6 let bomb = ref(`Var(-1,-666));;
9 The number of arguments which can applied to numbers
10 safely, depending on the encoding of numbers.
11 For Scott's encoding, two.
13 let num_more_args = 2;;
17 ; div: i_var option (* None = bomb *)
18 ; conv: i_n_var list (* the inerts that must converge *)
19 ; ps: i_n_var list (* the n-th inert must become n *)
20 ; sigma: (int * nf) list (* the computed substitution *)
21 ; deltas: (int * nf) list ref list (* collection of all branches *)
22 ; initialSpecialK: int
26 (match p.div with None -> [] | Some t -> [(t :> i_n_var)])
32 let rec aux = function
34 | `Var(_,ar) -> if ar = min_int then 0 else max 0 ar (*assert (ar >= 0); ar*)
36 | `I(v,args) -> aux (`Var v) + aux_many (Listx.to_list args)
37 | `Match(u,(_,ar),_,_,args) -> aux (u :> nf) + (if ar = min_int then 0 else ar - 1) + aux_many args
38 and aux_many tms = List.fold_right ((+) ++ aux) tms 0 in
39 aux_many (all_terms p :> nf list)
42 let count_fakevars p =
43 let rec aux = function
45 | `Var(_,ar) -> if ar = min_int then 1 else 0
47 | `I(v,args) -> aux (`Var v) + aux_many (Listx.to_list args)
48 | `Match(u,v,_,_,args) -> aux (u :> nf) + aux (`Var v) + aux_many args
49 and aux_many tms = List.fold_right ((+) ++ aux) tms 0 in
50 aux_many (all_terms p :> nf list)
53 (* let problem_measure p = count_fakevars p, sum_arities p;;
54 let string_of_measure (a,b) = "(fakevars="^string_of_int a^",sum_arities="^string_of_int b^")" *)
56 let problem_measure p = sum_arities p;;
57 let string_of_measure = string_of_int;;
59 let print_problem label ({freshno; div; conv; ps; deltas} as p) =
60 Console.print_hline ();
61 prerr_endline ("\n||||| Displaying problem: " ^ label ^ " |||||");
63 let deltas = String.concat nl (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
64 let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
65 nl ^ "measure="^string_of_measure(problem_measure p)^" freshno = " ^ string_of_int freshno
66 ^ nl ^ "\b> DISCRIMINATING SETS (deltas)"
67 ^ nl ^ deltas ^ (if deltas = "" then "" else nl)
68 ^ "\b> DIVERGENT" ^ nl
69 ^ "*: " ^ (match div with None -> "*" | Some div -> print ~l (div :> nf)) ^ "\n| "
70 ^ "\b> CONVERGENT" ^ nl
71 ^ String.concat "\n| " (List.map (fun t -> "_: " ^ (if t = `N (-1) then "_" else print ~l (t :> nf))) conv) ^
72 (if conv = [] then "" else "\n| ")
74 ^ String.concat "\n| " (List.mapi (fun i t -> string_of_int i ^ ": " ^ print ~l (t :> nf)) ps)
79 let failwithProblem p reason =
80 print_endline (print_problem "FAIL" p);
84 let make_fresh_var p arity =
85 let freshno = p.freshno + 1 in
86 {p with freshno}, `Var(freshno,arity)
89 let make_fresh_vars p arities =
91 (fun arity (p, vars) -> let p, var = make_fresh_var p arity in p, var::vars)
96 let simple_expand_match ps =
97 let rec aux level = function
98 | #i_num_var as t -> aux_i_num_var level t
99 | `Lam(b,t) -> `Lam(b,aux (level+1) t)
100 and aux_i_num_var level = function
101 | `Match(u,v,bs_lift,bs,args) as torig ->
102 let u = aux_i_num_var level u in
103 bs := List.map (fun (n, x) -> n, aux 0 x) !bs;
107 let i = index_of (lift (-level) u) (ps :> nf list) (* can raise Not_found *)
108 in let t = mk_match (`N i) v bs_lift bs args in
112 | _ -> raise Not_found)
114 `Match(cast_to_i_num_var u,v,bs_lift,bs,List.map (aux level) args))
115 | `I(v,args) -> `I(v,Listx.map (aux level) args)
116 | `N _ | `Var _ as t -> t
121 let rec aux x = let x' = f x in if x <> x' then aux x' else x in aux
124 let rec super_simplify_ps ps =
125 fixpoint (List.map (cast_to_i_num_var ++ (simple_expand_match ps)))
128 let super_simplify ({div; ps; conv} as p) =
129 let ps = super_simplify_ps p.ps (p.ps :> i_num_var list) in
130 let conv = super_simplify_ps ps (p.conv :> i_num_var list) in
131 let div = option_map (fun div ->
132 let divs = super_simplify_ps p.ps ([div] :> i_num_var list) in
134 {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}
136 exception ExpandedToLambda;;
138 let subst_in_problem x inst ({freshno; div; conv; ps; sigma} as p) =
139 let len_ps = List.length ps in
140 (*(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
141 prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
142 let rec aux ((freshno,acc_ps,acc_new_ps) as acc) =
146 (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
147 let t = subst false false x inst (t :> nf) in
148 (*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
149 let freshno,new_t,acc_new_ps =
150 expand_match (freshno,acc_ps@`Var(max_int/3,-666)::todo_ps,acc_new_ps) t
152 aux (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
154 (* cut&paste from aux above *)
155 and aux' ps ((freshno,acc_conv,acc_new_ps) as acc) =
159 (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
161 let t = subst false false x inst (t :> nf) in
162 (*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
163 let freshno,new_t,acc_new_ps =
164 expand_match (freshno,ps,acc_new_ps) t
166 aux' ps (freshno,acc_conv@[new_t],acc_new_ps) todo_conv
167 (* with ExpandedToLambda -> aux' ps (freshno,acc_conv@[`N(-1)],acc_new_ps) todo_conv *)
169 (* cut&paste from aux' above *)
170 and aux'' ps (freshno,acc_new_ps) =
172 | None -> freshno, None, acc_new_ps
174 let t = subst false false x inst (t :> nf) in
175 let freshno,new_t,acc_new_ps =
176 expand_match (freshno,ps,acc_new_ps) t
178 freshno,Some new_t,acc_new_ps
180 and expand_match ((freshno,acc_ps,acc_new_ps) as acc) t =
182 | `Match(u',orig,bs_lift,bs,args) ->
183 let freshno,u,acc_new_ps = expand_match acc (u' :> nf) in
186 | `N i -> acc_new_ps,i
188 let ps = List.map (fun t -> cast_to_i_num_var (subst false false x inst (t:> nf))) (acc_ps@acc_new_ps) in
189 let super_simplified_ps = super_simplify_ps ps ps in
190 (*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
191 List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
192 List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplified_ps;*)
193 match index_of_opt ~eq:eta_eq super_simplified_ps u with
194 Some i -> acc_new_ps, i
195 | None -> acc_new_ps@[u], len_ps + List.length acc_new_ps
198 if List.exists (fun (j,_) -> i=j) !bs then
201 let freshno,v = freshno+1, `Var (freshno+1, -666) in (* make_fresh_var freshno in *)
204 (*prerr_endlie ("t DA RIDURRE:" ^ print (`Match(`N i,arity,bs_lift,bs,args) :> nf) ^ " more_args=" ^ string_of_int more_args);*)
205 let t = mk_match (`N i) orig bs_lift bs args in
206 (*prerr_endline ("NUOVO t:" ^ print (fst t :> nf) ^ " more_args=" ^ string_of_int (snd t));*)
207 expand_match (freshno,acc_ps,acc_new_ps) t
208 | `Lam _ -> raise ExpandedToLambda
210 let x = simple_expand_match (acc_ps@acc_new_ps) x in
211 freshno,cast_to_i_num_var x,acc_new_ps in
213 let freshno,old_ps,new_ps = aux (freshno,[],[]) (ps :> i_num_var list) in
214 let freshno,conv,new_ps = aux' old_ps (freshno,[],new_ps) (conv :> i_num_var list) in
215 let freshno,div,new_ps = aux'' old_ps (freshno,new_ps) (div :> i_num_var option) in
216 let div = option_map cast_to_i_var div in
217 let ps = List.map cast_to_i_n_var (old_ps @ new_ps) in
218 let conv = List.map cast_to_i_n_var conv in
219 (let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
220 prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
221 let p = {p with freshno; div; conv; ps} in
222 ( (* check if double substituting a variable *)
223 if List.exists (fun (x',_) -> x = x') sigma
224 then failwithProblem p ("Variable "^ string_of_var x ^"replaced twice")
226 let p = {p with sigma = sigma@[x,inst]} in
227 let p = super_simplify p in
228 prerr_endline (print_problem "instantiate" p);
234 let arity_of arities k =
235 let _,pos,y = List.find (fun (v,_,_) -> v=k) arities in
236 let arity = match y with `Var _ -> 0 | `I(_,args) -> Listx.length args | _ -> assert false in
237 arity + if pos = -1 then - 1 else 0
240 let rec dangerous arities showstoppers =
245 | `Match(t,_,liftno,bs,args) ->
246 (* CSC: XXX partial dependency on the encoding *)
248 `N _ -> List.iter (dangerous arities showstoppers) args
249 | `Match _ as t -> dangerous arities showstoppers t ; List.iter (dangerous arities showstoppers) args
250 | `Var(x,_) -> dangerous_inert arities showstoppers x args num_more_args
251 | `I((x,_),args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) num_more_args
253 | `I((k,_),args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0
255 and dangerous_inert arities showstoppers k args more_args =
256 List.iter (dangerous arities showstoppers) args ;
257 if List.mem k showstoppers then raise Dangerous else
259 let arity = arity_of arities k in
260 if List.length args + more_args > arity then raise Dangerous else ()
264 (* cut & paste from above *)
265 let rec dangerous_conv arities showstoppers =
270 | `Match(t,_,liftno,bs,args) ->
271 (* CSC: XXX partial dependency on the encoding *)
273 `N _ -> concat_map (dangerous_conv arities showstoppers) args
274 | `Match _ as t -> dangerous_conv arities showstoppers t @ concat_map (dangerous_conv arities showstoppers) args
275 | `Var(x,_) -> dangerous_inert_conv arities showstoppers x args 2
276 | `I((x,_),args') -> dangerous_inert_conv arities showstoppers x (Listx.to_list args') (List.length args + 2)
278 | `I((k,_),args) -> dangerous_inert_conv arities showstoppers k (Listx.to_list args) 0
280 and dangerous_inert_conv arities showstoppers k args more_args =
281 concat_map (dangerous_conv arities showstoppers) args @
282 if List.mem k showstoppers then k :: concat_map free_vars args else
284 let arity = arity_of arities k in
285 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);
286 if more_args > 0 (* match argument*) && List.length args = arity then []
287 else if List.length args + more_args > arity then k :: concat_map free_vars args else []
291 (* inefficient algorithm *)
292 let rec edible arities div ps conv showstoppers =
293 let rec aux showstoppers =
296 | x::xs when List.exists (fun y -> hd_of x = Some y) showstoppers ->
297 (* se la testa di x e' uno show-stopper *)
298 let new_showstoppers = sort_uniq (showstoppers @ free_vars (x :> nf)) in
299 (* aggiungi tutte le variabili libere di x *)
300 if List.length showstoppers <> List.length new_showstoppers then
301 aux new_showstoppers ps
306 None -> aux showstoppers xs
309 dangerous arities showstoppers (x : i_n_var :> nf) ;
313 aux (sort_uniq (h::showstoppers)) ps
315 let showstoppers = sort_uniq (aux showstoppers ps) in
317 List.map (dangerous_conv arities showstoppers) (conv :> nf list) in
319 prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
320 List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv;
322 let showstoppers' = showstoppers @ List.concat dangerous_conv in
323 let showstoppers' = sort_uniq (match div with
324 | None -> showstoppers'
326 if List.exists ((=) (hd_of_i_var div)) showstoppers'
327 then showstoppers' @ free_vars (div :> nf) else showstoppers') in
328 if showstoppers <> showstoppers' then edible arities div ps conv showstoppers' else showstoppers', dangerous_conv
331 let precompute_edible_data {ps; div} xs =
332 (match div with None -> [] | Some div -> [hd_of_i_var div, -1, (div :> i_n_var)]) @
334 let i, tm = Util.findi (fun y -> hd_of y = Some hd) ps in
339 let critical_showstoppers p =
340 let p = super_simplify p in
341 let hd_of_div = match p.div with None -> [] | Some t -> [hd_of_i_var t] in
342 let showstoppers_step =
343 concat_map (fun bs ->
344 let heads = List.map (fun (i,_) -> List.nth p.ps i) !bs in
345 let heads = List.sort compare (hd_of_div @ filter_map hd_of heads) in
346 snd (split_duplicates heads)
348 if List.exists (fun t -> [hd_of t] = List.map (fun x -> Some x) hd_of_div) p.conv
349 then hd_of_div else [] in
350 let showstoppers_step = sort_uniq showstoppers_step in
351 let showstoppers_eat =
352 let heads_and_arities =
353 List.sort (fun (k,_) (h,_) -> compare k h)
354 (filter_map (function `Var(k,_) -> Some (k,0) | `I((k,_),args) -> Some (k,Listx.length args) | _ -> None ) p.ps) in
355 let rec multiple_arities =
359 | (x,i)::(y,j)::tl when x = y && i <> j ->
360 x::multiple_arities tl
361 | _::tl -> multiple_arities tl in
362 multiple_arities heads_and_arities in
364 let showstoppers_eat = sort_uniq showstoppers_eat in
365 let showstoppers_eat = List.filter
366 (fun x -> not (List.mem x showstoppers_step))
368 List.iter (fun v -> prerr_endline ("DANGEROUS STEP: " ^ string_of_var v)) showstoppers_step;
369 List.iter (fun v -> prerr_endline ("DANGEROUS EAT: " ^ string_of_var v)) showstoppers_eat;
370 p, showstoppers_step, showstoppers_eat
374 let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p in
375 let showstoppers = showstoppers_step @ showstoppers_eat in
376 let heads = List.sort compare (filter_map hd_of ps) in
377 let arities = precompute_edible_data p (uniq heads) in
378 let showstoppers, showstoppers_conv =
379 edible arities p.div ps p.conv showstoppers in
380 let l = List.filter (fun (x,_,_) -> not (List.mem x showstoppers)) arities in
382 List.fold_left (fun p (x,pos,(xx : i_n_var)) -> if pos = -1 then p else
383 let n = match xx with `I(_,args) -> Listx.length args | _ -> 0 in
385 let inst = make_lams v n in
386 (let l = Array.to_list (Array.init (p.freshno + 1) string_of_var) in
387 prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
388 { p with sigma = p.sigma @ [x,inst] }
390 (* to avoid applied numbers in safe positions that
391 trigger assert failures subst_in_problem x inst p*)
395 let _,j,_ = List.find (fun (h,_,_) -> hd_of t = Some h) l in
399 let p = match p.div with
402 if List.mem (hd_of_i_var div) showstoppers
405 let n = match div with `I(_,args) -> Listx.length args | `Var _ -> 0 in
406 let p, bomb' = make_fresh_var p (-666) in
407 (if !bomb <> `Var (-1,-666) then
409 ("Bomb was duplicated! It was " ^ string_of_nf !bomb ^
410 ", tried to change it to " ^ string_of_nf bomb'));
412 prerr_endline ("Just created bomb var: " ^ string_of_nf !bomb);
413 let x = hd_of_i_var div in
414 let inst = make_lams !bomb n in
415 prerr_endline ("# INST (div): " ^ string_of_var x ^ " := " ^ string_of_nf inst);
416 let p = {p with div=None} in
417 (* subst_in_problem (hd_of_i_var div) inst p in *)
418 {p with sigma=p.sigma@[x,inst]} in
419 let dangerous_conv = showstoppers_conv in
420 let _ = prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
421 List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv; in
423 List.map (function s,t ->
425 if s <> [] then t else (
426 (match t with | `Var _ -> raise Not_found | _ -> ());
427 let _ = List.find (fun h -> hd_of t = Some h) showstoppers in
429 with Not_found -> match hd_of t with
430 | None -> assert (t = `N ~-1); t
432 prerr_endline ("FREEZING " ^ string_of_var h);
433 `N ~-1 (* convergent dummy*)
434 ) (List.combine showstoppers_conv p.conv) in
440 match List.nth ps n with
445 let old_conv = p.conv in
446 let p = { p with ps; conv } in
447 if l <> [] || old_conv <> conv
448 then prerr_endline (print_problem "eat" p);
449 if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then
454 let instantiate p x n =
455 (if hd_of_i_var (cast_to_i_var !bomb) = x
456 then failwithProblem p ("BOMB (" ^ string_of_nf !bomb ^ ") cannot be instantiated!"));
457 let arity_of_x = max_arity_tms x (all_terms p) in
458 (if arity_of_x = None then failwithProblem p "step on var non occurring in problem");
459 (if Util.option_get(arity_of_x) = min_int then failwithProblem p "step on fake variable");
460 (if Util.option_get(arity_of_x) <= 0 then failwithProblem p "step on var of non-positive arity");
461 let n = (prerr_endline "WARNING: using constant initialSpecialK"); p.initialSpecialK in
462 (* AC: Once upon a time, it was:
463 let arities = Num.compute_arities x (n+1) (all_terms p :> nf list) in *)
464 (* let arities = Array.to_list (Array.make (n+1) 0) in *)
465 let arities = Array.to_list (Array.make (n+1) min_int) in
466 let p,vars = make_fresh_vars p arities in
467 let args = Listx.from_list (vars :> nf list) in
469 (* 666, since it will be replaced anyway during subst: *)
470 let inst = `Lam(false,`Match(`I((0,min_int),Listx.map (lift 1) args),(x,666),1,bs,[])) in
471 let p = {p with deltas=bs::p.deltas} in
472 subst_in_problem x inst p
475 let compute_special_k tms =
476 let rec aux k (t: nf) = Pervasives.max k (match t with
477 | `Lam(b,t) -> aux (k + if b then 1 else 0) t
478 | `I(n, tms) -> Listx.max (Listx.map (aux 0) tms)
479 | `Match(t, _, liftno, bs, args) ->
480 List.fold_left max 0 (List.map (aux 0) ((t :> nf)::args@List.map snd !bs))
483 ) in Listx.max (Listx.map (aux 0) tms)
486 let auto_instantiate (n,p) =
487 let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
489 match showstoppers_step, showstoppers_eat with
491 prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
494 (* Choose only variables still alive (with arity > 0) *)
495 List.sort compare (filter_map (
496 fun t -> match t with `Var _ -> None | x -> if arity_of_hd x <= 0 then None else hd_of x
497 ) ((match p.div with Some t -> [(t :> i_n_var)] | _ -> []) @ p.ps)) in
502 prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
505 prerr_endline ("INSTANTIATING " ^ string_of_var x);
507 (* Strategy that decreases the special_k to 0 first (round robin)
508 1:11m42 2:14m5 3:11m16s 4:14m46s 5:12m7s 6:6m31s *)
511 match hd_of (List.find (fun t ->
512 compute_special_k (Listx.Nil (t :> nf)) > 0 && arity_of_hd t > 0
513 ) (all_terms p)) with
516 prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
521 (* Instantiate in decreasing order of compute_special_k
522 1:15m14s 2:13m14s 3:4m55s 4:4m43s 5:4m34s 6:6m28s 7:3m31s
525 (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
528 prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
534 compute_special_k (Listx.from_list (all_terms p :> nf list) )in
535 if special_k < n then
536 prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@");
537 let p = instantiate p x special_k in
541 let rec auto_eat (n,p) =
542 prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}";
543 let m = problem_measure p in
544 let (n,p') = auto_instantiate (n,p) in
548 prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}";
549 let m' = problem_measure p in
550 let delta = compare m m' in
551 print_endline ("compare " ^ string_of_measure m' ^ " " ^ string_of_measure m ^ "= " ^ string_of_int delta);
552 (* let delta = m - problem_measure p' in *)
556 ("Measure did not decrease (delta=" ^ string_of_int delta ^ ")"))
557 else prerr_endline ("$ Measure decreased by " ^ string_of_int delta);
562 prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
565 | `Continue p -> auto_eat (n,p)
571 x y = y 0 a y = k k z = z 0 c y = k y u = u h1 h2 0 h2 a = h3
572 1 x a c 1 a 0 c 1 k c 1 c 0 1 k 1 k 1 k
573 2 x a y 2 a 0 y 2 k y 2 y 0 2 y 0 2 h2 0 2 h3
574 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)
575 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
576 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
577 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
580 b u = u l1 l2 0 e _ _ _ _ = f l3 n = n j 0
583 3 l2 0 (\u. u h1 (\w. h3) 0) 3 l3 (\u. u h1 (\w. h3) 0) 3 j h1 (\w. h3) 0 0
584 4 l2 0 c 4 l3 c 4 c j 0
585 5 e l1 l2 0 0 5 f 5 f
586 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
591 x a (b (a c)) a 0 = 1 ? (b (a c)) 8
592 x a (b d') a 0 = 1 ? (b d') 7
593 x b (a c) b 0 = 1 ? (a c) 4
594 x b (a c') b 0 = 1 ? (a c') 5
602 b 4 = 8 (* b (a c) *)
607 (************** Tests ************************)
609 let optimize_numerals p =
610 let replace_in_sigma perm =
611 let rec aux = function
612 | `N n -> `N (List.nth perm n)
613 | `I _ -> assert false
615 | `Lam(v,t) -> `Lam(v, aux t)
616 | `Match(_,_,_,bs,_) as t -> (bs := List.map (fun (n,t) -> (List.nth perm n, t)) !bs); t
617 in List.map (fun (n,t) -> (n,aux t))
619 let deltas' = List.mapi (fun n d -> (n, List.map fst !d)) p.deltas in
620 let maxs = Array.to_list (Array.init (List.length deltas') (fun _ -> 0)) in
621 let max = List.fold_left max 0 (concat_map snd deltas') in
622 let perm,_ = List.fold_left (fun (perm, maxs) (curr_n:int) ->
623 let containing = filter_map (fun (i, bs) -> if List.mem curr_n bs then Some i else None) deltas' in
624 (* (prerr_endline (string_of_int curr_n ^ " occurs in: " ^ (String.concat " " (List.map string_of_int containing)))); *)
625 let neww = List.fold_left Pervasives.max 0 (List.mapi (fun n max -> if List.mem n containing then max else 0) maxs) in
626 let maxs = List.mapi (fun i m -> if List.mem i containing then neww+1 else m) maxs in
628 ) ([],maxs) (Array.to_list (Array.init (max+1) (fun x -> x))) in
629 replace_in_sigma (List.rev perm) p.sigma
632 let env_of_sigma freshno sigma should_explode =
639 e,Pure.lift (-n-1) (snd (List.find (fun (i,_) -> i = n) sigma)),[]
642 if should_explode && n = hd_of_i_var (cast_to_i_var !bomb)
643 then ([], (let f t = Pure.A(t,t) in f (Pure.L (f (Pure.V 0)))), [])
644 else ([],Pure.V n,[]))::e
648 prerr_endline "########## main ##########";;
651 v ==> v := \a. a k1 .. kn \^m.0
652 + ==> v := \^k. numero for every v such that ...
653 * ==> tries v as long as possible and then +v as long as possible
656 let rec aux ({ps} as p) n l =
657 if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then begin
660 let _ = prerr_endline (print_problem "main" p) in
664 | [] -> read_line (),[] in
673 | `DoneWith -> assert false (*aux (eat p) n l*) (* CSC: TODO *)
675 let x = var_of_string x in
676 aux (instantiate p x n) n l
677 | `Auto -> aux (auto p n) n l
681 Console.print_hline();
682 bomb := `Var (-1,-666);
683 let p_finale = aux p n cmds in
684 let freshno,sigma = p_finale.freshno, p_finale.sigma in
685 prerr_endline ("------- <DONE> ------\n ");
686 (* prerr_endline (print_problem "Original problem" p); *)
687 prerr_endline "---------------------";
688 let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
689 prerr_endline (" BOMB == " ^ print ~l !bomb);
690 prerr_endline "---------------------";
691 List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
693 prerr_endline "----------------------";
695 List.fold_left (fun ps (x,inst) ->
696 (* CSC: XXXX Is the subst always sorted correctly? Otherwise, implement a recursive subst *)
697 (* In this non-recursive version, the intermediate states may containt Matchs *)
698 List.map (fun t -> let t = subst false x inst (t :> nf) in cast_to_i_num_var t) ps)
699 (p.ps :> i_num_var list) sigma in
700 prerr_endline (print_problem {p with ps= List.map (function t -> cast_to_i_n_var t) ps; freshno});
701 List.iteri (fun i (n,more_args) -> assert (more_args = 0 && n = `N i)) ps ;
703 prerr_endline "---------<OPT>----------";
704 let sigma = optimize_numerals p_finale in (* optimize numerals *)
705 let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
706 List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
707 prerr_endline "---------<PURE>---------";
708 let div = option_map (fun div -> ToScott.t_of_nf (div :> nf)) p.div in
709 let conv = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.conv in
710 let ps = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.ps in
711 let sigma = List.map (fun (x,inst) -> x, ToScott.t_of_nf inst) sigma in
712 (*let ps_ok = List.fold_left (fun ps (x,inst) ->
713 List.map (Pure.subst false x inst) ps) ps sigma in*)
714 let e = env_of_sigma freshno sigma true in
715 let e' = env_of_sigma freshno sigma false in
718 prerr_endline "---------<PPP>---------";
720 "[" ^ String.concat ";" (List.map (fun (e,t,[]) -> print_e e ^ ":" ^ Pure.print t) e) ^ "]"
722 prerr_endline (print_e e);
723 List.iter (fun (t,t_ok) ->
724 prerr_endline ("T0= " ^ Pure.print t ^ "\nTM= " ^ Pure.print (Pure.unwind (e,t,[])) ^ "\nOM= " ^ Pure.print t_ok);
725 (*assert (Pure.unwind (e,t,[]) = t_ok)*)
726 ) (List.combine ps ps_ok);
728 prerr_endline "--------<REDUCE>---------";
729 (function Some div ->
730 print_endline (Pure.print div);
731 let t = Pure.mwhd (e',div,[]) in
732 prerr_endline ("*:: " ^ (Pure.print t));
733 prerr_endline (print !bomb);
734 assert (t = ToScott.t_of_nf (!bomb:>nf))
737 prerr_endline ("_::: " ^ (Pure.print n));
738 let t = Pure.mwhd (e,n,[]) in
739 prerr_endline ("_:: " ^ (Pure.print t))
741 List.iteri (fun i n ->
742 prerr_endline ((string_of_int i) ^ "::: " ^ (Pure.print n));
743 let t = Pure.mwhd (e,n,[]) in
744 prerr_endline ((string_of_int i) ^ ":: " ^ (Pure.print t));
745 assert (t = Scott.mk_n i)
747 prerr_endline "-------- </DONE> --------"
750 (********************** problems *******************)
752 let zero = `Var(0,0);;
757 | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
761 type t = problem * int * string list;;
763 let magic_conv ~div ~conv ~nums cmds =
764 let all_tms = (match div with None -> [] | Some div -> [div]) @ nums @ conv in
765 let all_tms, var_names = parse' all_tms in
766 let div, (tms, conv) = match div with
767 | None -> None, list_cut (List.length nums, all_tms)
768 | Some _ -> Some (List.hd all_tms), list_cut (List.length nums, List.tl all_tms) in
770 if match div with None -> false | Some div -> List.exists (eta_subterm div) (tms@conv)
772 prerr_endline "--- TEST SKIPPED ---";
773 {freshno=0; div=None; conv=[]; ps=[]; sigma=[]; deltas=[]; initialSpecialK=0}, 0, []
775 let tms = sort_uniq ~compare:eta_compare tms in
776 let special_k = compute_special_k (Listx.from_list all_tms) in (* compute initial special K *)
778 let div = option_map cast_to_i_var div in
779 let conv = Util.filter_map (function #i_n_var as t -> Some (cast_to_i_n_var t) | _ -> None) conv in
780 let tms = List.map cast_to_i_n_var tms in
782 let ps = List.map append_zero tms in (* crea lista applicando zeri o dummies *)
783 let freshno = List.length var_names in
785 let dummy = `Var (max_int / 2, -666) in
786 [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
788 {freshno; div; conv; ps; sigma=[] ; deltas; initialSpecialK=special_k}, special_k, cmds
791 let magic strings cmds = magic_conv None [] strings cmds;;