7 The number of arguments which can applied to numbers
8 safely, depending on the encoding of numbers.
9 For Scott's encoding, two.
11 let num_more_args = 2;;
12 let _very_verbose = false;;
15 if _very_verbose then prerr_endline s
18 let convergent_dummy = `N(-1);;
20 type discriminating_set = (int * nf) list;;
24 ; div: i_var option (* None = bomb *)
25 ; conv: i_n_var list (* the inerts that must converge *)
26 ; ps: i_n_var list (* the n-th inert must become n *)
27 ; sigma: (int * nf) list (* the computed substitution *)
28 ; deltas: discriminating_set ref list (* collection of all branches *)
29 ; initialSpecialK: int
31 ; trail: discriminating_set list list
37 exception Backtrack of string
38 exception Fail of string
40 let first bound p var f =
41 let p = {p with trail = (List.map (!) p.deltas)::p.trail} in
44 raise (Backtrack ("no more alternatives for " ^ string_of_var var))
49 prerr_endline (">>>>>> BACKTRACK (reason: " ^ s ^") measure=$ ");
50 List.iter (fun (r,l) -> r := l) (List.combine p.deltas (List.hd p.trail)) ;
51 prerr_endline("Now trying var="^string_of_var var^" i="^string_of_int i);
58 (match p.div with None -> [] | Some t -> [(t :> i_n_var)])
64 let rec aux = function
65 | `N _ | `Bottom | `Pacman -> 0
66 | `Var(_,ar) -> if ar = min_int then 0 else max 0 ar (*assert (ar >= 0); ar*)
68 | `I(v,args) -> aux (`Var v) + aux_many (Listx.to_list args :> nf list)
69 | `Match(u,(_,ar),_,_,args) -> aux (u :> nf) + (if ar = min_int then 0 else ar - 1) + aux_many (args :> nf list)
70 and aux_many tms = List.fold_right ((+) ++ aux) tms 0 in
71 aux_many (all_terms p :> nf list)
74 let problem_measure p = sum_arities p;;
75 let string_of_measure = string_of_int;;
77 let string_of_problem label ({freshno; div; conv; ps; deltas} as p) =
78 Console.print_hline ();
79 prerr_string ("\n(* DISPLAY PROBLEM (" ^ label ^ ") - ");
81 let deltas = String.concat (nl^" ") (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
82 let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
83 "measure="^string_of_measure(problem_measure p) (* ^ " freshno = " ^ string_of_int freshno*)
84 ^ nl ^ " Discriminating sets (deltas):"
85 ^ nl ^ " " ^ deltas ^ (if deltas = " " then "" else nl) ^ "*)"
86 ^"(* DIVERGENT *)" ^ nl
87 ^" "^ (match div with None -> "None" | Some div -> "(Some\""^ print ~l (div :> nf) ^"\")") ^ nl
88 ^" (* CONVERGENT *) [" ^ nl ^ " "
89 ^ String.concat "\n " (List.map (fun t -> "(* _ *) " ^ (if t = convergent_dummy then "" else "\""^ print ~l (t :> nf) ^"\";")) conv) ^
90 (if conv = [] then "" else nl)
91 ^ "] (* NUMERIC *) [" ^ nl ^ " "
92 ^ String.concat "\n " (List.mapi (fun i t -> " (* "^ string_of_int i ^" *) \"" ^ print ~l (t :> nf) ^ "\";") ps)
93 ^ nl ^ "] [\"*\"];;" ^ nl
97 let failwithProblem p reason =
98 print_endline (string_of_problem "FAIL" p);
102 let make_fresh_var p arity =
103 let freshno = p.freshno + 1 in
104 {p with freshno}, `Var(freshno,arity)
107 let make_fresh_vars p arities =
109 (fun arity (p, vars) -> let p, var = make_fresh_var p arity in p, var::vars)
114 let simple_expand_match ps =
115 let rec aux_nob level = function
116 | #i_num_var as t -> aux_i_num_var level t
117 | `Lam(b,t) -> `Lam(b,aux (level+1) t)
119 and aux level = function
121 | #nf_nob as t -> aux_nob level t
122 and aux_i_num_var level = function
123 | `Match(u,v,bs_lift,bs,args) as torig ->
124 let u = aux_i_num_var level u in
125 bs := List.map (fun (n, x) -> n, aux 0 x) !bs;
129 let i = index_of (lift (-level) u) (ps :> nf list) (* can raise Not_found *)
130 in let t = mk_match (`N i) v bs_lift bs (args :> nf list) in
134 | _ -> raise Not_found)
136 mk_appl (`Match(cast_to_i_num_var u,v,bs_lift,bs,[])) (List.map (aux_nob level) args))
137 | `I(v,args) -> mk_appl (`Var v) (List.map (aux_nob level) (Listx.to_list args))
138 | `N _ | `Var _ as t -> t
143 let rec aux x = let x' = f x in if x <> x' then aux x' else x in aux
146 let rec super_simplify_ps ps =
147 fixpoint (List.map (fun x -> cast_to_i_n_var (simple_expand_match ps (x :> i_num_var))))
150 let rec super_simplify_ps_with_match ps =
151 fixpoint (List.map (cast_to_i_num_var ++ (simple_expand_match ps)))
154 let super_simplify ({div; ps; conv} as p) =
155 let ps = super_simplify_ps p.ps p.ps in
156 let conv = super_simplify_ps ps p.conv in
157 let div = option_map (fun div ->
158 let divs = super_simplify_ps p.ps ([div] :> i_n_var list) in
160 {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}
162 let cast_to_ps_with_match =
164 #i_num_var as y -> (y : i_num_var)
165 | `Bottom | `Pacman -> raise (Backtrack "BOT/PAC in ps")
167 prerr_endline (print (t :> nf));
168 assert false (* algorithm failed *)
170 let subst_in_problem x inst ({freshno; div; conv; ps; sigma} as p) =
171 let len_ps = List.length ps in
172 (*(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
173 prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
174 let rec aux_ps ((freshno,acc_ps,acc_new_ps) as acc) =
178 (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
179 let t = subst false false x inst (t :> nf) in
180 (*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
181 let freshno,new_t,acc_new_ps =
183 expand_match (freshno,acc_ps@`Var(max_int/3,-666)::todo_ps,acc_new_ps) t
184 with Pacman | Bottom -> raise (Backtrack "Pacman/Bottom in ps")
186 aux_ps (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
188 (* cut&paste from aux above *)
189 and aux_conv ps ((freshno,acc_conv,acc_new_ps) as acc) =
193 (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
194 let t = subst false false x inst (t :> nf) in
195 (*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
196 let freshno,new_t,acc_new_ps =
198 expand_match (freshno,ps,acc_new_ps) t
199 with Pacman -> freshno,convergent_dummy,acc_new_ps
200 | Bottom -> raise (Backtrack "Bottom in conv") in
201 aux_conv ps (freshno,acc_conv@[new_t],acc_new_ps) todo_conv
203 (* cut&paste from aux' above *)
204 and aux_div ps (freshno,acc_new_ps) =
206 | None -> freshno, None, acc_new_ps
208 let t = subst false false x inst (t :> nf) in
210 let freshno,new_t,acc_new_ps = expand_match (freshno,ps,acc_new_ps) t in
211 (* backtrack if it is a number or a variable *)
213 | `N _ -> raise (Backtrack "div=`N")
215 | `I _ as new_t -> freshno, Some(new_t), acc_new_ps
217 | Bottom -> freshno, None, acc_new_ps
218 | Pacman -> raise (Backtrack "div=PAC")
220 and expand_match ((freshno,acc_ps,acc_new_ps) as acc) t =
222 | `Match(u',orig,bs_lift,bs,args) ->
223 let freshno,u,acc_new_ps = expand_match acc (u' :> nf) in
226 | `N i -> acc_new_ps,i
228 let ps = List.map (fun t -> cast_to_ps_with_match (subst false false x inst (t:> nf))) (acc_ps@acc_new_ps) in
229 let super_simplified_ps = super_simplify_ps_with_match ps ps in
230 (*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
231 List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
232 List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplified_ps;*)
233 match index_of_opt ~eq:eta_eq super_simplified_ps (u :> i_num_var) with
234 Some i -> acc_new_ps, i
235 | None -> acc_new_ps@[u], len_ps + List.length acc_new_ps
238 if List.exists (fun (j,_) -> i=j) !bs then
241 let freshno,v = freshno+1, `Var (freshno+1, -666) in (* make_fresh_var freshno in *)
244 (*prerr_endlie ("t DA RIDURRE:" ^ print (`Match(`N i,arity,bs_lift,bs,args) :> nf) ^ " more_args=" ^ string_of_int more_args);*)
245 let t = mk_match (`N i) orig bs_lift bs (args :> nf list) in
246 (*prerr_endline ("NUOVO t:" ^ print (fst t :> nf) ^ " more_args=" ^ string_of_int (snd t));*)
247 expand_match (freshno,acc_ps,acc_new_ps) t
248 | `Lam _ -> assert false (* algorithm invariant/loose typing *)
249 | `Bottom -> raise Bottom
250 | `Pacman -> raise Pacman
252 let x = simple_expand_match (acc_ps@acc_new_ps) x in
253 freshno,cast_to_i_n_var x,acc_new_ps in
255 let freshno,old_ps,new_ps = aux_ps (freshno,[],[]) ps in
256 let freshno,conv,new_ps = aux_conv old_ps (freshno,[],new_ps) conv in
257 let freshno,div,new_ps = aux_div old_ps (freshno,new_ps) (div :> i_num_var option) in
259 let ps = List.map cast_to_i_n_var (old_ps @ new_ps) in
260 let conv = List.map cast_to_i_n_var conv in
261 (let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
262 prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
263 let p = {p with freshno; div; conv; ps} in
264 ( (* check if double substituting a variable *)
265 if List.exists (fun (x',_) -> x = x') sigma
266 then failwithProblem p ("Variable "^ string_of_var x ^"replaced twice")
268 let p = {p with sigma = sigma@[x,inst]} in
269 let p = super_simplify p in
270 prerr_endline (string_of_problem "instantiate" p);
276 let arity_of arities k =
277 let _,pos,y = List.find (fun (v,_,_) -> v=k) arities in
278 let arity = match y with `Var _ -> 0 | `I(_,args) -> Listx.length args | _ -> assert false in
279 arity + if pos = -1 then - 1 else 0
282 let rec dangerous arities showstoppers =
288 | `Match(t,_,liftno,bs,args) ->
289 (* CSC: XXX partial dependency on the encoding *)
291 `N _ -> List.iter (dangerous arities showstoppers) args
292 | `Match _ as t -> dangerous arities showstoppers t ; List.iter (dangerous arities showstoppers) args
293 | `Var(x,_) -> dangerous_inert arities showstoppers x args num_more_args
294 | `I((x,_),args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) num_more_args
296 | `I((k,_),args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0
298 and dangerous_inert arities showstoppers k args more_args =
299 List.iter (dangerous arities showstoppers) args ;
300 if List.mem k showstoppers then raise Dangerous else
302 let arity = arity_of arities k in
303 if List.length args + more_args > arity then raise Dangerous else ()
307 (* cut & paste from above *)
308 let rec dangerous_conv arities showstoppers =
314 | `Match(t,_,liftno,bs,args) ->
315 (* CSC: XXX partial dependency on the encoding *)
317 `N _ -> concat_map (dangerous_conv arities showstoppers) args
318 | `Match _ as t -> dangerous_conv arities showstoppers t @ concat_map (dangerous_conv arities showstoppers) args
319 | `Var(x,_) -> dangerous_inert_conv arities showstoppers x [] args 2
320 | `I((x,_),args') -> dangerous_inert_conv arities showstoppers x (Listx.to_list args') args 2
322 | `I((k,_),args) -> dangerous_inert_conv arities showstoppers k (Listx.to_list args) [] 0
324 and dangerous_inert_conv arities showstoppers k args match_args more_args =
325 let all_args = args @ match_args in
326 let dangerous_args = concat_map (dangerous_conv arities showstoppers) all_args in
327 let all_args = (all_args :> nf list) in
328 if dangerous_args = [] then (
329 if List.mem k showstoppers then k :: concat_map free_vars all_args else
331 let arity = arity_of arities k in
332 prerr_endline ("dangerous_inert_conv: ar=" ^ string_of_int arity ^ " k="^string_of_var k ^ " listlenargs=" ^ (string_of_int (List.length args)) ^ " more_args=" ^ string_of_int more_args);
333 if more_args > 0 (* match argument*) && List.length args = arity then []
334 else if List.length all_args + more_args > arity then k :: concat_map free_vars all_args else []
337 ) else k :: concat_map free_vars all_args
339 (* inefficient algorithm *)
340 let rec edible arities div ps conv showstoppers =
341 let rec aux showstoppers =
344 | x::xs when List.exists (fun y -> hd_of x = Some y) showstoppers ->
345 (* se la testa di x e' uno show-stopper *)
346 let new_showstoppers = sort_uniq (showstoppers @ free_vars (x :> nf)) in
347 (* aggiungi tutte le variabili libere di x *)
348 if List.length showstoppers <> List.length new_showstoppers then
349 aux new_showstoppers ps
354 None -> aux showstoppers xs
357 dangerous arities showstoppers (x : i_n_var :> nf_nob) ;
361 aux (sort_uniq (h::showstoppers)) ps
363 let showstoppers = sort_uniq (aux showstoppers ps) in
365 List.map (dangerous_conv arities showstoppers) conv in
367 prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
368 List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv;
370 let showstoppers' = showstoppers @ List.concat dangerous_conv in
371 let showstoppers' = sort_uniq (match div with
372 | None -> showstoppers'
374 if List.exists ((=) (hd_of_i_var div)) showstoppers'
375 then showstoppers' @ free_vars (div :> nf) else showstoppers') in
376 if showstoppers <> showstoppers' then edible arities div ps conv showstoppers' else showstoppers', dangerous_conv
379 let precompute_edible_data {ps; div} xs =
380 (match div with None -> [] | Some div -> [hd_of_i_var div, -1, (div :> i_n_var)]) @
382 let i, tm = Util.findi (fun y -> hd_of y = Some hd) ps in
387 let critical_showstoppers p =
388 let p = super_simplify p in
389 let hd_of_div = match p.div with None -> [] | Some t -> [hd_of_i_var t] in
390 let showstoppers_step =
391 concat_map (fun bs ->
392 let heads = List.map (fun (i,_) -> List.nth p.ps i) !bs in
393 let heads = List.sort compare (hd_of_div @ filter_map hd_of heads) in
394 snd (split_duplicates heads)
396 if List.exists (fun t -> [hd_of t] = List.map (fun x -> Some x) hd_of_div) p.conv
397 then hd_of_div else [] in
398 let showstoppers_step = sort_uniq showstoppers_step in
399 let showstoppers_eat =
400 let heads_and_arities =
401 List.sort (fun (k,_) (h,_) -> compare k h)
402 (filter_map (function `Var(k,_) -> Some (k,0) | `I((k,_),args) -> Some (k,Listx.length args) | _ -> None ) p.ps) in
403 let rec multiple_arities =
407 | (x,i)::(y,j)::tl when x = y && i <> j ->
408 x::multiple_arities tl
409 | _::tl -> multiple_arities tl in
410 multiple_arities heads_and_arities in
412 let showstoppers_eat = sort_uniq showstoppers_eat in
413 let showstoppers_eat = List.filter
414 (fun x -> not (List.mem x showstoppers_step))
416 List.iter (fun v -> prerr_endline ("DANGEROUS STEP: " ^ string_of_var v)) showstoppers_step;
417 List.iter (fun v -> prerr_endline ("DANGEROUS EAT: " ^ string_of_var v)) showstoppers_eat;
418 p, showstoppers_step, showstoppers_eat
422 let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p in
423 let showstoppers = showstoppers_step @ showstoppers_eat in
424 let heads = List.sort compare (filter_map hd_of ps) in
425 let arities = precompute_edible_data p (uniq heads) in
426 let showstoppers, showstoppers_conv =
427 edible arities p.div ps (p.conv :> nf_nob list) showstoppers in
428 let l = List.filter (fun (x,_,_) -> not (List.mem x showstoppers)) arities in
430 List.fold_left (fun p (x,pos,(xx : i_n_var)) -> if pos = -1 then p else
431 let n = match xx with `I(_,args) -> Listx.length args | _ -> 0 in
433 let inst = make_lams v n in
434 (let l = Array.to_list (Array.init (p.freshno + 1) string_of_var) in
435 prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
436 { p with sigma = p.sigma @ [x,inst] }
438 (* to avoid applied numbers in safe positions that
439 trigger assert failures subst_in_problem x inst p*)
443 let _,j,_ = List.find (fun (h,_,_) -> hd_of t = Some h) l in
447 let p = match p.div with
450 if List.mem (hd_of_i_var div) showstoppers
453 let n = match div with `I(_,args) -> Listx.length args | `Var _ -> 0 in
454 let x = hd_of_i_var div in
455 let inst = make_lams `Bottom n in
456 subst_in_problem x inst p in
457 let dangerous_conv = showstoppers_conv in
458 let _ = prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
459 List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv; in
461 List.map (function s,t ->
463 if s <> [] then t else (
464 (match t with | `Var _ -> raise Not_found | _ -> ());
465 let _ = List.find (fun h -> hd_of t = Some h) showstoppers in
467 with Not_found -> match hd_of t with
468 | None -> assert (t = convergent_dummy); t
470 prerr_endline ("FREEZING " ^ string_of_var h);
472 ) (List.combine showstoppers_conv p.conv) in
478 match List.nth ps n with
483 let old_conv = p.conv in
484 let p = { p with ps; conv } in
485 if l <> [] || old_conv <> conv
486 then prerr_endline (string_of_problem "eat" p);
487 if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then
493 let safe_arity_of_var p x =
494 (* Compute the minimum number of arguments when x is in head
495 position at p.div or p.ps *)
497 | `Var(y,_) -> if x = y then 0 else max_int
498 | `I((y,_),args) -> if x = y then Listx.length args else max_int
500 let tms = ((match p.div with None -> [] | Some t -> [(t :> i_n_var)]) @ p.ps) in
501 List.fold_left (fun acc t -> Pervasives.min acc (aux t)) max_int tms
504 let instantiate p x perm n =
505 let n = (prerr_endline "WARNING: using constant initialSpecialK"); p.initialSpecialK in
506 let arities = Array.to_list (Array.make (n+1) min_int) in
507 let p,vars = make_fresh_vars p arities in
508 (* manual lifting of vars by perm in next line *)
509 let vars = List.map (function `Var (n,ar) -> `Var (n+perm,ar)) vars in
510 let args = Listx.from_list vars in
512 (* other_vars are the variables which are delayed and re-applied to the match *)
513 let other_vars = Array.mapi (fun n () -> `Var(n+1,min_int)) (Array.make (perm-1) ()) in
514 let other_vars = Array.to_list other_vars in
515 (* 666, since it will be replaced anyway during subst: *)
516 let inst = `Match(`I((0,min_int),args),(x,-666),perm,bs,other_vars) in
517 (* Add a number of 'perm' leading lambdas *)
518 let inst = Array.fold_left (fun t () -> `Lam(false, t)) inst (Array.make perm ()) in
519 let p = {p with deltas=bs::p.deltas} in
520 subst_in_problem x inst p
523 let compute_special_k tms =
524 let rec aux k (t: nf) = Pervasives.max k (match t with
525 | `Lam(b,t) -> aux (k + if b then 1 else 0) t
526 | `I(n, tms) -> Listx.max (Listx.map (aux 0) (tms :> nf Listx.listx))
527 | `Match(t, _, liftno, bs, args) ->
528 List.fold_left max 0 (List.map (aux 0) ((t :> nf)::(args :> nf list)@List.map snd !bs))
533 ) in Listx.max (Listx.map (aux 0) tms)
536 let choose_step (n,p) =
537 let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
539 match showstoppers_step, showstoppers_eat with
541 prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
544 (* Choose only variables still alive (with arity > 0) *)
545 List.sort compare (filter_map (
546 fun t -> match t with `Var _ -> None | x -> if arity_of_hd x <= 0 then None else hd_of x
547 ) ((match p.div with Some t -> [(t :> i_n_var)] | _ -> []) @ p.ps)) in
551 fst (List.find (((<) 0) ++ snd) (concat_map free_vars' (p.conv :> nf list)))
553 Not_found -> assert false)
555 prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
558 prerr_endline ("INSTANTIATING " ^ string_of_var x);
560 (* Strategy that decreases the special_k to 0 first (round robin)
561 1:11m42 2:14m5 3:11m16s 4:14m46s 5:12m7s 6:6m31s *)
565 hd_of (List.find (fun t ->
566 compute_special_k (Listx.Nil (t :> nf)) > 0 && arity_of_hd t > 0
569 | None -> assert false
571 prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
575 let arity_of_x = max_arity_tms x (all_terms p) in
576 assert (Util.option_get arity_of_x > 0);
578 (* Instantiate in decreasing order of compute_special_k
579 1:15m14s 2:13m14s 3:4m55s 4:4m43s 5:4m34s 6:6m28s 7:3m31s
582 (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
585 prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
591 compute_special_k (Listx.from_list (all_terms p :> nf list) )in
592 if special_k < n then
593 prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@");
594 let arity_of_x = Util.option_get (max_arity_tms x (all_terms p)) in
595 let safe_arity_of_x = safe_arity_of_var p x in
596 x, min arity_of_x safe_arity_of_x, special_k
598 let rec auto_eat (n,p) =
599 prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}";
600 let m = problem_measure p in
601 let x, arity_of, n = choose_step (n,p) in
602 first arity_of p x (fun p j ->
603 let p' = instantiate p x j n in
607 prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}";
608 let delta = problem_measure p - m in
609 (* let delta = m - problem_measure p' in *)
613 ("Measure did not decrease (+=" ^ string_of_int delta ^ ")"))
614 else prerr_endline ("$ Measure decreased of " ^ string_of_int delta);
619 prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
622 | `Continue p -> auto_eat (n,p)
628 x y = y 0 a y = k k z = z 0 c y = k y u = u h1 h2 0 h2 a = h3
629 1 x a c 1 a 0 c 1 k c 1 c 0 1 k 1 k 1 k
630 2 x a y 2 a 0 y 2 k y 2 y 0 2 y 0 2 h2 0 2 h3
631 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)
632 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
633 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
634 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
637 b u = u l1 l2 0 e _ _ _ _ = f l3 n = n j 0
640 3 l2 0 (\u. u h1 (\w. h3) 0) 3 l3 (\u. u h1 (\w. h3) 0) 3 j h1 (\w. h3) 0 0
641 4 l2 0 c 4 l3 c 4 c j 0
642 5 e l1 l2 0 0 5 f 5 f
643 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
648 x a (b (a c)) a 0 = 1 ? (b (a c)) 8
649 x a (b d') a 0 = 1 ? (b d') 7
650 x b (a c) b 0 = 1 ? (a c) 4
651 x b (a c') b 0 = 1 ? (a c') 5
659 b 4 = 8 (* b (a c) *)
664 (************** Tests ************************)
666 let optimize_numerals p =
667 let replace_in_sigma perm =
668 let rec aux = function
669 | `N n -> `N (List.nth perm n)
671 | `I _ -> assert false
673 | `Lam(v,t) -> `Lam(v, aux t)
674 | `Match(_,_,_,bs,_) as t -> (bs := List.map (fun (n,t) -> (List.nth perm n, t)) !bs); t
676 in List.map (fun (n,t) -> (n,aux t))
678 let deltas' = List.mapi (fun n d -> (n, List.map fst !d)) p.deltas in
679 let maxs = Array.to_list (Array.init (List.length deltas') (fun _ -> 0)) in
680 let max = List.fold_left max 0 (concat_map snd deltas') in
681 let perm,_ = List.fold_left (fun (perm, maxs) (curr_n:int) ->
682 let containing = filter_map (fun (i, bs) -> if List.mem curr_n bs then Some i else None) deltas' in
683 (* (prerr_endline (string_of_int curr_n ^ " occurs in: " ^ (String.concat " " (List.map string_of_int containing)))); *)
684 let neww = List.fold_left Pervasives.max 0 (List.mapi (fun n max -> if List.mem n containing then max else 0) maxs) in
685 let maxs = List.mapi (fun i m -> if List.mem i containing then neww+1 else m) maxs in
687 ) ([],maxs) (Array.to_list (Array.init (max+1) (fun x -> x))) in
688 replace_in_sigma (List.rev perm) p.sigma
691 let env_of_sigma freshno sigma =
698 e,Pure.lift (-n-1) (snd (List.find (fun (i,_) -> i = n) sigma)),[]
700 Not_found -> ([],Pure.V n,[]))::e
705 if List.for_all (function `N _ -> true | _ -> false) p.ps && p.div = None
706 then (prerr_endline "Initial problem is already completed, nothing to do")
708 Console.print_hline();
709 prerr_endline (string_of_problem "main" p);
712 auto p p.initialSpecialK
713 with Backtrack _ -> raise (Fail "Unsolvable problem, apparently") in
714 let freshno,sigma = p_finale.freshno, p_finale.sigma in
715 prerr_endline ("------- <DONE> ------ measure=. \n ");
716 (* prerr_endline (string_of_problem "Original problem" p); *)
717 (* prerr_endline "---------------------"; *)
718 let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
719 (* prerr_endline "---------------------"; *)
720 List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
722 prerr_endline "----------------------";
724 List.fold_left (fun ps (x,inst) ->
725 (* CSC: XXXX Is the subst always sorted correctly? Otherwise, implement a recursive subst *)
726 (* In this non-recursive version, the intermediate states may containt Matchs *)
727 List.map (fun t -> let t = subst false x inst (t :> nf) in cast_to_i_num_var t) ps)
728 (p.ps :> i_num_var list) sigma in
729 prerr_endline (string_of_problem {p with ps= List.map (function t -> cast_to_i_n_var t) ps; freshno});
730 List.iteri (fun i (n,more_args) -> assert (more_args = 0 && n = `N i)) ps ;
732 prerr_endline "---------<OPT>----------";
733 let sigma = optimize_numerals p_finale in (* optimize numerals *)
734 let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
735 List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
737 prerr_endline "---------<PURE>---------";
738 let scott_of_nf t = ToScott.scott_of_nf (t :> nf) in
739 let div = option_map scott_of_nf p.div in
740 let conv = List.map scott_of_nf p.conv in
741 let ps = List.map scott_of_nf p.ps in
743 let sigma' = List.map (fun (x,inst) -> x, ToScott.scott_of_nf inst) sigma in
744 let e' = env_of_sigma freshno sigma' in
747 prerr_endline "---------<PPP>---------";
749 "[" ^ String.concat ";" (List.map (fun (e,t,[]) -> print_e e ^ ":" ^ Pure.print t) e) ^ "]"
751 prerr_endline (print_e e);
752 List.iter (fun (t,t_ok) ->
753 prerr_endline ("T0= " ^ Pure.print t ^ "\nTM= " ^ Pure.print (Pure.unwind (e,t,[])) ^ "\nOM= " ^ Pure.print t_ok);
754 (*assert (Pure.unwind (e,t,[]) = t_ok)*)
755 ) (List.combine ps ps_ok);
757 prerr_endline "--------<REDUCE>---------";
758 (function Some div ->
759 print_endline (Pure.print div);
760 let t = Pure.mwhd (e',div,[]) in
761 prerr_endline ("*:: " ^ (Pure.print t));
765 verbose ("_::: " ^ (Pure.print n));
766 let t = Pure.mwhd (e',n,[]) in
767 verbose ("_:: " ^ (Pure.print t));
770 List.iteri (fun i n ->
771 verbose ((string_of_int i) ^ "::: " ^ (Pure.print n));
772 let t = Pure.mwhd (e',n,[]) in
773 verbose ((string_of_int i) ^ ":: " ^ (Pure.print t));
774 assert (t = Scott.mk_n i)
776 prerr_endline "-------- </DONE> --------"
780 (********************** problems *******************)
782 let zero = `Var(0,0);;
787 | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
791 let problem_of ~div ~conv ~nums =
792 let all_tms = (match div with None -> [] | Some div -> [div]) @ nums @ conv in
793 let all_tms, var_names = parse' all_tms in
794 let div, (tms, conv) = match div with
795 | None -> None, list_cut (List.length nums, all_tms)
796 | Some _ -> Some (List.hd all_tms), list_cut (List.length nums, List.tl all_tms) in
798 if match div with None -> false | Some div -> List.exists (eta_subterm div) (tms@conv)
800 prerr_endline "--- TEST SKIPPED ---";
801 {freshno=0; div=None; conv=[]; ps=[]; sigma=[]; deltas=[]; initialSpecialK=0; trail=[]}
803 let tms = sort_uniq ~compare:eta_compare tms in
804 let special_k = compute_special_k (Listx.from_list all_tms) in (* compute initial special K *)
808 | None | Some `Bottom -> None
809 | Some (`I _ as t) -> Some t
810 | _ -> raise (Fail "div is not an inert or BOT in the initial problem") in
811 let conv = Util.filter_map (
813 | #i_n_var as t -> Some t
815 | _ -> raise (Fail "A term in conv is not i_n_var")
820 | _ -> raise (Fail "A term in num is not i_n_var")
823 let ps = List.map append_zero tms in (* crea lista applicando zeri o dummies *)
824 let freshno = List.length var_names in
826 let dummy = `Var (max_int / 2, -666) in
827 [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
829 {freshno; div; conv; ps; sigma=[] ; deltas; initialSpecialK=special_k; trail}
835 failwith "The problem should have failed"
837 prerr_endline "The problem failed, as expected"