6 let bomb = ref(`Var(-1,-666));;
10 ; div: i_var option (* None = bomb *)
11 ; conv: i_n_var list (* the inerts that must converge *)
12 ; ps: i_n_var list (* the n-th inert must become n *)
13 ; sigma: (int * nf) list (* the computed substitution *)
14 ; deltas: (int * nf) list ref list (* collection of all branches *)
18 (* let heads = Util.sort_uniq (List.map hd_of_i_var p.ps) in
20 List.map (fun (_, bs) -> List.map (fun (x,_) -> List.nth p.ps x) !bs) p.deltas *)
22 (* let ($) f x = f x;; *)
24 (* let subterms tms freshno =
26 let no = ref freshno in
27 function t -> incr no; mk_app t (`Var !no) in
28 let applicative hd args = snd (
29 List.fold_left (fun (hd, acc) t -> let hd = mk_app hd t in hd, hd::acc) (hd, []) args) in
30 let rec aux t = match t with
33 (* applicative (`Var v) (Listx.to_list ts) @ *)
34 Util.concat_map aux (Listx.to_list ts) @ List.map apply_var (Listx.to_list ts)
35 | `Lam(_,_,t) -> aux (lift ~-1 t)
36 | `Match(u,_,bs_lift,bs,args) ->
38 (* applicative (`Match(u,bs_lift,bs,[])) args @ *)
39 Util.concat_map aux args @ List.map apply_var args
40 (* @ Util.concat_map (aux ++ (lift bs_lift) ++ snd) !bs *)
42 in let tms' = (* Util.sort_uniq ~compare:eta_compare*) (Util.concat_map aux tms) in
44 (* 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)) *)
48 (match p.div with None -> [] | Some t -> [(t :> i_n_var)])
53 let problem_measure p = 0 ;;
55 let print_problem label ({freshno; div; conv; ps; deltas} as p) =
56 Console.print_hline ();
57 prerr_endline ("\n||||| Displaying problem: " ^ label ^ " |||||");
59 let deltas = String.concat nl (List.map (fun r -> String.concat " <> " (List.map (fun (i,_) -> string_of_int i) !r)) deltas) in
60 let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
61 nl ^ "measure="^string_of_int(problem_measure p)^" freshno = " ^ string_of_int freshno
62 ^ nl ^ "\b> DISCRIMINATING SETS (deltas)"
63 ^ nl ^ deltas ^ (if deltas = "" then "" else nl)
64 ^ "\b> DIVERGENT" ^ nl
65 ^ "*: " ^ (match div with None -> "*" | Some div -> print ~l (div :> nf)) ^ "\n| "
66 ^ "\b> CONVERGENT" ^ nl
67 ^ String.concat "\n| " (List.map (fun t -> "_: " ^ (if t = `N (-1) then "_" else print ~l (t :> nf))) conv) ^
68 (if conv = [] then "" else "\n| ")
70 ^ String.concat "\n| " (List.mapi (fun i t -> string_of_int i ^ ": " ^ print ~l (t :> nf)) ps)
75 let failwithProblem p reason =
76 print_endline (print_problem "FAIL" p);
80 let make_fresh_var p arity =
81 let freshno = p.freshno + 1 in
82 {p with freshno}, `Var(freshno,arity)
85 let make_fresh_vars p arities =
87 (* fold_left vs. fold_right hides/shows the bug in problem q7 *)
88 (fun arity (p, vars) -> let p, var = make_fresh_var p arity in p, var::vars)
93 let simple_expand_match ps =
94 let rec aux level = function
95 | #i_num_var as t -> aux_i_num_var level t
96 | `Lam(b,t) -> `Lam(b,aux (level+1) t)
97 and aux_i_num_var level = function
98 | `Match(u,v,bs_lift,bs,args) as torig ->
99 let u = aux_i_num_var level u in
100 bs := List.map (fun (n, x) -> n, aux 0 x) !bs;
104 let i = index_of (lift (-level) u) (ps :> nf list) (* can raise Not_found *)
105 in let t = mk_match (`N i) v bs_lift bs args in
109 | _ -> raise Not_found)
111 `Match(cast_to_i_num_var u,v,bs_lift,bs,List.map (aux level) args))
112 | `I(v,args) -> `I(v,Listx.map (aux level) args)
113 | `N _ | `Var _ as t -> t
117 let rec aux x = let x' = f x in if x <> x' then aux x' else x in aux
120 let rec super_simplify_ps ps =
121 fixpoint (List.map (cast_to_i_num_var ++ (simple_expand_match ps)))
124 let super_simplify ({div; ps; conv} as p) =
125 let ps = super_simplify_ps p.ps (p.ps :> i_num_var list) in
126 let conv = super_simplify_ps ps (p.conv :> i_num_var list) in
127 let div = option_map (fun div ->
128 let divs = super_simplify_ps p.ps ([div] :> i_num_var list) in
130 {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}
132 exception ExpandedToLambda;;
134 let subst_in_problem x inst ({freshno; div; conv; ps; sigma} as p) =
135 let len_ps = List.length ps in
136 (*(let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
137 prerr_endline ("# INST0: " ^ string_of_var x ^ " := " ^ print ~l inst));*)
138 let rec aux ((freshno,acc_ps,acc_new_ps) as acc) =
142 (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
143 let t = subst false x inst (t :> nf) in
144 (*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
145 let freshno,new_t,acc_new_ps =
146 expand_match (freshno,acc_ps@`Var(max_int/3,-666)::todo_ps,acc_new_ps) t
148 aux (freshno,acc_ps@[new_t],acc_new_ps) todo_ps
150 (* cut&paste from aux above *)
151 and aux' ps ((freshno,acc_conv,acc_new_ps) as acc) =
155 (*prerr_endline ("EXPAND t:" ^ print (t :> nf));*)
157 let t = subst false x inst (t :> nf) in
158 (*prerr_endline ("SUBSTITUTED t:" ^ print (t :> nf));*)
159 let freshno,new_t,acc_new_ps =
160 expand_match (freshno,ps,acc_new_ps) t
162 aux' ps (freshno,acc_conv@[new_t],acc_new_ps) todo_conv
163 (* with ExpandedToLambda -> aux' ps (freshno,acc_conv@[`N(-1)],acc_new_ps) todo_conv *)
165 (* cut&paste from aux' above *)
166 and aux'' ps (freshno,acc_new_ps) =
168 | None -> freshno, None, acc_new_ps
170 let t = subst false x inst (t :> nf) in
171 let freshno,new_t,acc_new_ps =
172 expand_match (freshno,ps,acc_new_ps) t
174 freshno,Some new_t,acc_new_ps
176 and expand_match ((freshno,acc_ps,acc_new_ps) as acc) t =
178 | `Match(u',orig,bs_lift,bs,args) ->
179 let freshno,u,acc_new_ps = expand_match acc (u' :> nf) in
182 | `N i -> acc_new_ps,i
184 let ps = List.map (fun t -> cast_to_i_num_var (subst false x inst (t:> nf))) (acc_ps@acc_new_ps) in
185 let super_simplified_ps = super_simplify_ps ps ps in
186 (*prerr_endline ("CERCO u:" ^ print (fst u :> nf));
187 List.iter (fun x -> prerr_endline ("IN: " ^ print (fst x :> nf))) ps;
188 List.iter (fun x -> prerr_endline ("IN2: " ^ print (fst x :> nf))) super_simplified_ps;*)
189 match index_of_opt ~eq:eta_eq super_simplified_ps u with
190 Some i -> acc_new_ps, i
191 | None -> acc_new_ps@[u], len_ps + List.length acc_new_ps
194 if List.exists (fun (j,_) -> i=j) !bs then
197 let freshno,v = freshno+1, `Var (freshno+1, snd orig - 1) in (* make_fresh_var freshno in *)
200 (*prerr_endlie ("t DA RIDURRE:" ^ print (`Match(`N i,arity,bs_lift,bs,args) :> nf) ^ " more_args=" ^ string_of_int more_args);*)
201 let t = mk_match (`N i) orig bs_lift bs args in
202 (*prerr_endline ("NUOVO t:" ^ print (fst t :> nf) ^ " more_args=" ^ string_of_int (snd t));*)
203 expand_match (freshno,acc_ps,acc_new_ps) t
204 | `Lam _ -> raise ExpandedToLambda
206 let x = simple_expand_match (acc_ps@acc_new_ps) x in
207 freshno,cast_to_i_num_var x,acc_new_ps in
209 let freshno,old_ps,new_ps = aux (freshno,[],[]) (ps :> i_num_var list) in
210 let freshno,conv,new_ps = aux' old_ps (freshno,[],new_ps) (conv :> i_num_var list) in
211 let freshno,div,new_ps = aux'' old_ps (freshno,new_ps) (div :> i_num_var option) in
212 let div = option_map cast_to_i_var div in
213 let ps = List.map cast_to_i_n_var (old_ps @ new_ps) in
214 let conv = List.map cast_to_i_n_var conv in
215 (let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
216 prerr_endline ("# INST: " ^ string_of_var x ^ " := " ^ print ~l inst));
217 let p = {p with freshno; div; conv; ps} in
218 ( (* check if double substituting a variable *)
219 if List.exists (fun (x',_) -> x = x') sigma
220 then failwithProblem p "Variable replaced twice"
222 let p = {p with sigma = sigma@[x,inst]} in
223 let p = super_simplify p in
224 prerr_endline (print_problem "instantiate" p);
230 let arity_of arities k =
231 let _,pos,y = List.find (fun (v,_,_) -> v=k) arities in
232 let arity = match y with `Var _ -> 0 | `I(_,args) -> Listx.length args | _ -> assert false in
233 arity + if pos = -1 then - 1 else 0
236 let rec dangerous arities showstoppers =
241 | `Match(t,_,liftno,bs,args) ->
242 (* CSC: XXX partial dependency on the encoding *)
244 `N _ -> List.iter (dangerous arities showstoppers) args
245 | `Match _ as t -> dangerous arities showstoppers t ; List.iter (dangerous arities showstoppers) args
246 | `Var(x,_) -> dangerous_inert arities showstoppers x args 2 (* 2 coming from Scott's encoding *)
247 | `I((x,_),args') -> dangerous_inert arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
249 | `I((k,_),args) -> dangerous_inert arities showstoppers k (Listx.to_list args) 0
251 and dangerous_inert arities showstoppers k args more_args =
252 List.iter (dangerous arities showstoppers) args ;
253 if List.mem k showstoppers then raise Dangerous else
255 let arity = arity_of arities k in
256 if List.length args + more_args > arity then raise Dangerous else ()
260 (* cut & paste from above *)
261 let rec dangerous_conv arities showstoppers =
266 | `Match(t,_,liftno,bs,args) ->
267 (* CSC: XXX partial dependency on the encoding *)
269 `N _ -> concat_map (dangerous_conv arities showstoppers) args
270 | `Match _ as t -> dangerous_conv arities showstoppers t @ concat_map (dangerous_conv arities showstoppers) args
271 | `Var(x,_) -> dangerous_inert_conv arities showstoppers x args 2 (* 2 coming from Scott's encoding *)
272 | `I((x,_),args') -> dangerous_inert_conv arities showstoppers x (Listx.to_list args' @ args) 2 (* 2 coming from Scott's encoding *)
274 | `I((k,_),args) -> dangerous_inert_conv arities showstoppers k (Listx.to_list args) 0
276 and dangerous_inert_conv arities showstoppers k args more_args =
277 concat_map (dangerous_conv arities showstoppers) args @
278 if List.mem k showstoppers then k :: concat_map free_vars args else
280 let arity = arity_of arities k in
281 prerr_endline ("dangerous_inert_conv: ar=" ^ string_of_int arity ^ " k="^string_of_var k ^ " listlenargs=" ^ (string_of_int (List.length args)) );
282 if List.length args + more_args > arity then k :: concat_map free_vars args else []
286 (* inefficient algorithm *)
287 let rec edible arities div ps conv showstoppers =
288 let rec aux showstoppers =
291 | x::xs when List.exists (fun y -> hd_of x = Some y) showstoppers ->
292 (* se la testa di x e' uno show-stopper *)
293 let new_showstoppers = sort_uniq (showstoppers @ free_vars (x :> nf)) in
294 (* aggiungi tutte le variabili libere di x *)
295 if List.length showstoppers <> List.length new_showstoppers then
296 aux new_showstoppers ps
301 None -> aux showstoppers xs
304 dangerous arities showstoppers (x : i_n_var :> nf) ;
308 aux (sort_uniq (h::showstoppers)) ps
310 let showstoppers = sort_uniq (aux showstoppers ps) in
312 List.map (dangerous_conv arities showstoppers) (conv :> nf list) in
314 prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
315 List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv;
316 let showstoppers' = showstoppers @ List.concat dangerous_conv in
317 let showstoppers' = sort_uniq (match div with
318 | None -> showstoppers'
320 if List.exists ((=) (hd_of_i_var div)) showstoppers'
321 then showstoppers' @ free_vars (div :> nf) else showstoppers') in
322 if showstoppers <> showstoppers' then edible arities div ps conv showstoppers' else showstoppers', dangerous_conv
325 let precompute_edible_data {ps; div} xs =
326 (match div with None -> [] | Some div -> [hd_of_i_var div, -1, (div :> i_n_var)]) @
328 let i, tm = Util.findi (fun y -> hd_of y = Some hd) ps in
333 let critical_showstoppers p =
334 let p = super_simplify p in
335 let hd_of_div = match p.div with None -> [] | Some t -> [hd_of_i_var t] in
336 let showstoppers_step =
337 concat_map (fun bs ->
338 let heads = List.map (fun (i,_) -> List.nth p.ps i) !bs in
339 let heads = List.sort compare (hd_of_div @ filter_map hd_of heads) in
340 snd (split_duplicates heads)
342 if List.exists (fun t -> [hd_of t] = List.map (fun x -> Some x) hd_of_div) p.conv
343 then hd_of_div else [] in
344 let showstoppers_step = sort_uniq showstoppers_step in
345 let showstoppers_eat =
346 let heads_and_arities =
347 List.sort (fun (k,_) (h,_) -> compare k h)
348 (filter_map (function `Var(k,_) -> Some (k,0) | `I((k,_),args) -> Some (k,Listx.length args) | _ -> None ) p.ps) in
349 let rec multiple_arities =
353 | (x,i)::(y,j)::tl when x = y && i <> j ->
354 x::multiple_arities tl
355 | _::tl -> multiple_arities tl in
356 multiple_arities heads_and_arities in
358 let showstoppers_eat = sort_uniq showstoppers_eat in
359 let showstoppers_eat = List.filter
360 (fun x -> not (List.mem x showstoppers_step))
362 List.iter (fun v -> prerr_endline ("DANGEROUS STEP: " ^ string_of_var v)) showstoppers_step;
363 List.iter (fun v -> prerr_endline ("DANGEROUS EAT: " ^ string_of_var v)) showstoppers_eat;
364 p, showstoppers_step, showstoppers_eat
368 let ({ps} as p), showstoppers_step, showstoppers_eat = critical_showstoppers p in
369 let showstoppers = showstoppers_step @ showstoppers_eat in
370 let heads = List.sort compare (filter_map hd_of ps) in
371 let arities = precompute_edible_data p (uniq heads) in
372 let showstoppers, showstoppers_conv =
373 edible arities p.div ps p.conv showstoppers in
374 let l = List.filter (fun (x,_,_) -> not (List.mem x showstoppers)) arities in
376 List.fold_left (fun p (x,pos,(xx : i_n_var)) -> if pos = -1 then p else
377 let n = match xx with `I(_,args) -> Listx.length args | _ -> 0 in
379 let inst = make_lams v n in
380 (let l = Array.to_list (Array.init (p.freshno + 1) string_of_var) in
381 prerr_endline ("# INST_IN_EAT: " ^ string_of_var x ^ " := " ^ print ~l inst));
382 { p with sigma = p.sigma @ [x,inst] }
384 (* to avoid applied numbers in safe positions that
385 trigger assert failures subst_in_problem x inst p*)
389 let _,j,_ = List.find (fun (h,_,_) -> hd_of t = Some h) l in
393 let p = match p.div with
396 if List.mem (hd_of_i_var div) showstoppers
399 let n = match div with `I(_,args) -> Listx.length args | `Var _ -> 0 in
400 let p, bomb' = make_fresh_var p (-666) in
401 (if !bomb <> `Var (-1,-666) then
403 ("Bomb was duplicated! It was " ^ string_of_nf !bomb ^
404 ", tried to change it to " ^ string_of_nf bomb'));
406 prerr_endline ("Just created bomb var: " ^ string_of_nf !bomb);
407 let x = hd_of_i_var div in
408 let inst = make_lams !bomb n in
409 prerr_endline ("# INST (div): " ^ string_of_var x ^ " := " ^ string_of_nf inst);
410 let p = {p with div=None} in
411 (* subst_in_problem (hd_of_i_var div) inst p in *)
412 {p with sigma=p.sigma@[x,inst]} in
413 let dangerous_conv = showstoppers_conv in
414 let _ = prerr_endline ("dangerous_conv lenght:" ^ string_of_int (List.length dangerous_conv));
415 List.iter (fun l -> prerr_endline (String.concat " " (List.map string_of_var l))) dangerous_conv; in
417 List.map (function s,t ->
419 if s <> [] then t else (
420 (match t with | `Var _ -> raise Not_found | _ -> ());
421 let _ = List.find (fun h -> hd_of t = Some h) showstoppers in
423 with Not_found -> match hd_of t with
424 | None -> assert (t = `N ~-1); t
426 prerr_endline ("FREEZING " ^ string_of_var h);
427 `N ~-1 (* convergent dummy*)
428 ) (List.combine showstoppers_conv p.conv) in
434 match List.nth ps n with
439 let old_conv = p.conv in
440 let p = { p with ps; conv } in
441 if l <> [] || old_conv <> conv
442 then prerr_endline (print_problem "eat" p);
443 if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then
448 let instantiate p x n =
449 (if hd_of_i_var (cast_to_i_var !bomb) = x
450 then failwithProblem p ("BOMB (" ^ string_of_nf !bomb ^ ") cannot be instantiated!"));
451 (* ACL FIXME compute arity of x correctly below! *)
452 let arity_of_x = -666 in
453 (* AC: FIXME compute arities correctly below! *)
454 let arities = Array.to_list (Array.make (n+1) 0) in
455 let p,vars = make_fresh_vars p arities in
456 (* let p,zero = make_fresh_var p in *)
457 (* let zero = Listx.Nil zero in *)
458 (* let args = if n = 0 then zero else Listx.append zero (Listx.from_list vars) in *)
459 let args = Listx.from_list (vars :> nf list) in
461 let inst = `Lam(false,`Match(`I((0,0),Listx.map (lift 1) args),(x,arity_of_x),1,bs,[])) in
462 let p = {p with deltas=bs::p.deltas} in
463 subst_in_problem x inst p
466 let compute_special_k tms =
467 let rec aux k (t: nf) = Pervasives.max k (match t with
468 | `Lam(b,t) -> aux (k + if b then 1 else 0) t
469 | `I(n, tms) -> Listx.max (Listx.map (aux 0) tms)
470 | `Match(t, _, liftno, bs, args) ->
471 List.fold_left max 0 (List.map (aux 0) ((t :> nf)::args@List.map snd !bs))
474 ) in Listx.max (Listx.map (aux 0) tms)
477 let auto_instantiate (n,p) =
478 let p, showstoppers_step, showstoppers_eat = critical_showstoppers p in
480 match showstoppers_step, showstoppers_eat with
482 prerr_endline ("INSTANTIATING CRITICAL TO EAT " ^ string_of_var y); y
484 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
488 prerr_endline ("INSTANTIATING TO EAT " ^ string_of_var x);
491 prerr_endline ("INSTANTIATING " ^ string_of_var x);
493 (* Strategy that decreases the special_k to 0 first (round robin)
494 1:11m42 2:14m5 3:11m16s 4:14m46s 5:12m7s 6:6m31s *)
497 match hd_of (List.find (fun t -> compute_special_k (Listx.Nil (t :> nf)) > 0) (all_terms p)) with
500 prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
505 (* Instantiate in decreasing order of compute_special_k
506 1:15m14s 2:13m14s 3:4m55s 4:4m43s 5:4m34s 6:6m28s 7:3m31s
509 (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
512 prerr_endline ("INSTANTIATING AND HOPING " ^ string_of_var x);
518 compute_special_k (Listx.from_list (all_terms p :> nf list) )in
519 if special_k < n then
520 prerr_endline ("@@@@ NEW INSTANTIATE PHASE (" ^ string_of_int special_k ^ ") @@@@");
521 let p = instantiate p x special_k in
525 let rec auto_eat (n,({ps} as p)) =
526 prerr_endline "{{{{{{{{ Computing measure before auto_instantiate }}}}}}";
527 let m = problem_measure p in
528 let (n,p') = auto_instantiate (n,p) in
532 prerr_endline "{{{{{{{{ Computing measure inafter auto_instantiate }}}}}}";
533 let delta = m - problem_measure p' in
535 (* failwithProblem p' *)
537 ("Measure did not decrease (delta=" ^ string_of_int delta ^ ")"))
538 else prerr_endline ("$ Measure decreased by " ^ string_of_int delta);
543 prerr_endline ("@@@@ FIRST INSTANTIATE PHASE (" ^ string_of_int n ^ ") @@@@");
546 | `Continue p -> auto_eat (n,p)
552 x y = y 0 a y = k k z = z 0 c y = k y u = u h1 h2 0 h2 a = h3
553 1 x a c 1 a 0 c 1 k c 1 c 0 1 k 1 k 1 k
554 2 x a y 2 a 0 y 2 k y 2 y 0 2 y 0 2 h2 0 2 h3
555 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)
556 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
557 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
558 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
561 b u = u l1 l2 0 e _ _ _ _ = f l3 n = n j 0
564 3 l2 0 (\u. u h1 (\w. h3) 0) 3 l3 (\u. u h1 (\w. h3) 0) 3 j h1 (\w. h3) 0 0
565 4 l2 0 c 4 l3 c 4 c j 0
566 5 e l1 l2 0 0 5 f 5 f
567 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
572 x a (b (a c)) a 0 = 1 ? (b (a c)) 8
573 x a (b d') a 0 = 1 ? (b d') 7
574 x b (a c) b 0 = 1 ? (a c) 4
575 x b (a c') b 0 = 1 ? (a c') 5
583 b 4 = 8 (* b (a c) *)
588 (************** Tests ************************)
590 let optimize_numerals p =
591 let replace_in_sigma perm =
592 let rec aux = function
593 | `N n -> `N (List.nth perm n)
594 | `I _ -> assert false
596 | `Lam(v,t) -> `Lam(v, aux t)
597 | `Match(_,_,_,bs,_) as t -> (bs := List.map (fun (n,t) -> (List.nth perm n, t)) !bs); t
598 in List.map (fun (n,t) -> (n,aux t))
600 let deltas' = List.mapi (fun n d -> (n, List.map fst !d)) p.deltas in
601 let maxs = Array.to_list (Array.init (List.length deltas') (fun _ -> 0)) in
602 let max = List.fold_left max 0 (concat_map snd deltas') in
603 let perm,_ = List.fold_left (fun (perm, maxs) (curr_n:int) ->
604 let containing = filter_map (fun (i, bs) -> if List.mem curr_n bs then Some i else None) deltas' in
605 (* (prerr_endline (string_of_int curr_n ^ " occurs in: " ^ (String.concat " " (List.map string_of_int containing)))); *)
606 let neww = List.fold_left Pervasives.max 0 (List.mapi (fun n max -> if List.mem n containing then max else 0) maxs) in
607 let maxs = List.mapi (fun i m -> if List.mem i containing then neww+1 else m) maxs in
609 ) ([],maxs) (Array.to_list (Array.init (max+1) (fun x -> x))) in
610 replace_in_sigma (List.rev perm) p.sigma
613 let env_of_sigma freshno sigma should_explode =
620 e,Pure.lift (-n-1) (snd (List.find (fun (i,_) -> i = n) sigma)),[]
623 if should_explode && n = hd_of_i_var (cast_to_i_var !bomb)
624 then ([], (let f t = Pure.A(t,t) in f (Pure.L (f (Pure.V 0)))), [])
625 else ([],Pure.V n,[]))::e
629 prerr_endline "########## main ##########";;
632 v ==> v := \a. a k1 .. kn \^m.0
633 + ==> v := \^k. numero for every v such that ...
634 * ==> tries v as long as possible and then +v as long as possible
637 let rec aux ({ps} as p) n l =
638 if List.for_all (function `N _ -> true | _ -> false) ps && p.div = None then begin
641 let _ = prerr_endline (print_problem "main" p) in
645 | [] -> read_line (),[] in
654 | `DoneWith -> assert false (*aux (eat p) n l*) (* CSC: TODO *)
656 let x = var_of_string x in
657 aux (instantiate p x n) n l
658 | `Auto -> aux (auto p n) n l
662 Console.print_hline();
663 bomb := `Var (-1,-666);
664 let p_finale = aux p n cmds in
665 let freshno,sigma = p_finale.freshno, p_finale.sigma in
666 prerr_endline ("------- <DONE> ------\n ");
667 (* prerr_endline (print_problem "Original problem" p); *)
668 prerr_endline "---------------------";
669 let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
670 prerr_endline (" BOMB == " ^ print ~l !bomb);
671 prerr_endline "---------------------";
672 List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
674 prerr_endline "----------------------";
676 List.fold_left (fun ps (x,inst) ->
677 (* CSC: XXXX Is the subst always sorted correctly? Otherwise, implement a recursive subst *)
678 (* In this non-recursive version, the intermediate states may containt Matchs *)
679 List.map (fun t -> let t = subst false x inst (t :> nf) in cast_to_i_num_var t) ps)
680 (p.ps :> i_num_var list) sigma in
681 prerr_endline (print_problem {p with ps= List.map (function t -> cast_to_i_n_var t) ps; freshno});
682 List.iteri (fun i (n,more_args) -> assert (more_args = 0 && n = `N i)) ps ;
684 prerr_endline "---------<OPT>----------";
685 let sigma = optimize_numerals p_finale in (* optimize numerals *)
686 let l = Array.to_list (Array.init (freshno + 1) string_of_var) in
687 List.iter (fun (x,inst) -> prerr_endline (string_of_var x ^ " := " ^ print ~l inst)) sigma;
688 prerr_endline "---------<PURE>---------";
689 let div = option_map (fun div -> ToScott.t_of_nf (div :> nf)) p.div in
690 let conv = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.conv in
691 let ps = List.map (fun t -> ToScott.t_of_nf (t :> nf)) p.ps in
692 let sigma = List.map (fun (x,inst) -> x, ToScott.t_of_nf inst) sigma in
693 (*let ps_ok = List.fold_left (fun ps (x,inst) ->
694 List.map (Pure.subst false x inst) ps) ps sigma in*)
695 let e = env_of_sigma freshno sigma true in
696 let e' = env_of_sigma freshno sigma false in
699 prerr_endline "---------<PPP>---------";
701 "[" ^ String.concat ";" (List.map (fun (e,t,[]) -> print_e e ^ ":" ^ Pure.print t) e) ^ "]"
703 prerr_endline (print_e e);
704 List.iter (fun (t,t_ok) ->
705 prerr_endline ("T0= " ^ Pure.print t ^ "\nTM= " ^ Pure.print (Pure.unwind (e,t,[])) ^ "\nOM= " ^ Pure.print t_ok);
706 (*assert (Pure.unwind (e,t,[]) = t_ok)*)
707 ) (List.combine ps ps_ok);
709 prerr_endline "--------<REDUCE>---------";
710 (function Some div ->
711 print_endline (Pure.print div);
712 let t = Pure.mwhd (e',div,[]) in
713 prerr_endline ("*:: " ^ (Pure.print t));
714 prerr_endline (print !bomb);
715 assert (t = ToScott.t_of_nf (!bomb:>nf))
718 prerr_endline ("_::: " ^ (Pure.print n));
719 let t = Pure.mwhd (e,n,[]) in
720 prerr_endline ("_:: " ^ (Pure.print t))
722 List.iteri (fun i n ->
723 prerr_endline ((string_of_int i) ^ "::: " ^ (Pure.print n));
724 let t = Pure.mwhd (e,n,[]) in
725 prerr_endline ((string_of_int i) ^ ":: " ^ (Pure.print t));
726 assert (t = Scott.mk_n i)
728 prerr_endline "-------- </DONE> --------"
731 (********************** problems *******************)
733 let zero = `Var(0,-1);;
738 | `Var _ as i -> cast_to_i_n_var (mk_app i zero)
742 type t = problem * int * string list;;
744 let magic_conv ~div ~conv ~nums cmds =
745 let all_tms = (match div with None -> [] | Some div -> [div]) @ nums @ conv in
746 let all_tms, var_names = parse' all_tms in
747 let div, (tms, conv) = match div with
748 | None -> None, list_cut (List.length nums, all_tms)
749 | Some _ -> Some (List.hd all_tms), list_cut (List.length nums, List.tl all_tms) in
751 if match div with None -> false | Some div -> List.exists (eta_subterm div) (tms@conv)
753 prerr_endline "--- TEST SKIPPED ---";
754 {freshno=0; div=None; conv=[]; ps=[]; sigma=[]; deltas=[]}, 0, []
756 let tms = sort_uniq ~compare:eta_compare tms in
757 let special_k = compute_special_k (Listx.from_list all_tms) in (* compute initial special K *)
759 let div = option_map cast_to_i_var div in
760 let conv = List.map cast_to_i_n_var conv in
761 let tms = List.map cast_to_i_n_var tms in
763 let ps = List.map append_zero tms in (* crea lista applicando zeri o dummies *)
764 let freshno = List.length var_names in
766 let dummy = `Var (max_int / 2, -666) in
767 [ ref (Array.to_list (Array.init (List.length ps) (fun i -> i, dummy))) ] in
769 {freshno; div; conv; ps; sigma=[] ; deltas}, special_k, cmds
772 let magic strings cmds = magic_conv None [] strings cmds;;