1 (* Copyright (C) 2003-2005, HELM Team.
3 * This file is part of HELM, an Hypertextual, Electronic
4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
7 * HELM is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU General Public License
9 * as published by the Free Software Foundation; either version 2
10 * of the License, or (at your option) any later version.
12 * HELM is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
17 * You should have received a copy of the GNU General Public License
18 * along with HELM; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
22 * For details, see the HELM World-Wide-Web page,
23 * http://cs.unibo.it/helm/.
28 module S = CicSubstitution
29 module R = CicReduction
30 module TC = CicTypeChecker
32 module UM = UriManager
33 module Obj = LibraryObjects
36 module E = CicEnvironment
38 module PEH = ProofEngineHelpers
40 module DTI = DoubleTypeInference
41 module NU = CicNotationUtil
45 module Cl = ProceduralClassify
46 module T = ProceduralTypes
47 module Cn = ProceduralConversion
48 module H = ProceduralHelpers
51 sorts : (C.id, A.sort_kind) Hashtbl.t;
52 types : (C.id, A.anntypes) Hashtbl.t;
53 params : G.inline_param list;
54 max_depth: int option;
64 (* helpers ******************************************************************)
66 let split2_last l1 l2 =
68 let n = pred (List.length l1) in
69 let before1, after1 = HEL.split_nth n l1 in
70 let before2, after2 = HEL.split_nth n l2 in
71 before1, before2, List.hd after1, List.hd after2
72 with Invalid_argument _ -> failwith "A2P.split2_last"
74 let string_of_head = function
76 | C.AConst _ -> "const"
77 | C.AMutInd _ -> "mutind"
78 | C.AMutConstruct _ -> "mutconstruct"
82 | C.ALambda _ -> "lambda"
83 | C.ALetIn _ -> "letin"
85 | C.ACoFix _ -> "cofix"
88 | C.AMutCase _ -> "mutcase"
90 | C.AImplicit _ -> "implict"
92 let next st = {st with depth = succ st.depth}
94 let add st entry = {st with context = entry :: st.context}
96 let push st = {st with case = 1 :: st.case}
99 {st with case = match st.case with
101 | hd :: tl -> succ hd :: tl
105 let case = String.concat "." (List.rev_map string_of_int st.case) in
106 Printf.sprintf "case %s: %s" case str
110 let msg = Printf.sprintf "Depth %u: " st.depth in
111 match st.max_depth with
113 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
114 with Invalid_argument _ -> failwith "A2P.test_depth"
116 let is_rewrite_right st = function
117 | C.AConst (_, uri, []) -> st.defaults && Obj.is_eq_ind_r_URI uri
120 let is_rewrite_left st = function
121 | C.AConst (_, uri, []) -> st.defaults && Obj.is_eq_ind_URI uri
124 let is_fwd_rewrite_right st hd tl =
125 if is_rewrite_right st hd then match List.nth tl 3 with
130 let is_fwd_rewrite_left st hd tl =
131 if is_rewrite_left st hd then match List.nth tl 3 with
136 let get_inner_types st v =
138 let id = Ut.id_of_annterm v in
139 try match Hashtbl.find st.types id with
140 | {A.annsynthesized = ity; A.annexpected = Some ety} -> Some (ity, ety)
141 | {A.annsynthesized = ity; A.annexpected = None} -> Some (ity, ity)
142 with Not_found -> None
143 with Invalid_argument _ -> failwith "P2.get_inner_types"
145 let get_entry st id =
146 let rec aux = function
148 | Some (C.Name name, e) :: _ when name = id -> e
153 let string_of_atomic = function
154 | C.ARel (_, _, _, s) -> s
155 | C.AVar (_, uri, _) -> H.name_of_uri uri None None
156 | C.AConst (_, uri, _) -> H.name_of_uri uri None None
157 | C.AMutInd (_, uri, i, _) -> H.name_of_uri uri (Some i) None
158 | C.AMutConstruct (_, uri, i, j, _) -> H.name_of_uri uri (Some i) (Some j)
161 let get_sub_names head l =
162 let s = string_of_atomic head in
163 if s = "" then [] else
164 let map (names, i) _ =
165 let name = Printf.sprintf "%s_%u" s i in name :: names, succ i
167 let names, _ = List.fold_left map ([], 1) l in
170 let get_type msg st t = H.get_type msg st.context (H.cic t)
172 let get_uri_of_head = function
173 | C.AConst (_, u, _) ->
175 | C.AAppl (_, C.AConst (_, u, _) :: vs) ->
176 Some (u, 0, 0, List.length vs)
177 | C.AMutInd (_, u, i, _) ->
178 Some (u, succ i, 0, 0)
179 | C.AAppl (_, C.AMutInd (_, u, i, _) :: vs) ->
180 Some (u, succ i, 0, List.length vs)
181 | C.AMutConstruct (_, u, i, j, _) ->
182 Some (u, succ i, j, 0)
183 | C.AAppl (_, C.AMutConstruct (_, u, i, j, _) :: vs) ->
184 Some (u, succ i, j, List.length vs)
188 let get_uri_of_apply = function
190 | T.Apply (t, _) -> get_uri_of_head t
193 let is_reflexivity st step =
194 match get_uri_of_apply step with
196 | Some (uri, i, j, n) ->
197 st.defaults && Obj.is_eq_URI uri && i = 1 && j = 1 && n = 0
199 let is_ho_reflexivity st step =
200 match get_uri_of_apply step with
202 | Some (uri, i, j, n) ->
203 st.defaults && Obj.is_eq_URI uri && i = 1 && j = 1 && n > 0
205 let are_convertible st pred sx dx =
206 let pred, sx, dx = H.cic pred, H.cic sx, H.cic dx in
207 let sx, dx = C.Appl [pred; sx], C.Appl [pred; dx] in
208 fst (R.are_convertible st.context sx dx Un.default_ugraph)
210 (* proof construction *******************************************************)
212 let anonymous_premise = C.Name "UNNAMED"
214 let mk_lapply_args hd tl classes =
215 let map _ = Cn.meta "" in
216 let args = List.rev_map map tl in
217 if args = [] then hd else C.AAppl ("", hd :: args)
219 let mk_apply_args hd tl classes synth qs =
222 if I.overlaps synth cl
223 then if b then v, v else Cn.meta "", v
224 else Cn.meta "", Cn.meta ""
226 let rec rev a = function
229 if snd hd <> Cn.meta "" then incr exp;
232 let rec aux = function
235 if fst hd = Cn.meta "" then aux tl else rev [] (hd :: tl)
237 let args = T.list_rev_map2 map tl classes in
238 let args = aux args in
239 let part = !exp < List.length tl in
240 if args = [] then part, hd, qs else part, C.AAppl ("", hd :: args), qs
242 let mk_convert st ?name sty ety note =
244 let a = ref "" in Ut.pp_term (fun s -> a := !a ^ s) [] st.context t; !a
246 let e = Cn.hole "" in
247 let csty, cety = H.cic sty, H.cic ety in
250 let sname = match name with None -> "" | Some (id, _) -> id in
251 Printf.sprintf "%s: %s\nSINTH: %s\nEXP: %s"
252 note sname (ppterm csty) (ppterm cety)
255 if H.alpha ~flatten:true st.context csty cety then [T.Note note] else
256 let sty, ety = H.acic_bc st.context sty, H.acic_bc st.context ety in
258 | None -> [T.Change (sty, ety, None, e, note)]
260 begin match get_entry st id with
262 [T.Change (ety, sty, Some (id, Some id), e, note);
266 [T.Change (ety, sty, Some (id, Some id), e, note)]
269 let convert st ?name v =
270 match get_inner_types st v with
272 if !debug then [T.Note "NORMAL: NO INNER TYPES"] else []
273 | Some (sty, ety) -> mk_convert st ?name sty ety "NORMAL"
275 let get_intro = function
276 | C.Anonymous -> None
279 let mk_preamble st what script = match script with
280 | step :: script when is_reflexivity st step ->
281 T.Reflexivity (T.note_of_step step) :: script
282 | step :: script when is_ho_reflexivity st step ->
283 convert st what @ T.Reflexivity (T.note_of_step step) :: script
284 | T.Exact _ :: _ -> script
285 | _ -> convert st what @ script
287 let mk_arg st = function
288 | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
291 let mk_fwd_rewrite st dtext name tl direction v t ity ety =
292 let compare premise = function
294 | Some s -> s = premise
296 assert (List.length tl = 6);
297 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
298 let e = Cn.mk_pattern 1 ety predicate in
299 if (Cn.does_not_occur e) then st, [] else
301 | C.ARel (_, _, i, premise) as w ->
303 let where = Some (premise, name) in
304 let script = mk_arg st what @ mk_arg st w in
305 T.Rewrite (direction, what, where, e, dtext) :: script
307 if DTI.does_not_occur (succ i) (H.cic t) || compare premise name then
308 {st with context = Cn.clear st.context premise}, script name
310 assert (Ut.is_sober st.context (H.cic ity));
311 let ity = H.acic_bc st.context ity in
312 let br1 = [T.Id ""] in
313 let br2 = List.rev (T.Exact (w, "assumption") :: script None) in
314 let text = "non-linear rewrite" in
315 st, [T.Branch ([br2; br1], ""); T.Cut (name, ity, text)]
319 let mk_rewrite st dtext where qs tl direction t ity =
321 let a = ref "" in Ut.pp_term (fun s -> a := !a ^ s) [] st.context t; !a
323 assert (List.length tl = 5);
324 let pred, sx, dx = List.nth tl 2, List.nth tl 1, List.nth tl 4 in
325 let dtext = if !debug then dtext ^ ppterm (H.cic pred) else dtext in
326 let e = Cn.mk_pattern 1 ity pred in
327 let script = [T.Branch (qs, "")] in
328 if Cn.does_not_occur e then script else
329 if st.cr && are_convertible st pred sx dx then
330 let dtext = "convertible rewrite" ^ dtext in
331 let ity, ety, e = Cn.beta sx pred, Cn.beta dx pred, Cn.hole "" in
332 let city, cety = H.cic ity, H.cic ety in
333 if H.alpha ~flatten:true st.context city cety then script else
334 T.Change (ity, ety, None, e, dtext) :: script
336 T.Rewrite (direction, where, None, e, dtext) :: script
338 let rec proc_lambda st what name v t =
339 let dtext = if !debug then CicPp.ppcontext st.context else "" in
340 let name = match name with
341 | C.Anonymous -> H.mk_fresh_name true st.context anonymous_premise
344 let entry = Some (name, C.Decl (H.cic v)) in
345 let intro = get_intro name in
346 let script = proc_proof (add st entry) t in
347 let script = T.Intros (Some 1, [intro], dtext) :: script in
348 mk_preamble st what script
350 and proc_letin st what name v w t =
351 let intro = get_intro name in
352 let proceed, dtext = test_depth st in
353 let script = if proceed then
354 let st, hyp, rqv = match get_inner_types st what, get_inner_types st v with
355 | Some (C.ALetIn (_, _, iv, iw, _), _), _ when
356 H.alpha ~flatten:true st.context (H.cic v) (H.cic iv) &&
357 H.alpha ~flatten:true st.context (H.cic w) (H.cic iw)
359 st, C.Def (H.cic v, H.cic w), [T.Intros (Some 1, [intro], dtext)]
360 | _, Some (ity, ety) ->
361 let st, rqv = match v with
362 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right st hd tl ->
363 mk_fwd_rewrite st dtext intro tl true v t ity ety
364 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left st hd tl ->
365 mk_fwd_rewrite st dtext intro tl false v t ity ety
366 | C.AAppl (_, hd :: tl) ->
367 let ty = match get_inner_types st hd with
368 | Some (ity, _) -> H.cic ity
369 | None -> get_type "TC3" st hd
371 let classes, _ = Cl.classify st.context ty in
372 let parsno, argsno = List.length classes, List.length tl in
373 let decurry = parsno - argsno in
374 if decurry <> 0 then begin
375 (* FG: we fall back in the cut case *)
376 assert (Ut.is_sober st.context (H.cic ety));
377 let ety = H.acic_bc st.context ety in
378 let qs = [proc_proof (next st) v; [T.Id ""]] in
379 st, [T.Branch (qs, ""); T.Cut (intro, ety, dtext)]
381 let names, synth = get_sub_names hd tl, I.S.empty in
382 let qs = proc_bkd_proofs (next st) synth names classes tl in
383 let hd = mk_lapply_args hd tl classes in
384 let qs = [T.Id ""] :: qs in
385 st, [T.Branch (qs, ""); T.LApply (intro, hd, dtext)]
387 assert (Ut.is_sober st.context (H.cic ety));
388 let ety = H.acic_bc st.context ety in
389 let qs = [proc_proof (next st) v; [T.Id ""]] in
390 st, [T.Branch (qs, ""); T.Cut (intro, ety, dtext)]
392 st, C.Decl (H.cic ity), rqv
394 st, C.Def (H.cic v, H.cic w), [T.LetIn (intro, v, dtext)]
396 let entry = Some (name, hyp) in
397 let qt = proc_proof (next (add st entry)) t in
398 List.rev_append rqv qt
400 [T.Exact (what, dtext)]
402 mk_preamble st what script
404 and proc_rel st what =
405 let _, dtext = test_depth st in
406 let text = "assumption" in
407 let script = [T.Exact (what, dtext ^ text)] in
408 mk_preamble st what script
410 and proc_mutconstruct st what =
411 let _, dtext = test_depth st in
412 let script = [T.Exact (what, dtext)] in
413 mk_preamble st what script
415 and proc_const st what =
416 let _, dtext = test_depth st in
417 let script = [T.Exact (what, dtext)] in
418 mk_preamble st what script
420 and proc_appl st what hd tl =
421 let proceed, dtext = test_depth st in
422 let script = if proceed then
423 let ty = match get_inner_types st hd with
424 | Some (ity, _) -> H.cic ity
425 | None -> get_type "TC2" st hd
427 let classes, rc = Cl.classify st.context ty in
428 let goal_arity, goal = match get_inner_types st what with
431 snd (PEH.split_with_whd (st.context, H.cic ity)), Some (H.cic ity)
433 let parsno, argsno = List.length classes, List.length tl in
434 let decurry = parsno - argsno in
435 let diff = goal_arity - decurry in
437 let text = Printf.sprintf "partial application: %i" diff in
438 prerr_endline ("Procedural 2: " ^ text);
439 [T.Exact (what, dtext ^ text)]
441 let classes = Cl.adjust st.context tl ?goal classes in
442 let rec mk_synth a n =
443 if n < 0 then a else mk_synth (I.S.add n a) (pred n)
445 let synth = mk_synth I.S.empty decurry in
447 then Printf.sprintf "%u %s" parsno (Cl.to_string synth (classes, rc))
450 let script = List.rev (mk_arg st hd) in
451 let tactic b t n = if b then T.Apply (t, n) else T.Exact (t, n) in
453 | Some (i, j, uri, tyno) when decurry = 0 ->
454 let classes2, tl2, _, where = split2_last classes tl in
455 let script2 = List.rev (mk_arg st where) @ script in
456 let synth2 = I.S.add 1 synth in
457 let names = H.get_ind_names uri tyno in
458 let qs = proc_bkd_proofs (next st) synth2 names classes2 tl2 in
459 let ity = match get_inner_types st what with
460 | Some (ity, _) -> ity
462 Cn.fake_annotate "" st.context (get_type "TC3" st what)
464 if List.length qs <> List.length names then
465 let qs = proc_bkd_proofs (next st) synth [] classes tl in
466 let b, hd, qs = mk_apply_args hd tl classes synth qs in
467 script @ [tactic b hd (dtext ^ text); T.Branch (qs, "")]
468 else if is_rewrite_right st hd then
469 script2 @ mk_rewrite st dtext where qs tl2 false what ity
470 else if is_rewrite_left st hd then
471 script2 @ mk_rewrite st dtext where qs tl2 true what ity
473 let predicate = List.nth tl2 (parsno - i) in
474 let e = Cn.mk_pattern j ity predicate in
475 let using = Some hd in
477 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
479 let names = get_sub_names hd tl in
480 let qs = proc_bkd_proofs (next st) synth names classes tl in
481 let b, hd, qs = mk_apply_args hd tl classes synth qs in
482 script @ [tactic b hd (dtext ^ text); T.Branch (qs, "")]
484 [T.Exact (what, dtext)]
486 mk_preamble st what script
488 and proc_case st what uri tyno u v ts =
489 let proceed, dtext = test_depth st in
490 let script = if proceed then
491 let synth, classes = I.S.empty, Cl.make ts in
492 let names = H.get_ind_names uri tyno in
493 let qs = proc_bkd_proofs (next st) synth names classes ts in
494 let lpsno, _ = H.get_ind_type uri tyno in
495 let ps, _ = H.get_ind_parameters st.context (H.cic v) in
496 let _, rps = HEL.split_nth lpsno ps in
497 let rpsno = List.length rps in
498 let ity = match get_inner_types st what with
499 | Some (ity, _) -> ity
501 Cn.fake_annotate "" st.context (get_type "TC4" st what)
503 let e = Cn.mk_pattern rpsno ity u in
505 let script = List.rev (mk_arg st v) in
506 script @ [T.Cases (v, e, dtext ^ text); T.Branch (qs, "")]
508 [T.Exact (what, dtext)]
510 mk_preamble st what script
512 and proc_other st what =
513 let _, dtext = test_depth st in
514 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
515 let script = [T.Exact (what, dtext ^ text)] in
516 mk_preamble st what script
518 and proc_proof st t =
521 let xtypes, note = match get_inner_types st t with
522 | Some (it, et) -> Some (H.cic it, H.cic et),
523 (Printf.sprintf "\nInferred: %s\nExpected: %s"
524 (Pp.ppterm (H.cic it)) (Pp.ppterm (H.cic et)))
525 | None -> None, "\nNo types"
527 let context, clears = Cn.get_clears st.context (H.cic t) xtypes in
528 {st with context = context}
533 | C.ALambda (_, name, w, t) as what -> proc_lambda (f st) what name w t
534 | C.ALetIn (_, name, v, w, t) as what -> proc_letin (f st) what name v w t
535 | C.ARel _ as what -> proc_rel (f st) what
536 | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
537 | C.AConst _ as what -> proc_const (f st) what
538 | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
539 (* FG: we deactivate the tactic "cases" because it does not work properly
540 | C.AMutCase (_, uri, i, u, v, ts) as what -> proc_case (f st) what uri i u v ts
542 | what -> proc_other (f st) what
544 and proc_bkd_proofs st synth names classes ts =
546 let get_names b = ref (names, if b then push st else st) in
547 let get_note f b names =
550 | "" :: tl, st -> names := tl, st; f st
552 let note = case st hd in
554 if b then T.Note note :: f st else f st
556 let _, dtext = test_depth st in
558 if I.overlaps synth inv then None else
559 if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
560 Some (get_note (fun _ -> [T.Exact (v, dtext ^ "dependent")]))
562 let ps = T.list_map2_filter aux classes ts in
563 let b = List.length ps > 1 in
564 let names = get_names b in
565 List.rev_map (fun f -> f b names) ps
567 with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
569 (* initialization ***********************************************************)
571 let init ~ids_to_inner_sorts ~ids_to_inner_types params context =
572 let depth_map x y = match x, y with
573 | None, G.IPDepth depth -> Some depth
577 sorts = ids_to_inner_sorts;
578 types = ids_to_inner_types;
580 max_depth = List.fold_left depth_map None params;
582 defaults = not (List.mem G.IPNoDefaults params);
583 cr = List.mem G.IPCR params;