.cmx num.cmx
-all: a.out test.out test34.out
+all: andrea.out
-a.out: $(UTILS) lambda3.cmx lambda4.cmx problems.cmx
- $(OCAMLC) -o a.out $(LIB) $^
-
-test.out: $(UTILS) lambda3.cmx test1.ml
- $(OCAMLC) -o test.out $(LIB) $^
-
-test34.out: $(UTILS) lambda3.cmx lambda4.cmx test.ml
- $(OCAMLC) -o test34.out $(LIB) $^
-
-andrea.out: $(UTILS) a.out andrea7.ml
- $(OCAMLC) -o andrea.out $(LIB) $(UTILS) andrea7.ml
-
-#test2.out: $(UTILS) lambda3.ml test2.ml andrea
-# ocamlc -o test2.out $(LIB) $(UTILS) lambda3.ml andrea4.ml test2.ml
+andrea.out: $(UTILS) andrea8.ml
+ $(OCAMLC) -o andrea.out $(LIB) $(UTILS) andrea8.ml
%.cmi: %.mli
$(OCAMLC) -c $<
$(OCAMLC) -c $<
clean:
- rm -f *.cm* *.out .depend log
+ rm -f *.cm* *.out *.o .depend log
.depend: *.ml *.mli
ocamldep *.ml *.mli > .depend
--- /dev/null
+let (++) f g x = f (g x);;\r
+\r
+let print_hline = Console.print_hline;;\r
+\r
+type var = int;;\r
+type t =\r
+ | V of var\r
+ | A of t * t\r
+ | L of t\r
+ | B (* bottom *)\r
+ | P (* pacman *)\r
+ (* | Stuck of var * int *)\r
+ (* | Ptr of int *)\r
+;;\r
+\r
+let rec consts = (* const_apps, const_lambda *)\r
+ let rec aux1 = function\r
+ | A(t, _) -> 1 + aux1 t\r
+ | _ -> 0 in\r
+ let rec aux2 = function\r
+ | L t -> 1 + aux2 t\r
+ | _ -> 0 in\r
+ function\r
+ | A(t1, t2) as t ->\r
+ let a1, b1 = consts t1 in\r
+ let a2, b2 = consts t2 in\r
+ max (aux1 t) (max a1 a2), max b1 b2\r
+ | L t' as t ->\r
+ let a, b = consts t' in\r
+ a, max (aux2 t) b\r
+ | _ -> 0, 0\r
+;;\r
+\r
+\r
+type problem = {\r
+ orig_freshno: int\r
+ ; freshno : int\r
+ ; div : t\r
+ ; conv : t list\r
+ ; matches : (var (* variable originating this match *) * ((bool (* coming from div *) * t (* term to discriminate *) * var (* continuation *))) list) list\r
+ ; sigma : (var * t) list (* substitutions *)\r
+ ; stepped : var list\r
+ ; arities : (var * int) list\r
+ ; k_app : int\r
+ ; k_lam : int\r
+}\r
+\r
+let dummy_p = {orig_freshno=0; freshno=0; div=B; conv=[]; matches=[]; sigma=[]; stepped=[]; arities=[]; k_app=0;k_lam=0};;\r
+\r
+let append_conv p t = let len = List.length p.conv in let p = {p with conv=t::p.conv} in p, len;;\r
+let get_conv p n = List.nth p.conv (List.length p.conv - 1 - n);;\r
+let index_of_conv t conv = List.length conv - 1 - (Util.index_of t conv);;\r
+\r
+let eq_conv = (=);;\r
+let eq_conv_indices p i j = eq_conv (get_conv p i) (get_conv p j);;\r
+let all_terms p = (p.div :: p.conv) @ Util.concat_map (fun (_, lst) -> List.map (fun (_,x,_) -> x) lst) p.matches;;\r
+\r
+exception Done of (var * t) list (* substitution *);;\r
+exception Fail of int * string;;\r
+\r
+let string_of_t p =\r
+ let bound_vars = ["x"; "y"; "z"; "w"; "q"; "x1"; "x2"; "x3"; "x4"; "x5"] in\r
+ let rec string_of_term_w_pars level = function\r
+ | V v -> if v >= level then "`" ^ string_of_int (v-level) else List.nth bound_vars (level - v-1)\r
+ | A _\r
+ | L _ as t -> "(" ^ string_of_term_no_pars_lam level t ^ ")"\r
+ | B -> "BOT"\r
+ | P -> "PAC"\r
+ (* | Stuck _ as t -> "(" ^ string_of_term_no_pars_app level t ^ ")" *)\r
+ (* | Ptr _ as t-> "(" ^ string_of_term_no_pars_app level t ^ ")" *)\r
+ (* "&" ^ string_of_int n *)\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
+ (* | Stuck(v,n) -> ":" ^ string_of_term_no_pars_app level (V v) ^ " " ^ (string_of_term_w_pars level (get_conv p n)) *)\r
+ (* | Ptr n -> string_of_term_no_pars_app level (get_conv p n) *)\r
+ (* | Ptr n -> "&" ^ string_of_int n *)\r
+ | _ as t -> string_of_term_w_pars level t\r
+ and string_of_term_no_pars_lam level = function\r
+ | L t -> "λ" ^ string_of_term_w_pars (level+1) (V 0) ^ ". " ^ (string_of_term_no_pars_lam (level+1) t)\r
+ | _ as t -> string_of_term_no_pars level t\r
+ and string_of_term_no_pars level = function\r
+ | L _ as t -> string_of_term_no_pars_lam level t\r
+ | _ as t -> string_of_term_no_pars_app level t\r
+ in string_of_term_no_pars 0\r
+;;\r
+\r
+let string_of_problem p =\r
+ let lines = [\r
+ "[arities] " ^ String.concat " " (List.map (fun (v,n) -> "`" ^ string_of_int v ^ "=" ^ string_of_int n) p.arities);\r
+ "[stepped] " ^ String.concat " " (List.map string_of_int p.stepped);\r
+ "[DV] " ^ (string_of_t p p.div);\r
+ "[CV] " ^ String.concat "\n " (List.map (string_of_t p) p.conv);\r
+ (* "" ; *)\r
+ ] @ Util.concat_map (fun (v, lst) -> ("[<>] of "^(string_of_t p (V v))) :: List.map (fun (b,t,c) -> (if b then " * " else " ") ^ string_of_t p t\r
+ ^ " -> " ^ string_of_t p (V c)\r
+ ) lst) p.matches @ [""] in\r
+ String.concat "\n" lines\r
+;;\r
+\r
+let problem_fail p reason =\r
+ print_endline "!!!!!!!!!!!!!!! FAIL !!!!!!!!!!!!!!!";\r
+ print_endline (string_of_problem p);\r
+ raise (Fail (-1, reason))\r
+;;\r
+\r
+let freshvar ({freshno} as p) =\r
+ {p with freshno=freshno+1}, freshno+1\r
+;;\r
+\r
+let add_to_match p id fromdiv t =\r
+ let p, v = freshvar p in\r
+ let arity = (List.assoc id p.arities) - 1 in\r
+ let entry = fromdiv, t, v in\r
+ let matches =\r
+ List.map (fun (id',lst as x) -> if id <> id' then x else (id, entry::lst)) p.matches\r
+ in\r
+ let arities = (v,arity) :: p.arities in\r
+ {p with matches; arities}, V v\r
+;;\r
+\r
+let var_occurs_in p v =\r
+ let rec aux level = function\r
+ | V v' -> v + level = v'\r
+ (* | Stuck(v',n) -> assert (v <> v'); aux level (get_conv p n) *)\r
+ | A(t1,t2) -> (aux level t1) || (aux level t2)\r
+ | L t -> aux (level+1) t\r
+ | B -> false\r
+ | P -> false\r
+ (* | Ptr n -> aux level (get_conv p n) *)\r
+\r
+ in aux 0\r
+;;\r
+\r
+let rec is_inert p =\r
+ function\r
+ | A(t,_) -> is_inert p t\r
+ (* | Ptr n -> is_inert p (get_conv p n) *)\r
+ | V _ -> true\r
+ | L _ | B | P -> false\r
+;;\r
+\r
+let is_var = function V _ -> true | _ -> false;;\r
+let is_lambda = function L _ -> true | _ -> false;;\r
+let is_pacman = function P -> true | _ -> false;;\r
+\r
+let rec subst level delift fromdiv sub p =\r
+ function\r
+ | V v -> p, if v = level + fst sub then lift level (snd sub) else V (if delift && v > level then v-1 else v)\r
+ | L t -> let p, t = subst (level + 1) delift fromdiv sub p t in p, L t\r
+ | A (t1,t2) ->\r
+ let p, t1 = subst level delift fromdiv sub p t1 in\r
+ let p, t2 = subst level delift fromdiv sub p t2 in\r
+ if t1 = B || t2 = B then p, B else\r
+ if level = 0 then mk_app fromdiv p t1 t2 else p, A (t1, t2)\r
+ | B -> p, B\r
+ | P -> p, P\r
+and mk_app fromdiv p t1 t2 = let t1 = if t1 = P then L P else t1 in match t1 with\r
+ | B | _ when t2 = B -> p, B\r
+ | L t1 -> subst 0 true fromdiv (0, t2) p t1\r
+ | V v when List.mem v p.stepped ->\r
+ let p, x = add_to_match p v fromdiv t2 in\r
+ p, x\r
+ | t1 -> p, A (t1, t2)\r
+and mk_apps fromdiv p t =\r
+ function\r
+ | [] -> p, t\r
+ | t'::ts -> let p, t = mk_app fromdiv p t t' in mk_apps fromdiv p t ts\r
+and lift n =\r
+ let rec aux n' =\r
+ function\r
+ | V m -> V (if m >= n' then m + n else m)\r
+ | L t -> L (aux (n'+1) t)\r
+ | A (t1, t2) -> A (aux n' t1, aux n' t2)\r
+ | B -> B\r
+ | P -> P\r
+ in aux 0\r
+;;\r
+\r
+let subst = subst 0 false;;\r
+\r
+let mk_lambda t = L (lift 1 t) ;;\r
+\r
+let subst_conv sub =\r
+ let rec aux p = function\r
+ | [] -> p, []\r
+ | t::tms ->\r
+ let p, tms = aux p tms in\r
+ let p, t = subst false sub p t in\r
+ p, t :: tms\r
+ in aux\r
+;;\r
+\r
+let subst_in_problem (sub: var * t) (p: problem) =\r
+print_endline ("SUBST IN PROBLEM: " ^ string_of_t p (V (fst sub)) ^ " |-> " ^ string_of_t p (snd sub));\r
+(* BUG QUI FIXME!!!! *)\r
+ let rec mix l1 l2 = match l1, l2 with\r
+ | [], l2 -> l2\r
+ | x::xs, _::ys -> x:: (mix xs ys)\r
+ | _ -> assert false in\r
+ let p = {p with stepped=(fst sub)::p.stepped} in\r
+ let p, conv = subst_conv sub p p.conv in\r
+ let p, div = subst true sub p p.div in\r
+ let conv = List.rev (mix (List.rev conv) (List.rev p.conv)) in\r
+ let p = {p with div; conv} in\r
+ (* print_endline ("after sub: \n" ^ string_of_problem p); *)\r
+ {p with sigma=sub::p.sigma}\r
+;;\r
+\r
+(* FIXME *)\r
+let unify_terms p v1 v2 =\r
+ if List.mem v1 p.stepped\r
+ then problem_fail p "The collapse of a match came after too many steps :(";\r
+ subst_in_problem (v1, V v2) p\r
+;;\r
+\r
+let rec unify p =\r
+ let rec give_duplicates =\r
+ let rec aux' t = function\r
+ | [] -> [], None\r
+ | (b',t',c')::ts -> if t = t' (* FIXME! eta-eq here *) then ts, Some (b',c') else (\r
+ let ts, res = aux' t ts in (b',t',c')::ts, res) in\r
+ let rec aux = function\r
+ | [] -> [], None\r
+ | (b,t,c)::rest -> (\r
+ match aux' t rest with\r
+ | rest, None -> aux rest\r
+ | rest, Some(b',c') -> (b || b', t, c) :: rest, Some(c', c)\r
+ ) in\r
+ function\r
+ | [] -> [], None\r
+ | (orig,branches) :: ms ->\r
+ match aux branches with\r
+ | _, None -> let ms, res = give_duplicates ms in (orig,branches) :: ms, res\r
+ | branches', Some subst -> (orig,branches') :: ms, Some subst in\r
+ let matches, vars_to_be_unified = give_duplicates p.matches in\r
+ let p = {p with matches=matches} in\r
+ match vars_to_be_unified with\r
+ | None -> p\r
+ | Some(t', t) ->\r
+ (* print_endline ("> unify " ^ string_of_t p (t') ^ " with " ^ string_of_t p t); *)\r
+ unify (unify_terms p t' t)\r
+;;\r
+\r
+let problem_done p =\r
+ let condition (b, t, cont) =\r
+ (b && t = B) ||\r
+ (not (List.mem cont p.stepped)) ||\r
+ is_var t in\r
+ let all_separated = List.for_all (fun (_, lst) -> List.for_all condition lst) p.matches in\r
+ all_separated && p.div = B\r
+;;\r
+\r
+let free_vars p t =\r
+ let rec aux level = function\r
+ | V v -> if v >= level then [v] else []\r
+ | A(t1,t2) -> (aux level t1) @ (aux level t2)\r
+ | L t -> aux (level+1) t\r
+ | B | P -> []\r
+ in Util.sort_uniq (aux 0 t)\r
+;;\r
+\r
+let visible_vars p t =\r
+ let rec aux = function\r
+ | V v -> [v]\r
+ | A(t1,t2) -> (aux t1) @ (aux t2)\r
+ | B | P\r
+ | L _ -> []\r
+ (* | Ptr n -> aux (get_conv p n) *)\r
+ in Util.sort_uniq (aux t)\r
+;;\r
+\r
+\r
+let rec simple_explode p =\r
+ match p.div with\r
+ | V var ->\r
+ let subst = var, B in\r
+ sanity (subst_in_problem subst p)\r
+ | _ -> p\r
+\r
+and sanity p =\r
+ (* Sanity checks: *)\r
+ if (function | P | L _ -> true | _ -> false) p.div then problem_fail p "p.div converged";\r
+ if List.mem B p.conv then problem_fail p "p.conv diverged";\r
+ let solvable (b,t,c) = (b && not (List.mem c p.stepped)) || is_inert p t in\r
+ if not (List.for_all (fun (_, lst) -> List.for_all solvable lst) p.matches)\r
+ then problem_fail p "Unsolvable discrimination";\r
+\r
+ let p = unify p in\r
+ print_endline (string_of_problem p); (* non cancellare *)\r
+ let p = if problem_done p then raise (Done p.sigma) else p in\r
+ let p = if is_var p.div then simple_explode p else p in\r
+ p\r
+;;\r
+\r
+let print_cmd s1 s2 = print_endline (">> " ^ s1 ^ " " ^ s2);;\r
+\r
+let rec hd_args t = match t with\r
+ | V v -> v, []\r
+ | A(t1,t2) -> let a, b = hd_args t1 in a, b @ [t2]\r
+ | _ -> -666, []\r
+;;\r
+\r
+let max_arity_of_var v =\r
+ let rec aux level =\r
+ function\r
+ | V _ -> 0\r
+ | A _ as t -> print_string (string_of_t dummy_p t); let hd, args = hd_args t in\r
+ let acc = if hd = level + v then List.length args else 0 in\r
+ List.fold_right (max ++ (aux level)) args acc\r
+ | L t -> aux (level + 1) t\r
+ | P | B -> 0\r
+ in aux 0\r
+;;\r
+\r
+let ignore var n p =\r
+ print_cmd "EAT" ("on " ^ string_of_t p (V var) ^ " (of:" ^ string_of_int n ^ ")");\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 p, fresh = freshvar p in\r
+ let subst = var, aux n (V fresh) in\r
+ sanity (subst_in_problem subst p)\r
+;;\r
+\r
+\r
+\r
+let eat var p =\r
+ print_cmd "EAT" ("var " ^ string_of_t p (V var));\r
+ let rec is_hd v' = function\r
+ | A (t,_) -> is_hd v' t\r
+ | V v -> v' = v\r
+ | _ -> false in\r
+ let rec app_length = function\r
+ | A (t,_) -> 1 + app_length t\r
+ | _ -> 0 in\r
+ let rec find_app_no = function\r
+ | V _ | L _ | P | B -> 0\r
+ | A (t1,t2) as t ->\r
+ max (max (find_app_no t1) (find_app_no t2))\r
+ (if is_hd var t1 then app_length t else 0)\r
+ in let n = List.fold_right (max ++ find_app_no) (all_terms p) 0 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 p, fresh = freshvar p in\r
+ let subst = var, aux n (V fresh) in\r
+ sanity (subst_in_problem subst p)\r
+;;\r
+\r
+(* let explode p =\r
+ let fv1 = visible_vars p p.div in\r
+ let fv2 = List.concat (List.map (visible_vars p) p.conv) in\r
+ let fv = List.filter (fun x -> not (List.mem x fv2)) fv1 in\r
+ let fv = List.filter ((<) p.orig_freshno) fv in\r
+ match fv with\r
+ | var::_ ->\r
+ print_cmd "EXPLODE" ("on " ^ string_of_t p (V var));\r
+ let subst = var, B in\r
+ sanity (subst_in_problem subst p)\r
+ | _ -> raise (Fail (-1,"premature explosion"))\r
+;; *)\r
+\r
+(* let step var p =
+ print_cmd "STEP" ("on " ^ string_of_t p (V var));
+ let matches = (var,[])::p.matches in
+ let p = {p with matches;stepped=var::p.stepped} in
+ let subst = var, V var in
+ sanity (subst_in_problem subst p)\r
+;; *)\r
+\r
+let choose n p =\r
+ print_cmd "CHOOSE" ("#" ^ string_of_int n);\r
+ let rec aux n t = match t with\r
+ | V _ -> 0, t\r
+ | A(t1,_) -> let n', t' = aux n t1 in if n = n' then n', t' else n'+1, t\r
+ | _ -> assert false\r
+ in let n', div = aux n p.div in\r
+ if n' <> n then problem_fail p "wrong choose";\r
+ let p = {p with div} in\r
+ sanity p\r
+;;\r
+\r
+let apply var appk p =\r
+ print_cmd "APPLY"\r
+ (string_of_t p (V var) ^ " applies no." ^ string_of_int appk ^ " fresh variables");\r
+ let rec mk_freshvars n p =\r
+ if n = 0\r
+ then p, []\r
+ else\r
+ let p, vs = mk_freshvars (n-1) p in\r
+ let p, v = freshvar p in\r
+ p, V(v)::vs in\r
+ let p, vars = mk_freshvars appk p in\r
+ let p, t = mk_apps false p (V 0) (List.map (lift 1) vars) in\r
+ let t = L (A (lift 1 (V var), t)) in\r
+ let subst = var, t in\r
+ sanity (subst_in_problem subst p)\r
+;;\r
+\r
+let find_arities_after_app p =\r
+ let rec aux level n = function\r
+ | L t -> assert (n > 0); max_arity_of_var level t :: aux (level+1) (n-1) t\r
+ | _ -> Array.to_list (Array.make n 0)\r
+ in aux 0\r
+;;\r
+let find_all_first_args_of v =\r
+ let rec aux level = function\r
+ | L t -> aux (level+1) t\r
+ | V _ -> []\r
+ | A(V v', t2) -> (if v + level = v' then [t2] else []) @ aux level t2\r
+ | A(t1,t2) -> aux level t1 @ aux level t2\r
+ | _ -> []\r
+ in aux 0\r
+;;\r
+\r
+let step' var p =\r
+ let appk = p.k_lam + p.k_app + 1 in\r
+ print_cmd "STEP'" ("on " ^ string_of_t p (V var) ^ " and applies no." ^ string_of_int appk ^ " fresh variables");\r
+ let p, vars = (* +1 below because of lifting *)\r
+ Array.fold_left (fun (p,vars) _ -> let p, v = freshvar p in p, (v+1)::vars)\r
+ (p, []) (Array.make appk ()) in\r
+ let p, t = mk_apps false p (V 0) (List.map (fun x -> V x) vars) in\r
+\r
+ let first_args = Util.sort_uniq (List.fold_right ((@) ++ (find_all_first_args_of var)) (all_terms p) []) in\r
+ let map = List.fold_left (fun acc t -> let acc' = find_arities_after_app p appk t in List.map (fun (x,y) -> max x y) (List.combine acc acc')) (Array.to_list (Array.make appk 0)) first_args in\r
+ let arities = List.combine (List.map ((+) (-1)) vars) map in\r
+\r
+ (* let p, var' = freshvar p in *)\r
+ let p, var' = p, var in\r
+ let matches = (var', []) :: p.matches in\r
+ let p = {p with matches; arities=arities@p.arities} in\r
+ let t = L (A (lift 1 (V var'), t)) in\r
+ let subst = var, t in\r
+ sanity (subst_in_problem subst p)\r
+;;\r
+\r
+let perm var n p =\r
+ if n = 1 then p else (\r
+ print_cmd "PERM" ("on " ^ string_of_t p (V var) ^ " (of:" ^ string_of_int n ^ ")");\r
+ (* let p, v = freshvar p in *)\r
+ let p, v = p, var in\r
+ let rec aux' m t = if m < 0 then t else A(aux' (m-1) t, V m) in\r
+ let rec aux m t =\r
+ if m = 0\r
+ then aux' (n-1) t\r
+ else L (aux (m-1) t) in\r
+ let t = aux n (lift n (V v)) in\r
+ let subst = var, t in\r
+ (* let p = {p with arities=(v, List.assoc var p.arities)::p.arities} in *)\r
+ sanity (subst_in_problem subst p)\r
+) ;;\r
+\r
+let free_vars_of_p p =\r
+ Util.sort_uniq (Util.concat_map (free_vars p) (all_terms p));;\r
+\r
+let rec applied_vars p = function\r
+| B | P -> []\r
+| L _ -> [] (* ??? *)\r
+| V _ -> []\r
+| A(V v,t2) -> v :: applied_vars p t2\r
+| A(t1,t2) -> applied_vars p t1 @ applied_vars p t2\r
+;;\r
+\r
+let applied_vars_of_p p =\r
+ Util.sort_uniq (Util.concat_map (applied_vars p) (all_terms p));;\r
+\r
+let rec auto p =\r
+ let aux f var =\r
+ try\r
+ auto (f var); ()\r
+ with\r
+ (* | Done _ as d -> raise d *)\r
+ | Fail(_, s) -> print_endline ("<<< Backtracking because: " ^ s) in\r
+ print_endline ">>> auto called";\r
+ (* Compute useful free variables *)\r
+ let fv = applied_vars_of_p p in\r
+ let fv = List.filter (fun v -> not (List.mem v p.stepped)) fv in\r
+ List.iter (fun v -> print_string ("@`" ^ string_of_int v)) fv;\r
+ let fv0 = List.filter (fun v -> List.assoc v p.arities > 0) fv in (* remove variable with arity left 0, cannot step there *)\r
+ if fv0 = [] then (print_endline "warning! empty step fv0"; List.iter (fun v -> print_string ("@`" ^ string_of_int v)) fv);\r
+ let permute_and_step p v =\r
+ let step'' problem prm var =\r
+ let problem = perm var prm problem in\r
+ (* let _ = read_line () in *)\r
+ let problem = step' var problem in\r
+ problem in\r
+ let arity = List.assoc v p.arities in\r
+ let _, perms = Array.fold_left (fun (arity, acc) () -> let a = arity + 1 in a, a::acc) (1,[1]) (Array.make (arity-1) ()) in\r
+ List.iter (fun perm -> aux (step'' p perm) v) perms\r
+ in\r
+ List.iter (permute_and_step p) fv0;\r
+ List.iter (aux (fun v -> eat v p)) fv;\r
+ (* mancano: applicazioni e choose; ??? *)\r
+;;\r
+\r
+let parse strs =\r
+ let rec aux level = function\r
+ | Parser.Lam t -> L (aux (level + 1) t)\r
+ | Parser.App (t1, t2) ->\r
+ if level = 0 then snd (mk_app false dummy_p (aux level t1) (aux level t2))\r
+ else A(aux level t1, aux level t2)\r
+ | Parser.Var v -> V v\r
+ in let (tms, free) = Parser.parse_many strs\r
+ in (List.map (aux 0) tms, free)\r
+;;\r
+\r
+let magic6 div conv cmds =\r
+ print_hline ();\r
+ let all_tms, var_names = parse (div :: conv) in\r
+ let div, conv = List.hd all_tms, List.tl all_tms in\r
+ let varno = List.length var_names in\r
+ let k_app, k_lam = List.fold_left (fun (a, b) t -> let a', b' = consts t in max a a', max b b') (0,0) all_tms in\r
+ let p = {orig_freshno=varno; freshno=1+varno; div; conv; matches=[]; sigma=[]; stepped=[];k_app;k_lam;arities=[]} in\r
+ let fv = Util.sort_uniq (Util.concat_map (free_vars p) all_tms) in\r
+ let arities = List.map (fun var -> var, k_app) fv in\r
+ let p = {p with arities} in\r
+ let p = try\r
+ let subst = Util.index_of "BOMB" var_names, L B in\r
+ let p = subst_in_problem subst p in p\r
+ with Not_found -> p in\r
+ let p = sanity p in\r
+ try\r
+ problem_fail (List.fold_left (|>) p cmds) "Problem not completed"\r
+ with\r
+ | Done _ -> ()\r
+;;\r
+\r
+let auto div conv =\r
+ print_hline ();\r
+ let all_tms, var_names = parse (div :: conv) in\r
+ let div, conv = List.hd all_tms, List.tl all_tms in\r
+ let varno = List.length var_names in\r
+ let k_app, k_lam = List.fold_left (fun (a, b) t -> let a', b' = consts t in max a a', max b b') (0,0) all_tms in\r
+ let p = {orig_freshno=varno; freshno=1+varno; div; conv; matches=[]; sigma=[]; stepped=[];k_app;k_lam;arities=[]} in\r
+ let fv = Util.sort_uniq (Util.concat_map (free_vars p) all_tms) in\r
+ let max_arity_of_var_in_p var p =\r
+ 1 + List.fold_right (max ++ (max_arity_of_var var)) (all_terms p) 0 in\r
+ let arities = List.map (fun var -> var, max_arity_of_var_in_p var p) fv in\r
+ let p = {p with arities} in\r
+ let p = try\r
+ let subst = Util.index_of "BOMB" var_names, L B in\r
+ let p = subst_in_problem subst p in p\r
+ with Not_found -> p in\r
+ let p = sanity p in\r
+ try\r
+ auto p;\r
+ failwith "auto failed."\r
+ with\r
+ | Done _ -> print_endline "<<< auto ok >>>"; (* TODO: print and verify substitution *)\r
+;;\r
+\r
+(* let interactive div conv cmds =\r
+ print_hline ();\r
+ let all_tms, var_names = parse (div @ conv) in\r
+ let div, conv = list_split (List.length div) all_tms in\r
+ let varno = List.length var_names in\r
+ let p = {orig_freshno=varno; freshno=1+varno; div; conv; matches=[]; sigma=[]} 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
+ (* activate pacmans *)\r
+ let p = try\r
+ let subst = Util.index_of "PACMAN" var_names, P in\r
+ let p = subst_in_problem subst p in\r
+ (print_endline ("after subst in problem " ^ string_of_problem p); p)\r
+ with Not_found -> p in\r
+ (* initial sanity check *)\r
+ let p = sanity p in\r
+ let p = List.fold_left (|>) p cmds in\r
+ let rec f p cmds =\r
+ let nth spl n = int_of_string (List.nth spl n) in\r
+ let read_cmd () =\r
+ let s = read_line () in\r
+ let spl = Str.split (Str.regexp " +") s in\r
+ s, let uno = List.hd spl in\r
+ try if uno = "explode" then explode\r
+ else if uno = "ignore" then ignore (nth spl 1) (nth spl 2)\r
+ else if uno = "step" then step (nth spl 1)\r
+ else if uno = "perm" then perm (nth spl 1) (nth spl 2)\r
+ else if uno = "apply" then apply (nth spl 1) (nth spl 2)\r
+ (* else if uno = "forget" then forget (nth spl 1) (nth spl 2) *)\r
+ else if uno = "id" then id (nth spl 1)\r
+ else failwith "Wrong input."\r
+ with Failure s -> print_endline s; (fun x -> x) in\r
+ let str, cmd = read_cmd () in\r
+ let cmds = (" " ^ str ^ ";")::cmds in\r
+ try\r
+ let p = cmd p in f p cmds\r
+ with\r
+ | Done -> print_endline "Done! Commands history: "; List.iter print_endline (List.rev cmds)\r
+ in f p []\r
+;; *)\r
+\r
+let _ = auto\r
+ "x x"\r
+ [ "_. BOMB" ]\r
+ (* [ eat 1 ] *)\r
+;;\r
+\r
+\r
+let _ = auto\r
+ "x y BOMB b"\r
+ [ "x BOMB y c" ]\r
+ (* [ perm 1 3; step' 8 ; eat 4; eat 5; eat 15; ] *)\r
+;;\r
+\r
+\r
+let _ = auto\r
+ "x BOMB a1 c"\r
+ [ "x y BOMB d"; "x BOMB a2 c" ]\r
+ (* [ perm 1 3 ; step' 10 ; eat 4; eat 6; step' 17; eat 3; eat 7; eat 27; ] *)\r
+;;\r
+\r
+\r
+let _ = auto\r
+ "x (x x)"\r
+ [ "x x" ; "x x x" ]\r
+ (* [\r
+ step' 1;\r
+ eat 6; eat 9; eat 13;\r
+]*)\r
+;;\r
+\r
+\r
+(* let _ = auto\r
+ "x (_.BOMB)"\r
+ [ "x (_._. BOMB)" ]\r
+ (* [ apply 1 2; ] *)\r
+;; *)\r
+\r
+\r
+let _ = auto\r
+ "x (_.y)"\r
+ [ "y (_. x)" ]\r
+ (* [ apply 1 1; ignore 1 1; explode; ] *)\r
+;;\r
+\r
+\r
+let _ = auto\r
+ "y (x a1 BOMB c) (x BOMB b1 d)"\r
+ [ "y (x a2 BOMB c) (x BOMB b1 d)";\r
+ "y (x a1 BOMB c) (x BOMB b2 d)";]\r
+ (* [perm 2 3;\r
+ step 12;\r
+ perm 17 2;\r
+ step 19;\r
+ step 18;\r
+ ignore 22 1;\r
+ ignore 21 1;\r
+ ignore 24 1;\r
+ ignore 25 1;\r
+ step 1;\r
+ step 32;\r
+ explode;\r
+ ] *)\r
+;;\r
+\r
+let _ = auto\r
+"PACMAN (x x x)" ["PACMAN (x x)"];;\r
+\r
+(*\r
+let _ = magic6\r
+ ["z (y x)"]\r
+ [ "z (y (x.x))"; "y (_. BOMB)" ]\r
+ [ apply 2 1; step 3; explode; ]\r
+;;\r
+\r
+let _ = magic6\r
+ ["y x"]\r
+ [ "y (x.x)"; "x (_. BOMB)" ]\r
+ [ apply 1 1; ignore 2 1; step 1; explode; ]\r
+;;\r
+\r
+let _ = magic6\r
+ ["z (y x)"]\r
+ [ "z (y (x.x))"; "y (_. BOMB)" ]\r
+ [ step 1; explode; apply 2 1; id 2; ignore 3 1; ]\r
+;;\r
+\r
+let _ = magic6\r
+ ["y (x a)"]\r
+ [ "y (x b)"; "x BOMB" ] [\r
+ id 2;\r
+ step 1;\r
+ explode;\r
+];;\r
+\r
+magic6\r
+ ["y (x a)"] [ "y (x b)"; "x BOMB"; "y a" ]\r
+ [\r
+ apply 1 1;\r
+ perm 2 2;\r
+ ignore 9 1;\r
+ step 10;\r
+ explode;\r
+ ];;\r
+(* "y (a c)"\r
+[ "y (b c)"; "y (x a)"; "y (x b)"; "x BOMB" ] *)\r
+\r
+magic6\r
+["x a (x (a.y BOMB))"]\r
+[ "x b"; "x (y c)"; "x (y d)" ]\r
+[apply 1 1;\r
+apply 2 1;\r
+explode;]\r
+(* [\r
+step 1;\r
+step 3;\r
+explode' 10;\r
+(* ma si puo' fare anche senza forget *) *)\r
+(* ] *)\r
+;;\r
+\r
+(* dipendente dalla codifica? no, ma si risolve solo con id *)\r
+magic6\r
+ ["y a"] ["y b"; "x (y (_.BOMB))"]\r
+[\r
+apply 1 1;\r
+apply 2 1;\r
+explode;\r
+];;\r
+ (* [id 1; explode];; *)\r
+\r
+magic6\r
+ ["PACMAN (x x x)"] ["PACMAN (x x)"]\r
+ [\r
+ ignore 2 2;\r
+ explode;\r
+ ];; *)\r
+\r
+print_hline();\r
+print_endline "ALL DONE. "\r
+++ /dev/null
-open Util
-open Util.Vars
-open Pure
-open Num
-
-type problem =
- { freshno: int
- ; ps: i_n_var list (* the n-th inert must become n *)
- ; sigma: (int * nf) list (* the computed substitution *)
- ; deltas: (int * nf) list ref list (* collection of all branches *)
- }
-
-let print_problem {freshno; ps; deltas} =
- let deltas = String.concat "\n" (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- deltas ^ (if deltas = "" then "" else "\n") ^
- String.concat "\n" (List.mapi (fun i t -> string_of_int i ^ ": " ^ print ~l (t :> nf)) ps)
-;;
-
-let make_fresh_var freshno =
- freshno+1, freshno+1
-
-let make_fresh_vars p m =
- let rec aux =
- function
- 0 -> p.freshno,[]
- | n when n > 0 ->
- let freshno,vars = aux (n-1) in
- let freshno,v = make_fresh_var freshno in
- freshno,`Var v::vars
- | _ -> assert false in
- let freshno,vars = aux m in
- {p with freshno}, vars
-
-let simple_expand_match ps =
- let rec aux level = function
- | #i_num_var as t -> aux_i_num_var level t
- | `Lam(b,t) -> `Lam(b, aux (level+1) t)
- and aux_i_num_var level = function
- | `Match(u,bs_lift,bs,args) as torig ->
- let u = aux_i_num_var level u in
- bs := List.map (fun (n, x) -> n, aux 0 x) !bs;
- (try
- (match u with
- | #i_n_var as u ->
- let i = index_of (lift (-level) u) (ps :> nf list) (* can raise Not_found *)
- in let t = mk_match (`N i) bs_lift bs args in
- if t <> torig then
- aux level (t :> nf)
- else raise Not_found
- | _ -> raise Not_found)
- with Not_found ->
- `Match(cast_to_i_num_var u,bs_lift,bs,List.map (aux level) args))
- | `I(k,args) -> `I(k,Listx.map (aux level) args)
- | `N _ | `Var _ as t -> t
-in aux_i_num_var 0;;
-
-let rec super_simplify_ps ps it =
- let it' = List.map (fun t -> cast_to_i_num_var (simple_expand_match ps t)) (it :> i_num_var list) in
- if it <> it' then super_simplify_ps ps it' else it'
-
-let super_simplify ({ps} as p) =
- let ps = super_simplify_ps p.ps (p.ps :> i_num_var list) in
- {p with ps=List.map cast_to_i_n_var ps}
-
-let subst_in_problem x inst ({freshno; ps; sigma} as p) =
- let len_ps = List.length ps in
-(*(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
- let rec aux ((freshno,acc_ps,acc_new_ps) as acc) =
- function
- [] -> acc
- | t::todo_ps ->
-(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
- let t = subst false x inst (t :> nf) in
-(*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
- let freshno,new_t,acc_new_ps =
- expand_match (freshno,acc_ps@`Var(max_int/3)::todo_ps,acc_new_ps) t
- in
- aux (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
-
- and expand_match ((freshno,acc_ps, acc_new_ps) as acc) t =
- match t with
- | `Match(u',bs_lift,bs,args) ->
- let freshno,u,acc_new_ps = expand_match acc (u' :> nf) in
- let acc_new_ps,i =
- match u with
- `N i -> acc_new_ps,i
- | _ ->
- let ps = List.map (fun t -> cast_to_i_num_var (subst false x inst (t:> nf))) (acc_ps@acc_new_ps) in
- let super_simplified_ps = super_simplify_ps ps ps in
-(*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
-List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
-List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplified_ps;*)
- match index_of_opt ~eq:eta_eq super_simplified_ps u with
- Some i -> acc_new_ps, i
- | None -> acc_new_ps@[u], len_ps + List.length acc_new_ps
- in
- let freshno=
- if List.exists (fun (j,_) -> i=j) !bs then
- freshno
- else
- let freshno,v = make_fresh_var freshno in
- bs := !bs @ [i, `Var v] ;
- freshno in
-(*prerr_endlie ("t DA RIDURRE:" ^ print (`Match(`N i,arity,bs_lift,bs,args) :> nf) ^ " more_args=" ^ string_of_int more_args);*)
- let t = mk_match (`N i) bs_lift bs args in
-(*prerr_endline ("NUOVO t:" ^ print (fst t :> nf) ^ " more_args=" ^ string_of_int (snd t));*)
- expand_match (freshno,acc_ps,acc_new_ps) t
- | `Lam _ ->
- (* the cast will fail *)
- (* freshno,(cast_to_i_n_var t),acc_new_ps *)
- assert false
- | #i_n_var as x ->
- let x = simple_expand_match (acc_ps@acc_new_ps) x in
- freshno,cast_to_i_num_var x,acc_new_ps in
- let freshno,old_ps,new_ps = aux (freshno,[],[]) (ps :> i_num_var list) in
- let ps = List.map cast_to_i_n_var (old_ps @ new_ps) in
-(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
- let p = {p with freshno; ps; sigma = sigma@[x,inst]} in
- let p = super_simplify p in
-prerr_endline (print_problem p); p
-
-exception Dangerous
-
-let rec dangerous arities showstoppers =
- function
- `N _
- | `Var _
- | `Lam _ -> ()
- | `Match(t,liftno,bs,args) ->
- (* CSC: XXX partial dependency on the encoding *)
- (match t with
- `N _ -> List.iter (dangerous arities showstoppers) args
- | `Match _ as t -> dangerous arities showstoppers t ; List.iter (dangerous arities showstoppers) args
- | `Var x -> dangerous_inert arities showstoppers x args 2 (* 2 coming from Scott's encoding *)
- | `I(x,args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
- )
- | `I(k,args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0
-
-and dangerous_inert arities showstoppers k args more_args =
- List.iter (dangerous arities showstoppers) args ;
- if List.mem k showstoppers then raise Dangerous else
- try
- let _,_,y = List.find (fun (v,_,_) -> v=k) arities in
- let arity = match y with `Var _ -> 0 | `I(_,args) -> Listx.length args | _ -> assert false in
- if List.length args + more_args > arity then raise Dangerous else ()
- with
- Not_found -> ()
-
-(* inefficient algorithm *)
-let edible arities showstoppers ps =
- let rec aux showstoppers =
- function
- [] -> showstoppers
- | x::xs when List.exists (fun y -> hd_of x = Some y) showstoppers ->
- (* se la testa di x e' uno show-stopper *)
- let new_showstoppers = sort_uniq (showstoppers @ free_vars (x :> nf)) in
- (* aggiungi tutte le variabili libere di x *)
- if List.length showstoppers <> List.length new_showstoppers then
- aux new_showstoppers ps
- else
- aux showstoppers xs
- | x::xs ->
- match hd_of x with
- None -> aux showstoppers xs
- | Some h ->
- try
- dangerous arities showstoppers (x : i_n_var :> nf) ;
- aux showstoppers xs
- with
- Dangerous ->
- aux (sort_uniq (h::showstoppers)) ps
- in
- aux showstoppers ps
-
-let precompute_edible_data {ps} xs =
- List.map (fun x ->
- let y = List.find (fun y -> hd_of y = Some x) ps in
- x, index_of ~eq:eta_eq y ps, y) xs
-;;
-
-let critical_showstoppers p =
- let p = super_simplify p in
- let showstoppers_step =
- List.concat (List.map (fun bs ->
- let heads = List.map (fun (i,_) -> List.nth p.ps i) !bs in
- let heads = List.sort compare (filter_map hd_of heads) in
- snd (split_duplicates heads)
- ) p.deltas) in
- let showstoppers_step = sort_uniq showstoppers_step in
- let showstoppers_eat =
- let heads_and_arities =
- List.sort (fun (k,_) (h,_) -> compare k h)
- (filter_map (function `Var k -> Some (k,0) | `I(k,args) -> Some (k,Listx.length args) | _ -> None ) p.ps) in
- let rec multiple_arities =
- function
- []
- | [_] -> []
- | (x,i)::(y,j)::tl when x = y && i <> j ->
- x::multiple_arities tl
- | _::tl -> multiple_arities tl in
- multiple_arities heads_and_arities in
-
- let showstoppers_eat = sort_uniq showstoppers_eat in
- let showstoppers_eat = List.filter
- (fun x -> not (List.mem x showstoppers_step))
- showstoppers_eat in
- List.iter (fun v -> prerr_endline ("DANGEROUS STEP: " ^ string_of_var v)) showstoppers_step;
- List.iter (fun v -> prerr_endline ("DANGEROUS EAT: " ^ string_of_var v)) showstoppers_eat;
- p, showstoppers_step, showstoppers_eat
- ;;
-
-let eat p =
- let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p in
- let showstoppers = showstoppers_step @ showstoppers_eat in
- let heads = List.sort compare (filter_map hd_of ps) in
- let arities = precompute_edible_data p (uniq heads) in
- let showstoppers = edible arities showstoppers ps in
- let l = List.filter (fun (x,_,_) -> not (List.mem x showstoppers)) arities in
- let p =
- List.fold_left (fun p (x,pos,(xx : i_n_var)) ->
- let n = match xx with `I(_,args) -> Listx.length args | _ -> 0 in
- let v = `N(pos) in
- let inst = make_lams v n in
-(let l = Array.to_list (Array.init (p.freshno + 1) string_of_var) in
- prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
- (* CSC: XXX to avoid applied numbers in safe positions that
- trigger assert failures subst_in_problem x inst p*)
- { p with sigma = p.sigma @ [x,inst] }
- ) p l in
- let ps =
- List.map (fun t ->
- try
- let _,j,_ = List.find (fun (h,_,_) -> hd_of t = Some h) l in
- `N j
- with Not_found -> t
- ) ps in
- List.iter
- (fun bs ->
- bs :=
- List.map
- (fun (n,t as res) ->
- match List.nth ps n with
- `N m -> m,t
- | _ -> res
- ) !bs
- ) p.deltas ;
- let p = { p with ps } in
- if l <> [] then prerr_endline (print_problem p);
- if List.for_all (function `N _ -> true | _ -> false) ps then
- `Finished p
- else
- `Continue p
-
-let instantiate p x n =
- let p,vars = make_fresh_vars p n in
- let freshno,zero = make_fresh_var p.freshno in
- let p = {p with freshno} in
- let zero = Listx.Nil (`Var zero) in
- let args = if n = 0 then zero else Listx.append zero (Listx.from_list vars) in
- let bs = ref [] in
- let inst = `Lam(false,`Match(`I(0,Listx.map (lift 1) args),1,bs,[])) in
- let p = {p with deltas=bs::p.deltas} in
- subst_in_problem x inst p
-;;
-
-let compute_special_k tms =
- let rec aux k (t: nf) = Pervasives.max k (match t with
- | `Lam(b,t) -> aux (k + if b then 1 else 0) t
- | `I(n, tms) -> Listx.max (Listx.map (aux 0) tms)
- | `Match(t, liftno, bs, args) ->
- List.fold_left max 0 (List.map (aux 0) ((t :> nf)::args@List.map snd !bs))
- | `N _ -> 0
- | `Var _ -> 0
- ) in Listx.max (Listx.map (aux 0) tms)
-;;
-
-let auto_instantiate (n,p) =
- let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p in
- let x =
- match showstoppers_step, showstoppers_eat with
- | [], y::_ ->
- prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
- | [], [] ->
- let heads = List.sort compare (filter_map (fun t -> match t with `Var _ -> None | x -> hd_of x) ps) in
- (match heads with
- [] -> assert false
- | x::_ ->
- prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
- x)
- | x::_, _ ->
- prerr_endline ("INSTANTIATING " ^ string_of_var x);
- x in
-(* Strategy that decreases the special_k to 0 first (round robin)
-1:11m42 2:14m5 3:11m16s 4:14m46s 5:12m7s 6:6m31s *)
-let x =
- try
- (match hd_of (List.find (fun t -> compute_special_k (Listx.Nil (t :> nf)) > 0) ps) with
- None -> assert false
- | Some x ->
- prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
- x)
- with
- Not_found -> x
-in
-(* Instantiate in decreasing order of compute_special_k
-1:15m14s 2:13m14s 3:4m55s 4:4m43s 5:4m34s 6:6m28s 7:3m31s
-let x =
- try
- (match hd_of (snd (List.hd (List.sort (fun c1 c2 -> - compare (fst c1) (fst c2)) (filter_map (function `I _ as t -> Some (compute_special_k (Listx.Nil (t :> nf)),t) | _ -> None) ps)))) with
- None -> assert false
- | Some x ->
- prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
- x)
- with
- Not_found -> x
-in*)
- let special_k =
- compute_special_k (Listx.from_list (p.ps :> nf list) )in
- if special_k < n then
- prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@");
- let p = instantiate p x special_k in
- special_k,p
-
-let problem_measure {ps} =
- (* let rec term_size_i_n_var =
- function
- | `I(v,nfs) ->
- (Listx.length nfs) *
- (List.fold_right (fun (a,b) c -> 10 + ((a+1) * term_size b) + c) (List.mapi (fun x y -> (x,y)) (Listx.to_list nfs)) 0)
- | `Var _ -> 1
- | `N _ -> 0
- and term_size =
- function
- | #i_n_var as t -> term_size_i_n_var t
- | `Match(t,lift,bs,args) -> 1 + (term_size (t :> nf)) + 1 + (List.fold_right ((+) ++ term_size) args 0)
- | `Lam(b,t) -> (if b then 0 else 1) + term_size t
- (* in List.fold_right ((+) ++ term_size_i_n_var) ps 0;; *)
- in ... *)
- 0
-
-let rec auto_eat (n,({ps} as p)) =
- match eat p with
- `Finished p -> p
- | `Continue p ->
- let p' = auto_instantiate (n,p) in
- let m' = problem_measure (snd p') in
- let delta = m' - problem_measure p in
- (if delta >= 0
- then print_endline ("$$$$ MEASURE DID NOT DECREASE (after inst) delta=" ^ string_of_int delta));
- let p'' = auto_eat p' in
- (if m' <= problem_measure p''
- then print_endline ("$$$$ MEASURE DID NOT DECREASE (after eat) $$$"));
- p''
-;;
-
-let auto p n =
- prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
- auto_eat (n,p)
-;;
-
-(*
-0 = snd
-
- x y = y 0 a y = k k z = z 0 c y = k y u = u h1 h2 0 h2 a = h3
-1 x a c 1 a 0 c 1 k c 1 c 0 1 k 1 k 1 k
-2 x a y 2 a 0 y 2 k y 2 y 0 2 y 0 2 h2 0 2 h3
-3 x b y 3 b 0 y 3 b 0 y 3 b 0 y 3 b 0 y 3 b 0 (\u. u h1 h2 0) 3 b 0 (\u. u h1 (\w.h3) 0)
-4 x b c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c
-5 x (b e) 5 b e 0 5 b e 0 5 b e 0 5 b e 0 5 b e 0 5 b e 0
-6 y y 6 y y 6 y y 6 y y 6 y y 6 h1 h1 h2 0 h2 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0
-
- l2 _ = l3
-b u = u l1 l2 0 e _ _ _ _ = f l3 n = n j 0
-1 k 1 k 1 k
-2 h3 2 h3 2 h3
-3 l2 0 (\u. u h1 (\w. h3) 0) 3 l3 (\u. u h1 (\w. h3) 0) 3 j h1 (\w. h3) 0 0
-4 l2 0 c 4 l3 c 4 c j 0
-5 e l1 l2 0 0 5 f 5 f
-6 h1 h1 (\w. h3) 0 (\w. h3) 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0
-*)
-
-(*
- x n = n 0 ?
-x a (b (a c)) a 0 = 1 ? (b (a c)) 8
-x a (b d') a 0 = 1 ? (b d') 7
-x b (a c) b 0 = 1 ? (a c) 4
-x b (a c') b 0 = 1 ? (a c') 5
-
-c = 2
-c' = 3
-a 2 = 4 (* a c *)
-a 3 = 5 (* a c' *)
-d' = 6
-b 6 = 7 (* b d' *)
-b 4 = 8 (* b (a c) *)
-b 0 = 1
-a 0 = 1
-*)
-
-(************** Tests ************************)
-
-let optimize_numerals p =
- let replace_in_sigma perm =
- let rec aux = function
- | `N n -> `N (List.nth perm n)
- | `I _ | `Var _ -> assert false
- | `Lam(v,t) -> `Lam(v, aux t)
- | `Match(_,_,bs,_) as t -> (bs := List.map (fun (n,t) -> (List.nth perm n, t)) !bs); t
- in List.map (fun (n,t) -> (n,aux t))
- in
- let deltas' = List.mapi (fun n d -> (n, List.map fst !d)) p.deltas in
- let maxs = Array.to_list (Array.init (List.length deltas') (fun _ -> 0)) in
- let max = Listx.max (Listx.from_list (
- List.concat (List.map snd deltas')
- )) in
- let perm,_ = List.fold_left (fun (perm, maxs) (curr_n:int) ->
- let containing = filter_map (fun (i, bs) -> if List.mem curr_n bs then Some i else None) deltas' in
- (* (prerr_endline (string_of_int curr_n ^ " occurs in: " ^ (String.concat " " (List.map string_of_int containing)))); *)
- let neww = Listx.max (Listx.from_list (List.mapi (fun n max -> if List.mem n containing then max else 0) maxs)) in
- let maxs = List.mapi (fun i m -> if List.mem i containing then neww+1 else m) maxs in
- (neww::perm, maxs)
- ) ([],maxs) (Array.to_list (Array.init (max+1) (fun x -> x))) in
- replace_in_sigma (List.rev perm) p.sigma
-;;
-
-prerr_endline "########## main ##########";;
-
-(* Commands:
- v ==> v := \a. a k1 .. kn \^m.0
- + ==> v := \^k. numero for every v such that ...
- * ==> tries v as long as possible and then +v as long as possible
-*)
-let main problems =
- let rec aux ({ps} as p) n l =
- if List.for_all (function `N _ -> true | _ -> false) ps then begin
- assert (l = []);
- p
- end else
- let _ = prerr_endline (print_problem p) in
- let x,l =
- match l with
- | cmd::l -> cmd,l
- | [] -> read_line (),[] in
- let cmd =
- if x = "+" then
- `DoneWith
- else if x = "*" then
- `Auto
- else
- `Step x in
- match cmd with
- | `DoneWith -> assert false (*aux (eat p) n l*) (* CSC: TODO *)
- | `Step x ->
- let x = var_of_string x in
- aux (instantiate p x n) n l
- | `Auto -> aux (auto p n) n l
- in
- List.iter
- (fun (p,n,cmds) ->
- let p_finale = aux p n cmds in
- let freshno,sigma = p_finale.freshno, p_finale.sigma in
- prerr_endline "------- <DONE> ------";
- prerr_endline (print_problem p);
- prerr_endline "---------------------";
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
-(*
- prerr_endline "----------------------";
- let ps =
- List.fold_left (fun ps (x,inst) ->
- (* CSC: XXXX Is the subst always sorted correctly? Otherwise, implement a recursive subst *)
- (* In this non-recursive version, the intermediate states may containt Matchs *)
- List.map (fun t -> let t = subst false x inst (t :> nf) in cast_to_i_num_var t) ps)
- (p.ps :> i_num_var list) sigma in
- prerr_endline (print_problem {p with ps= List.map (function t -> cast_to_i_n_var t) ps; freshno});
- List.iteri (fun i (n,more_args) -> assert (more_args = 0 && n = `N i)) ps ;
-*)
- prerr_endline "---------<OPT>----------";
- let sigma = optimize_numerals p_finale in (* optimize numerals *)
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
- prerr_endline "---------<PURE>---------";
- let ps = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.ps in
- let sigma = List.map (fun (x,inst) -> x, ToScott.t_of_nf inst) sigma in
- (*let ps_ok = List.fold_left (fun ps (x,inst) ->
- List.map (Pure.subst false x inst) ps) ps sigma in*)
- let e =
- let rec aux n =
- if n > freshno then
- []
- else
- let e = aux (n+1) in
- (try
- e,Pure.lift (-n-1) (let t = (snd (List.find (fun (i,_) -> i = n) sigma)) in prerr_endline (string_of_var n ^ " := " ^ Pure.print t); t),[]
- with
- Not_found -> [],Pure.V n,[])::e
- in
- aux 0 in
-(*
- prerr_endline "---------<PPP>---------";
-let rec print_e e =
- "[" ^ String.concat ";" (List.map (fun (e,t,[]) -> print_e e ^ ":" ^ Pure.print t) e) ^ "]"
-in
- prerr_endline (print_e e);
- List.iter (fun (t,t_ok) ->
- prerr_endline ("T0= " ^ Pure.print t ^ "\nTM= " ^ Pure.print (Pure.unwind (e,t,[])) ^ "\nOM= " ^ Pure.print t_ok);
- (*assert (Pure.unwind (e,t,[]) = t_ok)*)
- ) (List.combine ps ps_ok);
-*)
- prerr_endline "--------<REDUCE>---------";
- List.iteri (fun i n ->
- (*prerr_endline ((string_of_int i) ^ "::: " ^ (Pure.print n));*)
- let t = Pure.mwhd (e,n,[]) in
- prerr_endline ((string_of_int i) ^ ":: " ^ (Pure.print t));
- assert (t = Scott.mk_n i)
- ) ps ;
- prerr_endline "-------- </DONE> --------"
- ) problems
-
-(********************** problems *******************)
-
-let zero = `Var 0;;
-
-let append_zero =
- function
- | `I _
- | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
- | _ -> assert false
-;;
-
-type t = problem * int * string list;;
-
-let magic strings cmds =
- let tms, _ = parse' strings in (* *)
- let tms = sort_uniq ~compare:eta_compare tms in
- let special_k = compute_special_k (Listx.from_list tms) in (* compute special K *)
- let fv = sort_uniq (List.concat (List.map free_vars tms)) in (* free variables *)
- let tms = List.map cast_to_i_n_var tms in (* cast nf list -> i_n_var list *)
- let ps = List.map append_zero tms in (* crea lista applicando zeri o dummies *)
- (*let _ = prerr_endline ("Free vars: " ^ String.concat ", " (List.map string_of_var fv)) in*)
- let freshno = Listx.max (Listx.from_list fv) in
- let dummy = `Var (max_int / 2) in
- let deltas = [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
- {freshno; ps; sigma=[] ; deltas}, special_k, cmds
-;;
-
-let magic_conv ~div:_ ~conv:_ ~nums:_ _ = assert false;;
+++ /dev/null
-open Util
-open Util.Vars
-open Pure
-open Num
-
-type problem =
- { freshno: int
- ; ps: i_n_var list (* the n-th inert must become n *)
- ; sigma: (int * nf) list (* the computed substitution *)
- ; deltas: (int * nf) list ref list (* collection of all branches *)
- }
-
-let print_problem {freshno; ps; deltas} =
- let deltas = String.concat "\n" (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- deltas ^ (if deltas = "" then "" else "\n") ^
- String.concat "\n" (List.mapi (fun i t -> string_of_int i ^ ": " ^ print ~l (t :> nf)) ps)
-;;
-
-let make_fresh_var freshno =
- freshno+1, freshno+1
-
-let make_fresh_vars p m =
- let rec aux =
- function
- 0 -> p.freshno,[]
- | n when n > 0 ->
- let freshno,vars = aux (n-1) in
- let freshno,v = make_fresh_var freshno in
- freshno,`Var (0,v)::vars
- | _ -> assert false in
- let freshno,vars = aux m in
- {p with freshno}, vars
-
-let simple_expand_match ps =
- let rec aux level = function
- | #i_num_var as t -> aux_i_num_var level t
- | `Lam(b,t) -> `Lam(b, aux (level+1) t)
- and aux_i_num_var level = function
- | `Match(ar,u,bs_lift,bs,args) as torig ->
- let u = aux_i_num_var level u in
- bs := List.map (fun (n, x) -> n, aux 0 x) !bs;
- (try
- (match u with
- | #i_n_var as u ->
- let i = index_of (lift (-level) u) (ps :> nf list) (* can raise Not_found *)
- in let t = mk_match ar (`N i) bs_lift bs args in
- if t <> torig then
- aux level (t :> nf)
- else raise Not_found
- | _ -> raise Not_found)
- with Not_found ->
- `Match(ar,cast_to_i_num_var u,bs_lift,bs,List.map (aux level) args))
- | `I(ar,k,args) -> `I(ar,k,Listx.map (aux level) args)
- | `N _ | `Var _ as t -> t
-in aux_i_num_var 0;;
-
-let rec super_simplify_ps ps it =
- let it' = List.map (fun t -> cast_to_i_num_var (simple_expand_match ps t)) (it :> i_num_var list) in
- if it <> it' then super_simplify_ps ps it' else it'
-
-let super_simplify ({ps} as p) =
- let ps = super_simplify_ps p.ps (p.ps :> i_num_var list) in
- {p with ps=List.map cast_to_i_n_var ps}
-
-let subst_in_problem x inst ({freshno; ps; sigma} as p) =
- let len_ps = List.length ps in
-(*(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
- let rec aux ((freshno,acc_ps,acc_new_ps) as acc) =
- function
- [] -> acc
- | t::todo_ps ->
-(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
- let t = subst false x inst (t :> nf) in
-(*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
- let freshno,new_t,acc_new_ps =
- expand_match (freshno,acc_ps@`Var(-1,max_int/3)::todo_ps,acc_new_ps) t
- in
- aux (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
-
- and expand_match ((freshno,acc_ps, acc_new_ps) as acc) t =
- match t with
- | `Match(ar,u',bs_lift,bs,args) ->
- let freshno,u,acc_new_ps = expand_match acc (u' :> nf) in
- let acc_new_ps,i =
- match u with
- `N i -> acc_new_ps,i
- | _ ->
- let ps = List.map (fun t -> cast_to_i_num_var (subst false x inst (t:> nf))) (acc_ps@acc_new_ps) in
- let super_simplified_ps = super_simplify_ps ps ps in
-(*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
-List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
-List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplified_ps;*)
- match index_of_opt ~eq:eta_eq super_simplified_ps u with
- Some i -> acc_new_ps, i
- | None -> acc_new_ps@[u], len_ps + List.length acc_new_ps
- in
- let freshno=
- if List.exists (fun (j,_) -> i=j) !bs then
- freshno
- else
- let freshno,v = make_fresh_var freshno in
- bs := !bs @ [i, `Var (ar - 1,v)] ;
- freshno in
-(*prerr_endlie ("t DA RIDURRE:" ^ print (`Match(`N i,arity,bs_lift,bs,args) :> nf) ^ " more_args=" ^ string_of_int more_args);*)
- let t = mk_match ar (`N i) bs_lift bs args in
-(*prerr_endline ("NUOVO t:" ^ print (fst t :> nf) ^ " more_args=" ^ string_of_int (snd t));*)
- expand_match (freshno,acc_ps,acc_new_ps) t
- | `Lam _ ->
- (* the cast will fail *)
- (* freshno,(cast_to_i_n_var t),acc_new_ps *)
- assert false
- | #i_n_var as x ->
- let x = simple_expand_match (acc_ps@acc_new_ps) x in
- freshno,cast_to_i_num_var x,acc_new_ps in
- let freshno,old_ps,new_ps = aux (freshno,[],[]) (ps :> i_num_var list) in
- let ps = List.map cast_to_i_n_var (old_ps @ new_ps) in
-(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
- let p = {p with freshno; ps; sigma = sigma@[x,inst]} in
- let p = super_simplify p in
-prerr_endline (print_problem p); p
-
-exception Dangerous
-
-let rec dangerous arities showstoppers =
- function
- `N _
- | `Var _
- | `Lam _ -> ()
- | `Match(_,t,liftno,bs,args) ->
- (* CSC: XXX partial dependency on the encoding *)
- (match t with
- `N _ -> List.iter (dangerous arities showstoppers) args
- | `Match _ as t -> dangerous arities showstoppers t ; List.iter (dangerous arities showstoppers) args
- | `Var (_,x) -> dangerous_inert arities showstoppers x args 2 (* 2 coming from Scott's encoding *)
- | `I(_,x,args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
- )
- | `I(_,k,args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0
-
-and dangerous_inert arities showstoppers k args more_args =
- List.iter (dangerous arities showstoppers) args ;
- if List.mem k showstoppers then raise Dangerous else
- try
- let _,_,y = List.find (fun (v,_,_) -> v=k) arities in
- let arity = match y with `Var _ -> 0 | `I(_,_,args) -> Listx.length args | _ -> assert false in
- if List.length args + more_args > arity then raise Dangerous else ()
- with
- Not_found -> ()
-
-(* inefficient algorithm *)
-let edible arities showstoppers ps =
- let rec aux showstoppers =
- function
- [] -> showstoppers
- | x::xs when List.exists (fun y -> hd_of x = Some y) showstoppers ->
- (* se la testa di x e' uno show-stopper *)
- let new_showstoppers = sort_uniq (showstoppers @ free_vars (x :> nf)) in
- (* aggiungi tutte le variabili libere di x *)
- if List.length showstoppers <> List.length new_showstoppers then
- aux new_showstoppers ps
- else
- aux showstoppers xs
- | x::xs ->
- match hd_of x with
- None -> aux showstoppers xs
- | Some h ->
- try
- dangerous arities showstoppers (x : i_n_var :> nf) ;
- aux showstoppers xs
- with
- Dangerous ->
- aux (sort_uniq (h::showstoppers)) ps
- in
- aux showstoppers ps
-
-let precompute_edible_data {ps} xs =
- List.map (fun x ->
- let y = List.find (fun y -> hd_of y = Some x) ps in
- x, index_of ~eq:eta_eq y ps, y) xs
-;;
-
-let critical_showstoppers p =
- let p = super_simplify p in
- let showstoppers_step =
- List.concat (List.map (fun bs ->
- let heads = List.map (fun (i,_) -> List.nth p.ps i) !bs in
- let heads = List.sort compare (filter_map hd_of heads) in
- snd (split_duplicates heads)
- ) p.deltas) in
- let showstoppers_step = sort_uniq showstoppers_step in
- let showstoppers_eat =
- let heads_and_arities =
- List.sort (fun (k,_) (h,_) -> compare k h)
- (filter_map (function `Var (_,k) -> Some (k,0) | `I(_,k,args) -> Some (k,Listx.length args) | _ -> None ) p.ps) in
- let rec multiple_arities =
- function
- []
- | [_] -> []
- | (x,i)::(y,j)::tl when x = y && i <> j ->
- x::multiple_arities tl
- | _::tl -> multiple_arities tl in
- multiple_arities heads_and_arities in
-
- let showstoppers_eat = sort_uniq showstoppers_eat in
- let showstoppers_eat = List.filter
- (fun x -> not (List.mem x showstoppers_step))
- showstoppers_eat in
- List.iter (fun v -> prerr_endline ("DANGEROUS STEP: " ^ string_of_var v)) showstoppers_step;
- List.iter (fun v -> prerr_endline ("DANGEROUS EAT: " ^ string_of_var v)) showstoppers_eat;
- p, showstoppers_step, showstoppers_eat
- ;;
-
-let eat p =
- let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p in
- let showstoppers = showstoppers_step @ showstoppers_eat in
- let heads = List.sort compare (filter_map hd_of ps) in
- let arities = precompute_edible_data p (uniq heads) in
- let showstoppers = edible arities showstoppers ps in
- let l = List.filter (fun (x,_,_) -> not (List.mem x showstoppers)) arities in
- let p =
- List.fold_left (fun p (x,pos,(xx : i_n_var)) ->
- let n = match xx with `I(_,_,args) -> Listx.length args | _ -> 0 in
- let v = `N(pos) in
- let inst = make_lams v n in
-(let l = Array.to_list (Array.init (p.freshno + 1) string_of_var) in
- prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
- (* CSC: XXX to avoid applied numbers in safe positions that
- trigger assert failures subst_in_problem x inst p*)
- { p with sigma = p.sigma @ [x,inst] }
- ) p l in
- let ps =
- List.map (fun t ->
- try
- let _,j,_ = List.find (fun (h,_,_) -> hd_of t = Some h) l in
- `N j
- with Not_found -> t
- ) ps in
- List.iter
- (fun bs ->
- bs :=
- List.map
- (fun (n,t as res) ->
- match List.nth ps n with
- `N m -> m,t
- | _ -> res
- ) !bs
- ) p.deltas ;
- let p = { p with ps } in
- if l <> [] then prerr_endline (print_problem p);
- if List.for_all (function `N _ -> true | _ -> false) ps then
- `Finished p
- else
- `Continue p
-
-let instantiate p x n =
- let p,vars = make_fresh_vars p n in
- let freshno,zero = make_fresh_var p.freshno in
- let p = {p with freshno} in
- let zero = Listx.Nil (`Var (0,zero)) in
- let args = if n = 0 then zero else Listx.append zero (Listx.from_list vars) in
- let bs = ref [] in
- let inst = `Lam(false,`Match(-1,`I(-1,0,Listx.map (lift 1) args),1,bs,[])) in
- let p = {p with deltas=bs::p.deltas} in
- subst_in_problem x inst p
-;;
-
-let compute_special_k tms =
- let rec aux k (t: nf) = Pervasives.max k (match t with
- | `Lam(b,t) -> aux (k + if b then 1 else 0) t
- | `I(_, n, tms) -> Listx.max (Listx.map (aux 0) tms)
- | `Match(_, t, liftno, bs, args) ->
- List.fold_left max 0 (List.map (aux 0) ((t :> nf)::args@List.map snd !bs))
- | `N _ -> 0
- | `Var _ -> 0
- ) in Listx.max (Listx.map (aux 0) tms)
-;;
-
-let auto_instantiate (n,p) =
- let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p in
- let x =
- match showstoppers_step, showstoppers_eat with
- | [], y::_ ->
- prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
- | [], [] ->
- let heads = List.sort compare (filter_map (fun t -> match t with `Var _ -> None | x -> hd_of x) ps) in
- (match heads with
- [] -> assert false
- | x::_ ->
- prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
- x)
- | x::_, _ ->
- prerr_endline ("INSTANTIATING " ^ string_of_var x);
- x in
-(* Strategy that decreases the special_k to 0 first (round robin)
-1:11m42 2:14m5 3:11m16s 4:14m46s 5:12m7s 6:6m31s *)
-let x =
- try
- (match hd_of (List.find (fun t -> compute_special_k (Listx.Nil (t :> nf)) > 0) ps) with
- None -> assert false
- | Some x ->
- prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
- x)
- with
- Not_found -> x
-in
-(* Instantiate in decreasing order of compute_special_k
-1:15m14s 2:13m14s 3:4m55s 4:4m43s 5:4m34s 6:6m28s 7:3m31s
-let x =
- try
- (match hd_of (snd (List.hd (List.sort (fun c1 c2 -> - compare (fst c1) (fst c2)) (filter_map (function `I _ as t -> Some (compute_special_k (Listx.Nil (t :> nf)),t) | _ -> None) ps)))) with
- None -> assert false
- | Some x ->
- prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
- x)
- with
- Not_found -> x
-in*)
- let special_k =
- compute_special_k (Listx.from_list (p.ps :> nf list) )in
- if special_k < n then
- prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@");
- let p = instantiate p x special_k in
- special_k,p
-
-let problem_measure {ps} =
- (* let rec term_size_i_n_var =
- function
- | `I(v,nfs) ->
- (Listx.length nfs) *
- (List.fold_right (fun (a,b) c -> 10 + ((a+1) * term_size b) + c) (List.mapi (fun x y -> (x,y)) (Listx.to_list nfs)) 0)
- | `Var _ -> 1
- | `N _ -> 0
- and term_size =
- function
- | #i_n_var as t -> term_size_i_n_var t
- | `Match(t,lift,bs,args) -> 1 + (term_size (t :> nf)) + 1 + (List.fold_right ((+) ++ term_size) args 0)
- | `Lam(b,t) -> (if b then 0 else 1) + term_size t
- (* in List.fold_right ((+) ++ term_size_i_n_var) ps 0;; *)
- in ... *)
- 0
-
-let rec auto_eat (n,({ps} as p)) =
- match eat p with
- `Finished p -> p
- | `Continue p ->
- let p' = auto_instantiate (n,p) in
- let m' = problem_measure (snd p') in
- let delta = m' - problem_measure p in
- (if delta >= 0
- then print_endline ("$$$$ MEASURE DID NOT DECREASE (after inst) delta=" ^ string_of_int delta));
- let p'' = auto_eat p' in
- (if m' <= problem_measure p''
- then print_endline ("$$$$ MEASURE DID NOT DECREASE (after eat) $$$"));
- p''
-;;
-
-let auto p n =
- prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
- auto_eat (n,p)
-;;
-
-(*
-0 = snd
-
- x y = y 0 a y = k k z = z 0 c y = k y u = u h1 h2 0 h2 a = h3
-1 x a c 1 a 0 c 1 k c 1 c 0 1 k 1 k 1 k
-2 x a y 2 a 0 y 2 k y 2 y 0 2 y 0 2 h2 0 2 h3
-3 x b y 3 b 0 y 3 b 0 y 3 b 0 y 3 b 0 y 3 b 0 (\u. u h1 h2 0) 3 b 0 (\u. u h1 (\w.h3) 0)
-4 x b c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c
-5 x (b e) 5 b e 0 5 b e 0 5 b e 0 5 b e 0 5 b e 0 5 b e 0
-6 y y 6 y y 6 y y 6 y y 6 y y 6 h1 h1 h2 0 h2 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0
-
- l2 _ = l3
-b u = u l1 l2 0 e _ _ _ _ = f l3 n = n j 0
-1 k 1 k 1 k
-2 h3 2 h3 2 h3
-3 l2 0 (\u. u h1 (\w. h3) 0) 3 l3 (\u. u h1 (\w. h3) 0) 3 j h1 (\w. h3) 0 0
-4 l2 0 c 4 l3 c 4 c j 0
-5 e l1 l2 0 0 5 f 5 f
-6 h1 h1 (\w. h3) 0 (\w. h3) 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0
-*)
-
-(*
- x n = n 0 ?
-x a (b (a c)) a 0 = 1 ? (b (a c)) 8
-x a (b d') a 0 = 1 ? (b d') 7
-x b (a c) b 0 = 1 ? (a c) 4
-x b (a c') b 0 = 1 ? (a c') 5
-
-c = 2
-c' = 3
-a 2 = 4 (* a c *)
-a 3 = 5 (* a c' *)
-d' = 6
-b 6 = 7 (* b d' *)
-b 4 = 8 (* b (a c) *)
-b 0 = 1
-a 0 = 1
-*)
-
-(************** Tests ************************)
-
-let optimize_numerals p =
- let replace_in_sigma perm =
- let rec aux = function
- | `N n -> `N (List.nth perm n)
- | `I _ | `Var _ -> assert false
- | `Lam(v,t) -> `Lam(v, aux t)
- | `Match(_,_,_,bs,_) as t -> (bs := List.map (fun (n,t) -> (List.nth perm n, t)) !bs); t
- in List.map (fun (n,t) -> (n,aux t))
- in
- let deltas' = List.mapi (fun n d -> (n, List.map fst !d)) p.deltas in
- let maxs = Array.to_list (Array.init (List.length deltas') (fun _ -> 0)) in
- let max = Listx.max (Listx.from_list (
- List.concat (List.map snd deltas')
- )) in
- let perm,_ = List.fold_left (fun (perm, maxs) (curr_n:int) ->
- let containing = filter_map (fun (i, bs) -> if List.mem curr_n bs then Some i else None) deltas' in
- (* (prerr_endline (string_of_int curr_n ^ " occurs in: " ^ (String.concat " " (List.map string_of_int containing)))); *)
- let neww = Listx.max (Listx.from_list (List.mapi (fun n max -> if List.mem n containing then max else 0) maxs)) in
- let maxs = List.mapi (fun i m -> if List.mem i containing then neww+1 else m) maxs in
- (neww::perm, maxs)
- ) ([],maxs) (Array.to_list (Array.init (max+1) (fun x -> x))) in
- replace_in_sigma (List.rev perm) p.sigma
-;;
-
-prerr_endline "########## main ##########";;
-
-(* Commands:
- v ==> v := \a. a k1 .. kn \^m.0
- + ==> v := \^k. numero for every v such that ...
- * ==> tries v as long as possible and then +v as long as possible
-*)
-let main problems =
- let rec aux ({ps} as p) n l =
- if List.for_all (function `N _ -> true | _ -> false) ps then begin
- assert (l = []);
- p
- end else
- let _ = prerr_endline (print_problem p) in
- let x,l =
- match l with
- | cmd::l -> cmd,l
- | [] -> read_line (),[] in
- let cmd =
- if x = "+" then
- `DoneWith
- else if x = "*" then
- `Auto
- else
- `Step x in
- match cmd with
- | `DoneWith -> assert false (*aux (eat p) n l*) (* CSC: TODO *)
- | `Step x ->
- let x = var_of_string x in
- aux (instantiate p x n) n l
- | `Auto -> aux (auto p n) n l
- in
- List.iter
- (fun (p,n,cmds) ->
- let p_finale = aux p n cmds in
- let freshno,sigma = p_finale.freshno, p_finale.sigma in
- prerr_endline "------- <DONE> ------";
- prerr_endline (print_problem p);
- prerr_endline "---------------------";
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
-(*
- prerr_endline "----------------------";
- let ps =
- List.fold_left (fun ps (x,inst) ->
- (* CSC: XXXX Is the subst always sorted correctly? Otherwise, implement a recursive subst *)
- (* In this non-recursive version, the intermediate states may containt Matchs *)
- List.map (fun t -> let t = subst false x inst (t :> nf) in cast_to_i_num_var t) ps)
- (p.ps :> i_num_var list) sigma in
- prerr_endline (print_problem {p with ps= List.map (function t -> cast_to_i_n_var t) ps; freshno});
- List.iteri (fun i (n,more_args) -> assert (more_args = 0 && n = `N i)) ps ;
-*)
- prerr_endline "---------<OPT>----------";
- let sigma = optimize_numerals p_finale in (* optimize numerals *)
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
- prerr_endline "---------<PURE>---------";
- let ps = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.ps in
- let sigma = List.map (fun (x,inst) -> x, ToScott.t_of_nf inst) sigma in
- (*let ps_ok = List.fold_left (fun ps (x,inst) ->
- List.map (Pure.subst false x inst) ps) ps sigma in*)
- let e =
- let rec aux n =
- if n > freshno then
- []
- else
- let e = aux (n+1) in
- (try
- e,Pure.lift (-n-1) (let t = (snd (List.find (fun (i,_) -> i = n) sigma)) in prerr_endline (string_of_var n ^ " := " ^ Pure.print t); t),[]
- with
- Not_found -> [],Pure.V n,[])::e
- in
- aux 0 in
-(*
- prerr_endline "---------<PPP>---------";
-let rec print_e e =
- "[" ^ String.concat ";" (List.map (fun (e,t,[]) -> print_e e ^ ":" ^ Pure.print t) e) ^ "]"
-in
- prerr_endline (print_e e);
- List.iter (fun (t,t_ok) ->
- prerr_endline ("T0= " ^ Pure.print t ^ "\nTM= " ^ Pure.print (Pure.unwind (e,t,[])) ^ "\nOM= " ^ Pure.print t_ok);
- (*assert (Pure.unwind (e,t,[]) = t_ok)*)
- ) (List.combine ps ps_ok);
-*)
- prerr_endline "--------<REDUCE>---------";
- List.iteri (fun i n ->
- (*prerr_endline ((string_of_int i) ^ "::: " ^ (Pure.print n));*)
- let t = Pure.mwhd (e,n,[]) in
- prerr_endline ((string_of_int i) ^ ":: " ^ (Pure.print t));
- assert (t = Scott.mk_n i)
- ) ps ;
- prerr_endline "-------- </DONE> --------"
- ) problems
-
-(********************** problems *******************)
-
-let zero = `Var (0,0);;
-
-let append_zero =
- function
- | `I _
- | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
- | _ -> assert false
-;;
-
-type t = problem * int * string list;;
-
-let magic strings cmds =
- let tms, _ = parse' strings in (* *)
- let tms = sort_uniq ~compare:eta_compare tms in
- let special_k = compute_special_k (Listx.from_list tms) in (* compute special K *)
- let fv = sort_uniq (List.concat (List.map free_vars tms)) in (* free variables *)
- let tms = List.map cast_to_i_n_var tms in (* cast nf list -> i_n_var list *)
- let ps = List.map append_zero tms in (* crea lista applicando zeri o dummies *)
- (*let _ = prerr_endline ("Free vars: " ^ String.concat ", " (List.map string_of_var fv)) in*)
- let freshno = Listx.max (Listx.from_list fv) in
- let dummy = `Var (-1,max_int / 2) in
- let deltas = [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
- {freshno; ps; sigma=[] ; deltas}, special_k, cmds
-;;
-
-let magic_conv ~div:_ ~conv:_ ~nums:_ _ = assert false;;
+++ /dev/null
-include Discriminator.Discriminator\r
+++ /dev/null
-open Util
-open Util.Vars
-open Pure
-open Num
-
-let bomb = ref(`Var ~-1);;
-
-type var = int;;
-
-type problem =
- { freshno: int
- ; div: i_var option (* None = bomb *)
- ; conv: i_n_var list (* the inerts that must converge *)
- ; ps: i_n_var list (* the n-th inert must become n *)
- ; sigma: (var * nf) list (* the computed substitution *)
- ; deltas: (int * nf) list ref list (* collection of all branches *)
- (* ; steps: int (* the bound on the number of steps *) *)
- ; arities: int list
- ; special_k: int
- }
-
-let string_of_nf {freshno} t =
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- print ~l (t :> nf)
-;;
-
-(* let heads = Util.sort_uniq (List.map hd_of_i_var p.ps) in
-for all head
- List.map (fun (_, bs) -> List.map (fun (x,_) -> List.nth p.ps x) !bs) p.deltas *)
-
-(* let ($) f x = f x;; *)
-
-
-let subterms tms freshno =
- let apply_var =
- let no = ref freshno in
- function t -> incr no; mk_app t (`Var !no) in
- let applicative hd args = snd (
- List.fold_left (fun (hd, acc) t -> let hd = mk_app hd t in hd, hd::acc) (hd, []) args) in
- let rec aux t = match t with
- | `Var _ -> []
- | `I(v,ts) ->
- (* applicative (`Var v) (Listx.to_list ts) @ *)
- Util.concat_map aux (Listx.to_list ts) @ List.map apply_var (Listx.to_list ts)
- | `Lam(_,t) -> aux (lift ~-1 t)
- | `Match(u,bs_lift,bs,args) ->
- aux (u :> nf) @
- (* applicative (`Match(u,bs_lift,bs,[])) args @ *)
- Util.concat_map aux args @ List.map apply_var args
- (* @ Util.concat_map (aux ++ (lift bs_lift) ++ snd) !bs *)
- | `N _ -> []
- in let tms' = (* Util.sort_uniq ~compare:eta_compare*) (Util.concat_map aux tms) in
- tms @ tms'
- (* List.map (fun (t, v) -> match t with `N _ -> t | _ -> mk_app t v) (List.combine tms (List.mapi (fun i _ -> `Var(freshno+i)) tms)) *)
-;;
-
-let all_terms p =
-(match p.div with None -> [] | Some t -> [(t :> i_n_var)])
-@ p.conv
-@ p.ps
-;;
-
-let problem_measure p =
- (* let l = Array.to_list (Array.init (p.freshno + 1) string_of_var) in *)
- let open Listx in
- (* aux |t1;t2| e' numero di step per portare la diff in testa
- INVARIANTE: t1 <eta> t2
- *)
- let rec aux t1 t2 =
- match t1, t2 with
- | `I(v1,nfs1), `I(v2,nfs2) ->
- if v1 <> v2
- then 0 else 1 + find_first_diff (to_list nfs1, to_list nfs2)
- | `Match (t1,bs_lift,bs,args), `Match (t2,bs_lift',bs',args') ->
- if bs != bs' then 0 (* TODO *)
- else if eta_eq (t1 :> nf) (t2 :> nf) then 1 + find_first_diff (args, args') else aux (t1 :> nf) (t2 :> nf) (* TODO *)
- | `Match _, _
- | _, `Match _ -> 0 (* FIXME!!! *)
- | `Lam(_,t1), `Lam(_,t2) -> aux t1 t2
- | _ -> 0
- and find_first_diff = function
- | [], [] -> assert false
- | [], t::_
- | t::_, [] -> 1
- | t1::ts1, t2::ts2 ->
- if eta_eq (t1 :> nf) (t2 :> nf) then 1 + find_first_diff (ts1, ts2) else aux t1 t2
- (* no. di step da fare per separare t1 e t2 *)
- in let diff t1 t2 = (
- let res = if eta_eq t1 t2 then 0 else aux t1 t2 in
- (* if res <> 0 then prerr_endline ("diff (" ^ print ~l t1 ^ ") (" ^ print ~l t2 ^ ") = " ^ string_of_int res); *)
- res
- )
- (* aux calcola la somma delle differenze tra i termini in una lista (quadratico) *)
- in let rec sum = function
- | [] -> 0
- | x::xs -> List.fold_right ((+) ++ (diff (x :> nf))) (xs :> nf list) (sum xs)
- in let subterms = subterms ((all_terms p) :> nf list) p.freshno
- (* let subterms = sort_uniq ~compare:eta_compare subterms in *)
- in let a = sum subterms
- in let b = List.fold_right (fun bs -> (+) (sum (List.map ((List.nth p.ps) ++ fst) !bs))) p.deltas 0
- in let _ = prerr_endline ("Computed measure: " ^ string_of_int a ^ "," ^ string_of_int b)
- in a + b
-;;
-
-(* AC MEASURE *)
-module ACMeasure = struct
-type var = int;;
-
-type state = {
- freshno : int;
- arities : int list;
- p : problem;
-}
-
-let string_of_state s =
- "STATE\n - arities: " ^
- String.concat " " (List.mapi (fun v n -> "`"^string_of_var v ^ "=" ^ string_of_int n) s.p.arities)
-;;
-
-let rec get_var_of_match bs p =
- let rec aux = function
- | (v,`Lam(_,`Match(_,_,bs',_)))::sigma -> if bs = bs' then v else aux sigma
- | _::sigma -> aux sigma
- | [] -> assert false
- in aux p.sigma
-;;
-
-let mk_freshvar s =
- let freshno = s.freshno + 1 in
- {s with freshno}, freshno
-;;
-
-let rec mk_apps vmap (h : nf) (args : var list) =
- let aux l = Listx.from_list (List.map (fun x -> `Var x) l) in
- match h,args with
- | _, [] -> vmap, h
- | `I(n,args'), _ -> vmap, `I(n, Listx.append (aux args) args')
- | `Var n, _ -> vmap, `I(n, aux args)
- | `Lam(_,nf), a::args -> mk_apps (a::vmap) (lift ~-1 nf) args
- | `Match(t,lift,bs,args'), _ -> vmap, `Match(t,lift,bs,List.append args' (Listx.to_list (aux args)))
- | _ -> assert false
-;;
-
-let mk_freshvars s n = Array.fold_right (fun () (s,acc) -> let s, v = mk_freshvar s in s, v::acc ) (Array.make n ()) (s, [])
-;;
-
-let get_arity_of_var p v t =
- (* prerr_endline (string_of_nf p t); *)
- let rec aux level = function
- | `Var _ | `N _-> 0
- | `I(v', tms) as t ->
- max
- (if v + level = v' then (
- (* prerr_endline("found applied " ^ string_of_var v ^" in "^print (lift (-level) t)); *)
- Listx.length tms) else 0)
- (aux_listx level tms)
- | `Lam(_,t) -> aux (level + 1) t
- | `Match(t, liftno, bs, args) -> max (aux level (t :> nf)) (aux_list level args)
- and aux_listx level listx = Listx.fold_left (fun x t -> max x (aux level t)) 0 listx
- and aux_list level lst = List.fold_left (fun x t -> max x (aux level t)) 0 lst
- in aux 0 t
-;;
-
-(* let mk_apps t args = List.fold_left mk_app t args;; *)
-
-let first_arg = function
- | Listx.Nil x
- | Listx.Cons(x,_) -> x
-;;
-
-let find_first_args var =
- let rec aux level : nf -> nf list = function
- | `Var _ | `N _ -> []
- | `I(v, args) -> (if var + level = v then [first_arg args] else []) @ (Util.concat_map (aux level) (Listx.to_list args))
- | `Lam(_,t) -> aux (level+1) t
- | `Match(t, liftno, bs, args) -> aux level (t :> nf) @ (Util.concat_map (aux level) (args))
- in aux 0
-;;
-
-let remove_lambdas k t =
- let rec aux = function
- | `Lam(_,t) -> aux t
- | _ as t -> t
- in lift (-k) (aux t)
-;;
-
-let get_arity_of_continuation p v =
- if !bomb = `Var v then 0 else (
- let bs = List.find (fun bs -> List.exists (fun (_,t) -> t = `Var v) !bs) p.deltas in
- let orig = get_var_of_match bs p in
- List.nth p.arities orig
- )
-;;
-
-let fix_arities p v freshvars =
- let all_terms = (all_terms p :> nf list) in
- let args = Util.concat_map (find_first_args v) all_terms in
- let k = List.length freshvars in
- let args = List.map (remove_lambdas k) args in
- prerr_endline ("delifted lambdas in which to look for "^ string_of_var v);
- (* List.iter (fun t -> prerr_endline(strilogng_of_nf p t)) args; *)
- (* assert (List.length args > 0); *)
- List.iter (fun v -> prerr_endline ("var to fix: fresh " ^ string_of_var v)) freshvars;
- let find_arities_args v = let i = List.fold_left (fun x t -> max x (get_arity_of_var p v t)) 0 args in prerr_endline ("found arity in args of " ^ string_of_var (List.nth (List.rev freshvars) (v+1)) ^ ": " ^ string_of_int i); i in
- (* let find_arities_all v = List.fold_left (fun x t -> max x (get_arity_of_var p v t)) 0 all_terms in *)
- let arities = List.mapi (fun var () ->
- if var < List.length p.arities
- then List.nth p.arities var
- else if List.mem var freshvars
- then 1 + find_arities_args (Util.index_of var (List.rev freshvars) - 1)
- (* else find_arities_all var *)
- else (get_arity_of_continuation p var) - 1
- ) (Array.to_list (Array.make (p.freshno+1) ())) in
- assert (List.length arities = (p.freshno + 1));
- (* prerr_endline ("arities added : " ^ string_of_int (List.length freshvars)); *)
- (* List.iter (fun (v,n) -> prerr_endline(string_of_int v ^ "=" ^ string_of_int n)) arities; *)
- {p with arities}
-;;
-
-let measure =
- let rec aux (s:state) vmap =
- let p = s.p in
- let realvar vmap v =
- (* prerr_endline ("waant " ^ string_of_int v ^ "; we have "^ string_of_int (List.length vmap)); *)
- if v < 0 then List.nth vmap (-1-v) else v in
- function
- | `Var _ | `N _-> 0
- | `I(v, tms) -> assert (List.length s.arities = (s.freshno + 1)); 1 +
- let v = realvar vmap v in
- (* prerr_endline ("lookup for arity of " ^ string_of_int v ^ "with freshno =" ^ string_of_int s.freshno ^ " and length = " ^ string_of_int (List.length s.arities)); *)
- let arity = List.nth s.arities v in
- 1 + if arity = 0 then 0 else (
- let first, rest = (match tms with
- | Listx.Nil x -> x, []
- | Listx.Cons(a,b) -> a, Listx.to_list b) in
- (
- let s, vars = mk_freshvars s (1+s.p.special_k) in
- let vmap, t = mk_apps vmap first (vars) in
- let arities = List.mapi (fun v () ->
- if v < List.length s.arities
- then List.nth s.arities v
- else get_arity_of_var p (realvar vmap v) t
- ) (Array.to_list (Array.make (s.freshno + 1) ())) in
- (* let arities = (List.map (fun v -> v, get_arity_of_var p (realvar vmap' v) t) vars) in *)
- (* let arities = arities @ s.arities in *)
- let s = {s with arities} in
- aux s vmap t
- ) + (
- let s, fresh = mk_freshvar s in
- let arities = s.arities @ [arity - 1] in
- let s = {s with arities} in
- if rest = [] then aux s vmap (`Var fresh) else
- aux s vmap (`I (fresh, Listx.from_list rest))
- )
- )
- | `Match(t, _, bs, rest) ->
- let tmp = aux s vmap (t :> nf) in
- let s, fresh = mk_freshvar s in
- let arity = List.nth s.arities (get_var_of_match bs s.p) in
- let arities = s.arities @ [arity - 1] in
- let s = {s with arities} in
- tmp + if rest = [] then aux s vmap (`Var(fresh)) else
- aux s vmap (`I(fresh, Listx.from_list rest))
- | `Lam _ -> assert false
- in fun s -> aux s []
-;;
-
-
-(* let measure p =
- let rec m = function
- | `N _ | `Var _ -> 0
- | `I(_,args) ->
- let args = Listx.to_list args in
- List.fold_left (fun acc t -> acc + m t) (1 + Listx.length args) args
- | `Lam(_,t) -> m t
- | `Match(t, lft, bs, rest) ->
- (* let var = get_var_of_match bs p in *)
- let args = rest in m (t :> nf) + List.fold_left (fun acc t -> acc + m t) (aux args) args
-
-and aux = function
- | [] -> 0
- | x::xs -> m x + if aux xs = 0 then 0 else 1 + aux xs
-in m
-;;*)
-
-let measure_many s tms = List.fold_left (fun x t -> x + (measure s t)) 0 tms;;
-
-let map_max f l = List.fold_left (fun x t -> max x (f t)) 0 l;;
-
-let measure_of_problem p =
- let tms = (all_terms p :> nf list) in
- let freshno = p.freshno in
- let arities = p.arities in
- let s = {arities; freshno; p} in
- prerr_endline (string_of_state s);
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- List.iter (fun t -> prerr_endline (string_of_int (measure s t) ^ " ::" ^ print ~l t)) tms;
- let m = measure_many s tms in
- (* prerr_endline (string_of_int m); *)
- m
-;;
-end;;
-
-let measure_of_problem = ACMeasure.measure_of_problem;;
-let problem_measure = measure_of_problem;;
-(* AC MEASURE *)
-
-let print_problem label ({freshno; div; conv; ps; deltas} as p) =
- (* assert (p.steps > List.length p.sigma); *)
- let measure = try
- problem_measure p
- with
- | _ -> -1 in
- Console.print_hline ();
- prerr_endline ("\n||||| Displaying problem: " ^ label ^ " |||||");
- let nl = "\n| " in
- let deltas = String.concat nl (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- nl ^
- (* (string_of_int (steps - List.length p.sigma)) ^ " steps left;" ^ *)
- "measure="^string_of_int measure ^" freshno = " ^ string_of_int freshno
- ^ nl ^ "\b> DISCRIMINATING SETS (deltas)"
- ^ nl ^ deltas ^ (if deltas = "" then "" else nl)
- ^ "\b> DIVERGENT" ^ nl
- ^ "*: " ^ (match div with None -> "*" | Some div -> print ~l (div :> nf)) ^ "\n| "
- ^ "\b> CONVERGENT" ^ nl
- ^ String.concat "\n| " (List.map (fun t -> "_: " ^ (if t = `N (-1) then "_" else print ~l (t :> nf))) conv) ^
- (if conv = [] then "" else "\n| ")
- ^ "\b> NUMERIC" ^ nl
- ^ String.concat "\n| " (List.mapi (fun i t -> string_of_int i ^ ": " ^ print ~l (t :> nf)) ps)
- ^ nl
-;;
-
-
-let failwithProblem p reason =
- print_endline (print_problem "FAIL" p);
- failwith reason
-;;
-
-let make_fresh_var p =
- let freshno = p.freshno + 1 in
- {p with freshno}, `Var freshno
-;;
-
-let make_fresh_vars p m =
- Array.fold_left
- (* fold_left vs. fold_right hides/shows the bug in problem q7 *)
- (fun (p, vars) _ -> let p, var = make_fresh_var p in p, var::vars)
- (p, [])
- (Array.make m ())
-;;
-
-let simple_expand_match ps =
- let rec aux level = function
- | #i_num_var as t -> aux_i_num_var level t
- | `Lam(b,t) -> `Lam(b, aux (level+1) t)
- and aux_i_num_var level = function
- | `Match(u,bs_lift,bs,args) as torig ->
- let u = aux_i_num_var level u in
- bs := List.map (fun (n, x) -> n, aux 0 x) !bs;
- (try
- (match u with
- | #i_n_var as u ->
- let i = index_of (lift (-level) u) (ps :> nf list) (* can raise Not_found *)
- in let t = mk_match (`N i) bs_lift bs args in
- if t <> torig then
- aux level (t :> nf)
- else raise Not_found
- | _ -> raise Not_found)
- with Not_found ->
- `Match(cast_to_i_num_var u,bs_lift,bs,List.map (aux level) args))
- | `I(k,args) -> `I(k,Listx.map (aux level) args)
- | `N _ | `Var _ as t -> t
-in aux_i_num_var 0;;
-
-let fixpoint f =
- let rec aux x = let x' = f x in if x <> x' then aux x' else x in aux
-;;
-
-let rec super_simplify_ps ps =
- fixpoint (List.map (cast_to_i_num_var ++ (simple_expand_match ps)))
-;;
-
-let super_simplify ({div; ps; conv} as p) =
- let ps = super_simplify_ps p.ps (p.ps :> i_num_var list) in
- let conv = super_simplify_ps ps (p.conv :> i_num_var list) in
- let div = option_map (fun div ->
- let divs = super_simplify_ps p.ps ([div] :> i_num_var list) in
- List.hd divs) div in
- {p with div=option_map cast_to_i_var div; ps=List.map cast_to_i_n_var ps; conv=List.map cast_to_i_n_var conv}
-
-exception ExpandedToLambda;;
-
-let subst_in_problem x inst ({freshno; div; conv; ps; sigma} as p) =
- let len_ps = List.length ps in
-(*(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
- let rec aux ((freshno,acc_ps,acc_new_ps) as acc) =
- function
- | [] -> acc
- | t::todo_ps ->
-(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
- let t = subst false x inst (t :> nf) in
-(*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
- let freshno,new_t,acc_new_ps =
- expand_match (freshno,acc_ps@`Var(max_int/3)::todo_ps,acc_new_ps) t
- in
- aux (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
-
- (* cut&paste from aux above *)
- and aux' ps ((freshno,acc_conv,acc_new_ps) as acc) =
- function
- | [] -> acc
- | t::todo_conv ->
-(*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
- (* try *)
- let t = subst false x inst (t :> nf) in
-(*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
- let freshno,new_t,acc_new_ps =
- expand_match (freshno,ps,acc_new_ps) t
- in
- aux' ps (freshno,acc_conv@[new_t],acc_new_ps) todo_conv
- (* with ExpandedToLambda -> aux' ps (freshno,acc_conv@[`N(-1)],acc_new_ps) todo_conv *)
-
- (* cut&paste from aux' above *)
- and aux'' ps (freshno,acc_new_ps) =
- function
- | None -> freshno, None, acc_new_ps
- | Some t ->
- let t = subst false x inst (t :> nf) in
- let freshno,new_t,acc_new_ps =
- expand_match (freshno,ps,acc_new_ps) t
- in
- freshno,Some new_t,acc_new_ps
-
- and expand_match ((freshno,acc_ps,acc_new_ps) as acc) t =
- match t with
- | `Match(u',bs_lift,bs,args) ->
- let freshno,u,acc_new_ps = expand_match acc (u' :> nf) in
- let acc_new_ps,i =
- match u with
- | `N i -> acc_new_ps,i
- | _ ->
- let ps = List.map (fun t -> cast_to_i_num_var (subst false x inst (t:> nf))) (acc_ps@acc_new_ps) in
- let super_simplified_ps = super_simplify_ps ps ps in
-(*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
-List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
-List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplified_ps;*)
- match index_of_opt ~eq:eta_eq super_simplified_ps u with
- Some i -> acc_new_ps, i
- | None -> acc_new_ps@[u], len_ps + List.length acc_new_ps
- in
- let freshno=
- if List.exists (fun (j,_) -> i=j) !bs then
- freshno
- else
- let freshno,v = freshno+1, `Var (freshno+1) in (* make_fresh_var freshno in *)
- bs := !bs @ [i, v] ;
- freshno in
-(*prerr_endlie ("t DA RIDURRE:" ^ print (`Match(`N i,arity,bs_lift,bs,args) :> nf) ^ " more_args=" ^ string_of_int more_args);*)
- let t = mk_match (`N i) bs_lift bs args in
-(*prerr_endline ("NUOVO t:" ^ print (fst t :> nf) ^ " more_args=" ^ string_of_int (snd t));*)
- expand_match (freshno,acc_ps,acc_new_ps) t
- | `Lam _ -> raise ExpandedToLambda
- | #i_n_var as x ->
- let x = simple_expand_match (acc_ps@acc_new_ps) x in
- freshno,cast_to_i_num_var x,acc_new_ps in
-
- let freshno,old_ps,new_ps = aux (freshno,[],[]) (ps :> i_num_var list) in
- let freshno,conv,new_ps = aux' old_ps (freshno,[],new_ps) (conv :> i_num_var list) in
- let freshno,div,new_ps = aux'' old_ps (freshno,new_ps) (div :> i_num_var option) in
- let div = option_map cast_to_i_var div in
- let ps = List.map cast_to_i_n_var (old_ps @ new_ps) in
- let conv = List.map cast_to_i_n_var conv in
-(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
-prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
- let p = {p with freshno; div; conv; ps} in
- ( (* check if double substituting a variable *)
- if List.exists (fun (x',_) -> x = x') sigma
- then failwithProblem p "Variable replaced twice"
- );
- let p = {p with sigma = sigma@[x,inst]} in
- let p = super_simplify p in
- print_endline (print_problem "instantiate" p);
- p
-;;
-
-exception Dangerous
-
-let arity_of arities k =
- let _,pos,y = List.find (fun (v,_,_) -> v=k) arities in
- let arity = match y with `Var _ -> 0 | `I(_,args) -> Listx.length args | _ -> assert false in
- arity + if pos = -1 then - 1 else 0
-;;
-
-let rec dangerous arities showstoppers =
- function
- `N _
- | `Var _
- | `Lam _ -> ()
- | `Match(t,liftno,bs,args) ->
- (* CSC: XXX partial dependency on the encoding *)
- (match t with
- `N _ -> List.iter (dangerous arities showstoppers) args
- | `Match _ as t -> dangerous arities showstoppers t ; List.iter (dangerous arities showstoppers) args
- | `Var x -> dangerous_inert arities showstoppers x args 2 (* 2 coming from Scott's encoding *)
- | `I(x,args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
- )
- | `I(k,args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0
-
-and dangerous_inert arities showstoppers k args more_args =
- List.iter (dangerous arities showstoppers) args ;
- if List.mem k showstoppers then raise Dangerous else
- try
- let arity = arity_of arities k in
- if List.length args + more_args > arity then raise Dangerous else ()
- with
- Not_found -> ()
-
-(* cut & paste from above *)
-let rec dangerous_conv arities showstoppers =
- function
- `N _
- | `Var _
- | `Lam _ -> []
- | `Match(t,liftno,bs,args) ->
- (* CSC: XXX partial dependency on the encoding *)
- (match t with
- `N _ -> concat_map (dangerous_conv arities showstoppers) args
- | `Match _ as t -> dangerous_conv arities showstoppers t @ concat_map (dangerous_conv arities showstoppers) args
- | `Var x -> dangerous_inert_conv arities showstoppers x args 2 (* 2 coming from Scott's encoding *)
- | `I(x,args') -> dangerous_inert_conv arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
- )
- | `I(k,args) -> dangerous_inert_conv arities showstoppers k (Listx.to_list args) 0
-
-and dangerous_inert_conv arities showstoppers k args more_args =
- concat_map (dangerous_conv arities showstoppers) args @
- if List.mem k showstoppers then k :: concat_map free_vars args else
- try
- let arity = arity_of arities k in
- prerr_endline ("dangerous_inert_conv: ar=" ^ string_of_int arity ^ " k="^string_of_var k ^ " listlenargs=" ^ (string_of_int (List.length args)) );
- if List.length args + more_args > arity then k :: concat_map free_vars args else []
- with
- Not_found -> []
-
-(* inefficient algorithm *)
-let rec edible arities div ps conv showstoppers =
- let rec aux showstoppers =
- function
- [] -> showstoppers
- | x::xs when List.exists (fun y -> hd_of x = Some y) showstoppers ->
- (* se la testa di x e' uno show-stopper *)
- let new_showstoppers = sort_uniq (showstoppers @ free_vars (x :> nf)) in
- (* aggiungi tutte le variabili libere di x *)
- if List.length showstoppers <> List.length new_showstoppers then
- aux new_showstoppers ps
- else
- aux showstoppers xs
- | x::xs ->
- match hd_of x with
- None -> aux showstoppers xs
- | Some h ->
- try
- dangerous arities showstoppers (x : i_n_var :> nf) ;
- aux showstoppers xs
- with
- Dangerous ->
- aux (sort_uniq (h::showstoppers)) ps
- in
- let showstoppers = sort_uniq (aux showstoppers ps) in
- let dangerous_conv =
- List.map (dangerous_conv arities showstoppers) (conv :> nf list) in
-
- prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
- List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv;
- let showstoppers' = showstoppers @ List.concat dangerous_conv in
- let showstoppers' = sort_uniq (match div with
- | None -> showstoppers'
- | Some div ->
- if List.exists ((=) (hd_of_i_var div)) showstoppers'
- then showstoppers' @ free_vars (div :> nf) else showstoppers') in
- if showstoppers <> showstoppers' then edible arities div ps conv showstoppers' else showstoppers', dangerous_conv
-;;
-
-let precompute_edible_data {ps; div} xs =
- (match div with None -> [] | Some div -> [hd_of_i_var div, -1, (div :> i_n_var)]) @
- List.map (fun hd ->
- let i, tm = Util.findi (fun y -> hd_of y = Some hd) ps in
- hd, i, tm
- ) xs
-;;
-
-let critical_showstoppers p =
- let p = super_simplify p in
- let hd_of_div = match p.div with None -> [] | Some t -> [hd_of_i_var t] in
- let showstoppers_step =
- concat_map (fun bs ->
- let heads = List.map (fun (i,_) -> List.nth p.ps i) !bs in
- let heads = List.sort compare (hd_of_div @ filter_map hd_of heads) in
- snd (split_duplicates heads)
- ) p.deltas @
- if List.exists (fun t -> [hd_of t] = List.map (fun x -> Some x) hd_of_div) p.conv
- then hd_of_div else [] in
- let showstoppers_step = sort_uniq showstoppers_step in
- let showstoppers_eat =
- let heads_and_arities =
- List.sort (fun (k,_) (h,_) -> compare k h)
- (filter_map (function `Var k -> Some (k,0) | `I(k,args) -> Some (k,Listx.length args) | _ -> None ) p.ps) in
- let rec multiple_arities =
- function
- []
- | [_] -> []
- | (x,i)::(y,j)::tl when x = y && i <> j ->
- x::multiple_arities tl
- | _::tl -> multiple_arities tl in
- multiple_arities heads_and_arities in
-
- let showstoppers_eat = sort_uniq showstoppers_eat in
- let showstoppers_eat = List.filter
- (fun x -> not (List.mem x showstoppers_step))
- showstoppers_eat in
- List.iter (fun v -> prerr_endline ("DANGEROUS STEP: " ^ string_of_var v)) showstoppers_step;
- List.iter (fun v -> prerr_endline ("DANGEROUS EAT: " ^ string_of_var v)) showstoppers_eat;
- p, showstoppers_step, showstoppers_eat
- ;;
-
-let eat p =
- let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p in
- let showstoppers = showstoppers_step @ showstoppers_eat in
- let heads = List.sort compare (filter_map hd_of ps) in
- let arities = precompute_edible_data p (uniq heads) in
- let showstoppers, showstoppers_conv =
- edible arities p.div ps p.conv showstoppers in
- let l = List.filter (fun (x,_,_) -> not (List.mem x showstoppers)) arities in
- let p =
- List.fold_left (fun p (x,pos,(xx : i_n_var)) -> if pos = -1 then p else
- let n = match xx with `I(_,args) -> Listx.length args | _ -> 0 in
- let v = `N(pos) in
- let inst = make_lams v n in
-(let l = Array.to_list (Array.init (p.freshno + 1) string_of_var) in
-prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
- { p with sigma = p.sigma @ [x,inst] }
- ) p l in
- (* to avoid applied numbers in safe positions that
- trigger assert failures subst_in_problem x inst p*)
- let ps =
- List.map (fun t ->
- try
- let _,j,_ = List.find (fun (h,_,_) -> hd_of t = Some h) l in
- `N j
- with Not_found -> t
- ) ps in
- let p = match p.div with
- | None -> p
- | Some div ->
- if List.mem (hd_of_i_var div) showstoppers
- then p
- else
- let n = match div with `I(_,args) -> Listx.length args | `Var _ -> 0 in
- let p, bomb' = make_fresh_var p in
- (if !bomb <> `Var (-1) then
- failwithProblem p
- ("Bomb was duplicated! It was " ^ string_of_nf p !bomb ^
- ", tried to change it to " ^ string_of_nf p bomb'));
- bomb := bomb';
- prerr_endline ("Just created bomb var: " ^ string_of_nf p !bomb);
- let x = hd_of_i_var div in
- let inst = make_lams !bomb n in
- prerr_endline ("# INST (div): " ^ string_of_var x ^ " := " ^ string_of_nf p inst);
- let p = {p with div=None} in
- (* subst_in_problem (hd_of_i_var div) inst p in *)
- {p with sigma=p.sigma@[x,inst]} in
- let dangerous_conv = showstoppers_conv in
-let _ = prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
-List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv; in
- let conv =
- List.map (function s,t ->
- try
- if s <> [] then t else (
- (match t with | `Var _ -> raise Not_found | _ -> ());
- let _ = List.find (fun h -> hd_of t = Some h) showstoppers in
- t)
- with Not_found -> match hd_of t with
- | None -> assert (t = `N ~-1); t
- | Some h ->
- prerr_endline ("FREEZING " ^ string_of_var h);
- `N ~-1 (* convergent dummy*)
- ) (List.combine showstoppers_conv p.conv) in
- List.iter
- (fun bs ->
- bs :=
- List.map
- (fun (n,t as res) ->
- match List.nth ps n with
- `N m -> m,t
- | _ -> res
- ) !bs
- ) p.deltas ;
- let old_conv = p.conv in
- let p = { p with ps; conv } in
- if l <> [] || old_conv <> conv
- then print_endline (print_problem "eat" p);
- if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then
- `Finished p
- else
- `Continue p
-
-let instantiate p x n =
- (if `Var x = !bomb
- then failwithProblem p ("BOMB (" ^ string_of_nf p !bomb ^ ") cannot be instantiated!"));
- prerr_endline ("stepping on " ^ string_of_var x);
- (if List.nth p.arities x <= 0 then failwith "stepped on a varible of arity <= 0");
- let p,vars = make_fresh_vars p n in
- let p,zero' = make_fresh_var p in
- let zero = Listx.Nil zero' in
- let args = if n = 0 then zero else Listx.append zero (Listx.from_list vars) in
- let bs = ref [] in
- let inst = `Lam(false,`Match(`I(0,Listx.map (lift 1) args),1,bs,[])) in
- let p = {p with deltas=bs::p.deltas} in
- let p = ACMeasure.fix_arities p x (List.map (function `Var x -> x | _ -> assert false) (Listx.to_list args)) in
- let p = subst_in_problem x inst p in
- p
-;;
-
-let auto_instantiate (n,p) =
- let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
- let x =
- match showstoppers_step, showstoppers_eat with
- | [], y::_ ->
- prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
- | [], [] ->
- let heads = List.sort compare (filter_map (fun t -> match t with `Var _ -> None | x -> hd_of x) ((match p.div with Some t -> [(t :> i_n_var)] | _ -> []) @ p.ps)) in
- (match heads with
- [] -> assert false
- | x::_ ->
- prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
- x)
- | x::_, _ ->
- prerr_endline ("INSTANTIATING " ^ string_of_var x);
- x in
-(* Strategy that decreases the special_k to 0 first (round robin)
-1:11m42 2:14m5 3:11m16s 4:14m46s 5:12m7s 6:6m31s *)
-let x =
- try
- match hd_of (List.find (fun t -> compute_special_k (Listx.Nil (t :> nf)) > 0) (all_terms p)) with
- None -> assert false
- | Some x ->
- prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
- x
- with
- Not_found -> x
-in
-(* Instantiate in decreasing order of compute_special_k
-1:15m14s 2:13m14s 3:4m55s 4:4m43s 5:4m34s 6:6m28s 7:3m31s
-let x =
- try
- (match hd_of (snd (List.hd (List.sort (fun c1 c2 -> - compare (fst c1) (fst c2)) (filter_map (function `I _ as t -> Some (compute_special_k (Listx.Nil (t :> nf)),t) | _ -> None) (all_terms p))))) with
- None -> assert false
- | Some x ->
- prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
- x)
- with
- Not_found -> x
-in*)
- let special_k =
- compute_special_k (Listx.from_list (all_terms p :> nf list) )in
- if special_k < n then
- prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@");
- let p = instantiate p x special_k in
- special_k,p
-
-
-let rec auto_eat (n,({ps} as p)) =
- prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}";
- let p = ACMeasure.fix_arities p (-1) [] in
- let m = problem_measure p in
- let (n,p') = auto_instantiate (n,p) in
- match eat p' with
- `Finished p -> p
- | `Continue p ->
- prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}";
- let p = ACMeasure.fix_arities p (-1) [] in
- let delta = m - problem_measure p in
- if delta <= 0 then (
- (* failwithProblem p *)
- prerr_endline
- ("Measure did not decrease (delta=" ^ string_of_int delta ^ ")"))
- else prerr_endline ("$ Measure decreased by " ^ string_of_int delta);
- (* let p' = {p' with steps=(p'.steps - 1)} in *)
- (* (if p'.steps < 0 then prerr_endline ">>>>>>>>>> STEPS ARE OVER <<<<<<<<<"
- (*failwithProblem p' "steps are over. sorry."*) ); *)
- auto_eat (n,p)
-;;
-
-let auto p n =
- prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
- match eat p with
- `Finished p -> p
- | `Continue p -> auto_eat (n,p)
-;;
-
-(*
-0 = snd
-
- x y = y 0 a y = k k z = z 0 c y = k y u = u h1 h2 0 h2 a = h3
-1 x a c 1 a 0 c 1 k c 1 c 0 1 k 1 k 1 k
-2 x a y 2 a 0 y 2 k y 2 y 0 2 y 0 2 h2 0 2 h3
-3 x b y 3 b 0 y 3 b 0 y 3 b 0 y 3 b 0 y 3 b 0 (\u. u h1 h2 0) 3 b 0 (\u. u h1 (\w.h3) 0)
-4 x b c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c 4 b 0 c
-5 x (b e) 5 b e 0 5 b e 0 5 b e 0 5 b e 0 5 b e 0 5 b e 0
-6 y y 6 y y 6 y y 6 y y 6 y y 6 h1 h1 h2 0 h2 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0
-
- l2 _ = l3
-b u = u l1 l2 0 e _ _ _ _ = f l3 n = n j 0
-1 k 1 k 1 k
-2 h3 2 h3 2 h3
-3 l2 0 (\u. u h1 (\w. h3) 0) 3 l3 (\u. u h1 (\w. h3) 0) 3 j h1 (\w. h3) 0 0
-4 l2 0 c 4 l3 c 4 c j 0
-5 e l1 l2 0 0 5 f 5 f
-6 h1 h1 (\w. h3) 0 (\w. h3) 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0 6 h1 h1 (\w. h3) 0 (\w. h3) 0
-*)
-
-(*
- x n = n 0 ?
-x a (b (a c)) a 0 = 1 ? (b (a c)) 8
-x a (b d') a 0 = 1 ? (b d') 7
-x b (a c) b 0 = 1 ? (a c) 4
-x b (a c') b 0 = 1 ? (a c') 5
-
-c = 2
-c' = 3
-a 2 = 4 (* a c *)
-a 3 = 5 (* a c' *)
-d' = 6
-b 6 = 7 (* b d' *)
-b 4 = 8 (* b (a c) *)
-b 0 = 1
-a 0 = 1
-*)
-
-(************** Tests ************************)
-
-let optimize_numerals p =
- let replace_in_sigma perm =
- let rec aux = function
- | `N n -> `N (List.nth perm n)
- | `I _ -> assert false
- | `Var _ as t -> t
- | `Lam(v,t) -> `Lam(v, aux t)
- | `Match(_,_,bs,_) as t -> (bs := List.map (fun (n,t) -> (List.nth perm n, t)) !bs); t
- in List.map (fun (n,t) -> (n,aux t))
- in
- let deltas' = List.mapi (fun n d -> (n, List.map fst !d)) p.deltas in
- let maxs = Array.to_list (Array.init (List.length deltas') (fun _ -> 0)) in
- let max = List.fold_left max 0 (concat_map snd deltas') in
- let perm,_ = List.fold_left (fun (perm, maxs) (curr_n:int) ->
- let containing = filter_map (fun (i, bs) -> if List.mem curr_n bs then Some i else None) deltas' in
- (* (prerr_endline (string_of_int curr_n ^ " occurs in: " ^ (String.concat " " (List.map string_of_int containing)))); *)
- let neww = List.fold_left Pervasives.max 0 (List.mapi (fun n max -> if List.mem n containing then max else 0) maxs) in
- let maxs = List.mapi (fun i m -> if List.mem i containing then neww+1 else m) maxs in
- (neww::perm, maxs)
- ) ([],maxs) (Array.to_list (Array.init (max+1) (fun x -> x))) in
- replace_in_sigma (List.rev perm) p.sigma
-;;
-
-let env_of_sigma freshno sigma should_explode =
- let rec aux n =
- if n > freshno then
- []
- else
- let e = aux (n+1) in
- (try
- e,Pure.lift (-n-1) (snd (List.find (fun (i,_) -> i = n) sigma)),[]
- with
- Not_found ->
- if should_explode && `Var n = !bomb
- then ([], (let f t = Pure.A(t,t) in f (Pure.L (f (Pure.V 0)))), [])
- else ([],Pure.V n,[]))::e
- in aux 0
-;;
-
-prerr_endline "########## main ##########";;
-
-(* Commands:
- v ==> v := \a. a k1 .. kn \^m.0
- + ==> v := \^k. numero for every v such that ...
- * ==> tries v as long as possible and then +v as long as possible
-*)
-let main problems =
- let rec aux ({ps} as p) n l =
- if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then begin
- p
- end else
- let _ = print_endline (print_problem "main" p) in
- let x,l =
- match l with
- | cmd::l -> cmd,l
- | [] -> read_line (),[] in
- let cmd =
- if x = "+" then
- `DoneWith
- else if x = "*" then
- `Auto
- else
- `Step x in
- match cmd with
- | `DoneWith -> assert false (*aux (eat p) n l*) (* CSC: TODO *)
- | `Step x ->
- let x = var_of_string x in
- aux (instantiate p x n) n l
- | `Auto -> aux (auto p n) n l
- in
- List.iter
- (fun (p,n,cmds) ->
- Console.print_hline();
- bomb := `Var (-1);
- let p_finale = aux p n cmds in
- let freshno,sigma = p_finale.freshno, p_finale.sigma in
- prerr_endline ("------- <DONE> ------\n "
- (* ^ (string_of_int (p.steps - (List.length p_finale.sigma))) ^ " steps of "^ (string_of_int p.steps) ^"." *)
- );
- (* print_endline (print_problem "Original problem" p); *)
- prerr_endline "---------------------";
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- prerr_endline (" BOMB == " ^ print ~l !bomb);
- prerr_endline "---------------------";
- List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
-(*
- prerr_endline "----------------------";
- let ps =
- List.fold_left (fun ps (x,inst) ->
- (* CSC: XXXX Is the subst always sorted correctly? Otherwise, implement a recursive subst *)
- (* In this non-recursive version, the intermediate states may containt Matchs *)
- List.map (fun t -> let t = subst false x inst (t :> nf) in cast_to_i_num_var t) ps)
- (p.ps :> i_num_var list) sigma in
- print_endline (print_problem {p with ps= List.map (function t -> cast_to_i_n_var t) ps; freshno});
- List.iteri (fun i (n,more_args) -> assert (more_args = 0 && n = `N i)) ps ;
-*)
- prerr_endline "---------<OPT>----------";
- let sigma = optimize_numerals p_finale in (* optimize numerals *)
- let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
- List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
- prerr_endline "---------<PURE>---------";
- let div = option_map (fun div -> ToScott.t_of_nf (div :> nf)) p.div in
- let conv = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.conv in
- let ps = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.ps in
- let sigma = List.map (fun (x,inst) -> x, ToScott.t_of_nf inst) sigma in
- (*let ps_ok = List.fold_left (fun ps (x,inst) ->
- List.map (Pure.subst false x inst) ps) ps sigma in*)
- let e = env_of_sigma freshno sigma true in
- let e' = env_of_sigma freshno sigma false in
-
-(*
- prerr_endline "---------<PPP>---------";
-let rec print_e e =
- "[" ^ String.concat ";" (List.map (fun (e,t,[]) -> print_e e ^ ":" ^ Pure.print t) e) ^ "]"
-in
- prerr_endline (print_e e);
- List.iter (fun (t,t_ok) ->
- prerr_endline ("T0= " ^ Pure.print t ^ "\nTM= " ^ Pure.print (Pure.unwind (e,t,[])) ^ "\nOM= " ^ Pure.print t_ok);
- (*assert (Pure.unwind (e,t,[]) = t_ok)*)
- ) (List.combine ps ps_ok);
-*)
- prerr_endline "--------<REDUCE>---------";
- (function Some div ->
- print_endline (Pure.print div);
- let t = Pure.mwhd (e',div,[]) in
- prerr_endline ("*:: " ^ (Pure.print t));
- prerr_endline (print !bomb);
- assert (t = ToScott.t_of_nf (!bomb:>nf))
- | None -> ()) div;
- List.iter (fun n ->
- prerr_endline ("_::: " ^ (Pure.print n));
- let t = Pure.mwhd (e,n,[]) in
- prerr_endline ("_:: " ^ (Pure.print t))
- ) conv ;
- List.iteri (fun i n ->
- prerr_endline ((string_of_int i) ^ "::: " ^ (Pure.print n));
- let t = Pure.mwhd (e,n,[]) in
- prerr_endline ((string_of_int i) ^ ":: " ^ (Pure.print t));
- assert (t = Scott.mk_n i)
- ) ps ;
- prerr_endline "-------- </DONE> --------"
- ) problems
-
-(********************** problems *******************)
-
-let zero = `Var 0;;
-
-let append_zero =
- function
- | `I _
- | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
- | _ -> assert false
-;;
-
-
-type t = problem * int * string list;;
-
-let magic_conv ~div ~conv ~nums cmds =
- let all_tms = (match div with None -> [] | Some div -> [div]) @ nums @ conv in
- let all_tms, var_names = parse' all_tms in
- let div, (tms, conv) = match div with
- | None -> None, list_cut (List.length nums, all_tms)
- | Some _ -> Some (List.hd all_tms), list_cut (List.length nums, List.tl all_tms) in
-
- if match div with None -> false | Some div -> List.exists (eta_subterm div) (tms@conv)
- then (
- prerr_endline "--- TEST SKIPPED ---";
- {freshno=0; div=None; conv=[]; ps=[]; sigma=[]; deltas=[]; arities=[]; special_k=(-1);}, 0, []
- ) else
- let tms = sort_uniq ~compare:eta_compare tms in
- let special_k = compute_special_k (Listx.from_list all_tms) in (* compute initial special K *)
- (* casts *)
- let div = option_map cast_to_i_var div in
- let conv = List.map cast_to_i_n_var conv in
- let tms = List.map cast_to_i_n_var tms in
-
- let ps = List.map append_zero tms in (* crea lista applicando zeri o dummies *)
- let freshno = List.length var_names in
- let sigma = [] in
- let deltas =
- let dummy = `Var (max_int / 2) in
- [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
- let p = {freshno; div; conv; ps; sigma; deltas; special_k; arities=[]} in
- let arities =
- List.mapi (fun i () -> ACMeasure.map_max (ACMeasure.get_arity_of_var p i) ((all_terms p) :> nf list)) (Array.to_list (Array.make (freshno+1) ())) in
- let p = {p with arities} in
- p, special_k, cmds
-;;
-
-let magic strings cmds = magic_conv None [] strings cmds;;
+++ /dev/null
-include Discriminator.Discriminator\r
projects / fireball-separation.git / commitdiff