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 TC = CicTypeChecker
31 module UM = UriManager
32 module Obj = LibraryObjects
35 module E = CicEnvironment
37 module PEH = ProofEngineHelpers
39 module DTI = DoubleTypeInference
40 module NU = CicNotationUtil
44 module Cl = ProceduralClassify
45 module T = ProceduralTypes
46 module Cn = ProceduralConversion
47 module H = ProceduralHelpers
50 sorts : (C.id, A.sort_kind) Hashtbl.t;
51 types : (C.id, A.anntypes) Hashtbl.t;
52 params : G.inline_param list;
53 max_depth: int option;
62 (* helpers ******************************************************************)
64 let split2_last l1 l2 =
66 let n = pred (List.length l1) in
67 let before1, after1 = HEL.split_nth n l1 in
68 let before2, after2 = HEL.split_nth n l2 in
69 before1, before2, List.hd after1, List.hd after2
70 with Invalid_argument _ -> failwith "A2P.split2_last"
72 let string_of_head = function
74 | C.AConst _ -> "const"
75 | C.AMutInd _ -> "mutind"
76 | C.AMutConstruct _ -> "mutconstruct"
80 | C.ALambda _ -> "lambda"
81 | C.ALetIn _ -> "letin"
83 | C.ACoFix _ -> "cofix"
86 | C.AMutCase _ -> "mutcase"
88 | C.AImplicit _ -> "implict"
90 let next st = {st with depth = succ st.depth}
92 let add st entry = {st with context = entry :: st.context}
94 let push st = {st with case = 1 :: st.case}
97 {st with case = match st.case with
99 | hd :: tl -> succ hd :: tl
103 let case = String.concat "." (List.rev_map string_of_int st.case) in
104 Printf.sprintf "case %s: %s" case str
108 let msg = Printf.sprintf "Depth %u: " st.depth in
109 match st.max_depth with
111 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
112 with Invalid_argument _ -> failwith "A2P.test_depth"
114 let is_rewrite_right st = function
115 | C.AConst (_, uri, []) -> st.defaults && Obj.is_eq_ind_r_URI uri
118 let is_rewrite_left st = function
119 | C.AConst (_, uri, []) -> st.defaults && Obj.is_eq_ind_URI uri
122 let is_fwd_rewrite_right st hd tl =
123 if is_rewrite_right st hd then match List.nth tl 3 with
128 let is_fwd_rewrite_left st hd tl =
129 if is_rewrite_left st hd then match List.nth tl 3 with
134 let get_inner_types st v =
136 let id = Ut.id_of_annterm v in
137 try match Hashtbl.find st.types id with
138 | {A.annsynthesized = ity; A.annexpected = Some ety} -> Some (ity, ety)
139 | {A.annsynthesized = ity; A.annexpected = None} -> Some (ity, ity)
140 with Not_found -> None
141 with Invalid_argument _ -> failwith "P2.get_inner_types"
143 let get_entry st id =
144 let rec aux = function
146 | Some (C.Name name, e) :: _ when name = id -> e
151 let string_of_atomic = function
152 | C.ARel (_, _, _, s) -> s
153 | C.AVar (_, uri, _) -> H.name_of_uri uri None None
154 | C.AConst (_, uri, _) -> H.name_of_uri uri None None
155 | C.AMutInd (_, uri, i, _) -> H.name_of_uri uri (Some i) None
156 | C.AMutConstruct (_, uri, i, j, _) -> H.name_of_uri uri (Some i) (Some j)
159 let get_sub_names head l =
160 let s = string_of_atomic head in
161 if s = "" then [] else
162 let map (names, i) _ =
163 let name = Printf.sprintf "%s_%u" s i in name :: names, succ i
165 let names, _ = List.fold_left map ([], 1) l in
168 let get_type msg st t = H.get_type msg st.context (H.cic t)
170 let get_uri_of_head = function
172 | C.AAppl (_, C.AConst (_, u, _) :: _) -> Some (u, 0, 0)
173 | C.AMutInd (_, u, i, _)
174 | C.AAppl (_, C.AMutInd (_, u, i, _) :: _) -> Some (u, succ i, 0)
175 | C.AMutConstruct (_, u, i, j, _)
176 | C.AAppl (_, C.AMutConstruct (_, u, i, j, _) :: _) -> Some (u, succ i, j)
179 let get_uri_of_apply = function
181 | T.Apply (t, _) -> get_uri_of_head t
184 let is_reflexivity st step =
185 match get_uri_of_apply step with
187 | Some (uri, i, j) -> st.defaults && Obj.is_eq_URI uri && i = 1 && j = 1
189 (* proof construction *******************************************************)
191 let anonymous_premise = C.Name "UNNAMED"
193 let mk_exp_args hd tl classes synth qs =
195 let meta id = C.AImplicit (id, None) in
197 if I.overlaps synth cl
198 then if b then v, v else meta "", v
199 else meta "", meta ""
201 let rec rev a = function
204 if snd hd <> meta "" then incr exp;
207 let rec aux = function
210 if fst hd = meta "" then aux tl else rev [] (hd :: tl)
212 let args = T.list_rev_map2 map tl classes in
213 let args = aux args in
214 let part = !exp < List.length tl in
215 if args = [] then part, hd, qs else part, C.AAppl ("", hd :: args), qs
217 let mk_convert st ?name sty ety note =
219 let a = ref "" in Ut.pp_term (fun s -> a := !a ^ s) [] st.context t; !a
221 let e = Cn.hole "" in
222 let csty, cety = H.cic sty, H.cic ety in
225 let sname = match name with None -> "" | Some (id, _) -> id in
226 Printf.sprintf "%s: %s\nSINTH: %s\nEXP: %s"
227 note sname (ppterm csty) (ppterm cety)
230 if H.alpha_equivalence ~flatten:true st.context csty cety then [T.Note note] else
231 let sty, ety = H.acic_bc st.context sty, H.acic_bc st.context ety in
233 | None -> [T.Change (sty, ety, None, e, note)]
235 begin match get_entry st id with
237 [T.Change (ety, sty, Some (id, Some id), e, note);
241 [T.Change (ety, sty, Some (id, Some id), e, note)]
244 let convert st ?name v =
245 match get_inner_types st v with
247 if !debug then [T.Note "NORMAL: NO INNER TYPES"] else []
248 | Some (sty, ety) -> mk_convert st ?name sty ety "NORMAL"
250 let get_intro = function
251 | C.Anonymous -> None
254 let mk_preamble st what script = match script with
255 | step :: script when is_reflexivity st step ->
256 convert st what @ T.Reflexivity (T.note_of_step step) :: script
257 | T.Exact _ :: _ -> script
258 | _ -> convert st what @ script
260 let mk_arg st = function
261 | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
264 let mk_fwd_rewrite st dtext name tl direction v t ity ety =
265 let compare premise = function
267 | Some s -> s = premise
269 assert (List.length tl = 6);
270 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
271 let e = Cn.mk_pattern 1 ety predicate in
272 if (Cn.does_not_occur e) then st, [] else
274 | C.ARel (_, _, i, premise) as w ->
276 let where = Some (premise, name) in
277 let script = mk_arg st what @ mk_arg st w in
278 T.Rewrite (direction, what, where, e, dtext) :: script
280 if DTI.does_not_occur (succ i) (H.cic t) || compare premise name then
281 {st with context = Cn.clear st.context premise}, script name
283 assert (Ut.is_sober st.context (H.cic ity));
284 let ity = H.acic_bc st.context ity in
285 let br1 = [T.Id ""] in
286 let br2 = List.rev (T.Exact (w, "assumption") :: script None) in
287 let text = "non-linear rewrite" in
288 st, [T.Branch ([br2; br1], ""); T.Cut (name, ity, text)]
292 let mk_rewrite st dtext where qs tl direction t ity =
294 let a = ref "" in Ut.pp_term (fun s -> a := !a ^ s) [] st.context t; !a
296 assert (List.length tl = 5);
297 let predicate = List.nth tl 2 in
298 let dtext = if !debug then dtext ^ ppterm (H.cic predicate) else dtext in
299 let e = Cn.mk_pattern 1 ity predicate in
300 let script = [T.Branch (qs, "")] in
301 if (Cn.does_not_occur e) then script else
302 T.Rewrite (direction, where, None, e, dtext) :: script
304 let rec proc_lambda st what name v t =
305 let dtext = if !debug then CicPp.ppcontext st.context else "" in
306 let name = match name with
307 | C.Anonymous -> H.mk_fresh_name true st.context anonymous_premise
310 let entry = Some (name, C.Decl (H.cic v)) in
311 let intro = get_intro name in
312 let script = proc_proof (add st entry) t in
313 let script = T.Intros (Some 1, [intro], dtext) :: script in
314 mk_preamble st what script
316 and proc_letin st what name v w t =
317 let intro = get_intro name in
318 let proceed, dtext = test_depth st in
319 let script = if proceed then
320 let st, hyp, rqv = match get_inner_types st what, get_inner_types st v with
321 | Some (C.ALetIn (_, _, iv, iw, _), _), _ when
322 H.alpha_equivalence ~flatten:true st.context (H.cic v) (H.cic iv) &&
323 H.alpha_equivalence ~flatten:true st.context (H.cic w) (H.cic iw)
325 st, C.Def (H.cic v, H.cic w), [T.Intros (Some 1, [intro], dtext)]
326 | _, Some (ity, ety) ->
327 let st, rqv = match v with
328 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right st hd tl ->
329 mk_fwd_rewrite st dtext intro tl true v t ity ety
330 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left st hd tl ->
331 mk_fwd_rewrite st dtext intro tl false v t ity ety
333 assert (Ut.is_sober st.context (H.cic ety));
334 let ety = H.acic_bc st.context ety in
335 let qs = [proc_proof (next st) v; [T.Id ""]] in
336 st, [T.Branch (qs, ""); T.Cut (intro, ety, dtext)]
338 st, C.Decl (H.cic ity), rqv
340 st, C.Def (H.cic v, H.cic w), [T.LetIn (intro, v, dtext)]
342 let entry = Some (name, hyp) in
343 let qt = proc_proof (next (add st entry)) t in
344 List.rev_append rqv qt
346 [T.Exact (what, dtext)]
348 mk_preamble st what script
350 and proc_rel st what =
351 let _, dtext = test_depth st in
352 let text = "assumption" in
353 let script = [T.Exact (what, dtext ^ text)] in
354 mk_preamble st what script
356 and proc_mutconstruct st what =
357 let _, dtext = test_depth st in
358 let script = [T.Exact (what, dtext)] in
359 mk_preamble st what script
361 and proc_const st what =
362 let _, dtext = test_depth st in
363 let script = [T.Exact (what, dtext)] in
364 mk_preamble st what script
366 and proc_appl st what hd tl =
367 let proceed, dtext = test_depth st in
368 let script = if proceed then
369 let ty = match get_inner_types st hd with
370 | Some (ity, _) -> H.cic ity
371 | None -> get_type "TC2" st hd
373 let classes, rc = Cl.classify st.context ty in
374 let goal_arity, goal = match get_inner_types st what with
377 snd (PEH.split_with_whd (st.context, H.cic ity)), Some (H.cic ity)
379 let parsno, argsno = List.length classes, List.length tl in
380 let decurry = parsno - argsno in
381 let diff = goal_arity - decurry in
383 let text = Printf.sprintf "partial application: %i" diff in
384 prerr_endline ("Procedural 2: " ^ text);
385 [T.Exact (what, dtext ^ text)]
387 let classes = Cl.adjust st.context tl ?goal classes in
388 let rec mk_synth a n =
389 if n < 0 then a else mk_synth (I.S.add n a) (pred n)
391 let synth = mk_synth I.S.empty decurry in
393 then Printf.sprintf "%u %s" parsno (Cl.to_string synth (classes, rc))
396 let script = List.rev (mk_arg st hd) in
397 let tactic b t n = if b then T.Apply (t, n) else T.Exact (t, n) in
399 | Some (i, j, uri, tyno) when decurry = 0 ->
400 let classes2, tl2, _, where = split2_last classes tl in
401 let script2 = List.rev (mk_arg st where) @ script in
402 let synth2 = I.S.add 1 synth in
403 let names = H.get_ind_names uri tyno in
404 let qs = proc_bkd_proofs (next st) synth2 names classes2 tl2 in
405 let ity = match get_inner_types st what with
406 | Some (ity, _) -> ity
408 Cn.fake_annotate "" st.context (get_type "TC3" st what)
410 if List.length qs <> List.length names then
411 let qs = proc_bkd_proofs (next st) synth [] classes tl in
412 let b, hd, qs = mk_exp_args hd tl classes synth qs in
413 script @ [tactic b hd (dtext ^ text); T.Branch (qs, "")]
414 else if is_rewrite_right st hd then
415 script2 @ mk_rewrite st dtext where qs tl2 false what ity
416 else if is_rewrite_left st hd then
417 script2 @ mk_rewrite st dtext where qs tl2 true what ity
419 let predicate = List.nth tl2 (parsno - i) in
420 let e = Cn.mk_pattern j ity predicate in
421 let using = Some hd in
423 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
425 let names = get_sub_names hd tl in
426 let qs = proc_bkd_proofs (next st) synth names classes tl in
427 let b, hd, qs = mk_exp_args hd tl classes synth qs in
428 script @ [tactic b hd (dtext ^ text); T.Branch (qs, "")]
430 [T.Exact (what, dtext)]
432 mk_preamble st what script
434 and proc_case st what uri tyno u v ts =
435 let proceed, dtext = test_depth st in
436 let script = if proceed then
437 let synth, classes = I.S.empty, Cl.make ts in
438 let names = H.get_ind_names uri tyno in
439 let qs = proc_bkd_proofs (next st) synth names classes ts in
440 let lpsno, _ = H.get_ind_type uri tyno in
441 let ps, _ = H.get_ind_parameters st.context (H.cic v) in
442 let _, rps = HEL.split_nth lpsno ps in
443 let rpsno = List.length rps in
444 let ity = match get_inner_types st what with
445 | Some (ity, _) -> ity
447 Cn.fake_annotate "" st.context (get_type "TC4" st what)
449 let e = Cn.mk_pattern rpsno ity u in
451 let script = List.rev (mk_arg st v) in
452 script @ [T.Cases (v, e, dtext ^ text); T.Branch (qs, "")]
454 [T.Exact (what, dtext)]
456 mk_preamble st what script
458 and proc_other st what =
459 let _, dtext = test_depth st in
460 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
461 let script = [T.Exact (what, dtext ^ text)] in
462 mk_preamble st what script
464 and proc_proof st t =
467 let xtypes, note = match get_inner_types st t with
468 | Some (it, et) -> Some (H.cic it, H.cic et),
469 (Printf.sprintf "\nInferred: %s\nExpected: %s"
470 (Pp.ppterm (H.cic it)) (Pp.ppterm (H.cic et)))
471 | None -> None, "\nNo types"
473 let context, clears = Cn.get_clears st.context (H.cic t) xtypes in
474 {st with context = context}
479 | C.ALambda (_, name, w, t) as what -> proc_lambda (f st) what name w t
480 | C.ALetIn (_, name, v, w, t) as what -> proc_letin (f st) what name v w t
481 | C.ARel _ as what -> proc_rel (f st) what
482 | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
483 | C.AConst _ as what -> proc_const (f st) what
484 | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
485 (* FG: we deactivate the tactic "cases" because it does not work properly
486 | C.AMutCase (_, uri, i, u, v, ts) as what -> proc_case (f st) what uri i u v ts
488 | what -> proc_other (f st) what
490 and proc_bkd_proofs st synth names classes ts =
492 let get_names b = ref (names, if b then push st else st) in
493 let get_note f b names =
496 | "" :: tl, st -> names := tl, st; f st
498 let note = case st hd in
500 if b then T.Note note :: f st else f st
502 let _, dtext = test_depth st in
504 if I.overlaps synth inv then None else
505 if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
506 Some (get_note (fun _ -> [T.Exact (v, dtext ^ "dependent")]))
508 let ps = T.list_map2_filter aux classes ts in
509 let b = List.length ps > 1 in
510 let names = get_names b in
511 List.rev_map (fun f -> f b names) ps
513 with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
515 (* initialization ***********************************************************)
517 let init ~ids_to_inner_sorts ~ids_to_inner_types params context =
518 let depth_map x y = match x, y with
519 | None, G.IPDepth depth -> Some depth
523 sorts = ids_to_inner_sorts;
524 types = ids_to_inner_types;
526 max_depth = List.fold_left depth_map None params;
528 defaults = not (List.mem G.IPNoDefaults params);