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
33 module HObj = HelmLibraryObjects
36 module E = CicEnvironment
38 module PEH = ProofEngineHelpers
40 module DTI = DoubleTypeInference
42 module Cl = ProceduralClassify
43 module T = ProceduralTypes
44 module Cn = ProceduralConversion
45 module H = ProceduralHelpers
48 sorts : (C.id, A.sort_kind) Hashtbl.t;
49 types : (C.id, A.anntypes) Hashtbl.t;
51 max_depth: int option;
54 intros: string option list;
58 skip_thm_and_qed : bool;
63 (* helpers ******************************************************************)
65 let split2_last l1 l2 =
67 let n = pred (List.length l1) in
68 let before1, after1 = HEL.split_nth n l1 in
69 let before2, after2 = HEL.split_nth n l2 in
70 before1, before2, List.hd after1, List.hd after2
71 with Invalid_argument _ -> failwith "A2P.split2_last"
73 let string_of_head = function
75 | C.AConst _ -> "const"
76 | C.AMutInd _ -> "mutind"
77 | C.AMutConstruct _ -> "mutconstruct"
81 | C.ALambda _ -> "lambda"
82 | C.ALetIn _ -> "letin"
84 | C.ACoFix _ -> "cofix"
87 | C.AMutCase _ -> "mutcase"
89 | C.AImplicit _ -> "implict"
91 let clear st = {st with intros = []}
93 let next st = {(clear st) with depth = succ st.depth}
95 let add st entry intro =
96 {st with context = entry :: st.context; intros = intro :: st.intros}
98 let push st = {st with case = 1 :: st.case}
101 {st with case = match st.case with
103 | hd :: tl -> succ hd :: tl
107 let case = String.concat "." (List.rev_map string_of_int st.case) in
108 Printf.sprintf "case %s: %s" case str
112 let msg = Printf.sprintf "Depth %u: " st.depth in
113 match st.max_depth with
115 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
116 with Invalid_argument _ -> failwith "A2P.test_depth"
118 let is_rewrite_right = function
119 | C.AConst (_, uri, []) ->
120 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
123 let is_rewrite_left = function
124 | C.AConst (_, uri, []) ->
125 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
128 let is_fwd_rewrite_right hd tl =
129 if is_rewrite_right hd then match List.nth tl 3 with
134 let is_fwd_rewrite_left hd tl =
135 if is_rewrite_left hd then match List.nth tl 3 with
140 let get_inner_types st v =
142 let id = Ut.id_of_annterm v in
143 try match Hashtbl.find st.types id with
144 | {A.annsynthesized = st; A.annexpected = Some et} -> Some (st, et)
145 | {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
146 with Not_found -> None
147 with Invalid_argument _ -> failwith "A2P.get_inner_types"
149 let get_inner_sort st v =
151 let id = Ut.id_of_annterm v in
152 try Hashtbl.find st.sorts id
153 with Not_found -> `Type (CicUniv.fresh())
154 with Invalid_argument _ -> failwith "A2P.get_sort"
156 let get_type msg st bo =
158 let ty, _ = TC.type_of_aux' [] st.context (H.cic bo) Un.oblivion_ugraph in
160 with e -> failwith (msg ^ ": " ^ Printexc.to_string e)
162 let get_entry st id =
163 let rec aux = function
165 | Some (C.Name name, e) :: _ when name = id -> e
170 let get_ind_names uri tno =
172 let ts = match E.get_obj Un.oblivion_ugraph uri with
173 | C.InductiveDefinition (ts, _, _, _), _ -> ts
176 match List.nth ts tno with
177 | (_, _, _, cs) -> List.map fst cs
178 with Invalid_argument _ -> failwith "A2P.get_ind_names"
180 (* proof construction *******************************************************)
182 let used_premise = C.Name "USED"
184 let mk_exp_args hd tl classes synth =
185 let meta id = C.AImplicit (id, None) in
187 if I.overlaps synth cl && b then v else meta ""
189 let rec aux = function
191 | hd :: tl -> if hd = meta "" then aux tl else List.rev (hd :: tl)
193 let args = T.list_rev_map2 map tl classes in
194 let args = aux args in
195 if args = [] then hd else C.AAppl ("", hd :: args)
197 let mk_convert st ?name sty ety note =
198 let e = Cn.hole "" in
199 let csty, cety = H.cic sty, H.cic ety in
202 let sname = match name with None -> "" | Some (id, _) -> id in
203 let note = Printf.sprintf "%s: %s\nSINTH: %s\nEXP: %s"
204 note sname (Pp.ppterm csty) (Pp.ppterm cety)
209 assert (Ut.is_sober csty);
210 assert (Ut.is_sober cety);
211 if Ut.alpha_equivalence csty cety then script else
212 let sty, ety = H.acic_bc st.context sty, H.acic_bc st.context ety in
214 | None -> T.Change (sty, ety, None, e, "") :: script
216 begin match get_entry st id with
217 | C.Def _ -> assert false (* T.ClearBody (id, "") :: script *)
219 T.Change (ety, sty, Some (id, Some id), e, "") :: script
222 let convert st ?name v =
223 match get_inner_types st v with
225 if debug then [T.Note "NORMAL: NO INNER TYPES"] else []
226 | Some (sty, ety) -> mk_convert st ?name sty ety "NORMAL"
228 let convert_elim st ?name t v pattern =
229 match t, get_inner_types st t, get_inner_types st v with
231 | _, _, None -> [(* T.Note "ELIM: NO INNER TYPES"*)]
232 | C.AAppl (_, hd :: tl), Some (tsty, _), Some (vsty, _) ->
233 let where = List.hd (List.rev tl) in
234 let cty = Cn.elim_inferred_type
235 st.context (H.cic vsty) (H.cic where) (H.cic hd) (H.cic pattern)
237 mk_convert st ?name (Cn.fake_annotate "" st.context cty) tsty "ELIM"
238 | _, Some _, Some _ -> assert false
240 let get_intro = function
241 | C.Anonymous -> None
244 let mk_intros st what script =
245 let intros st script =
246 if st.intros = [] then script else
247 let count = List.length st.intros in
248 T.Intros (Some count, List.rev st.intros, "") :: script
250 let clears st script =
251 if true (* st.clears = [] *) then script else T.Clear (st.clears, st.clears_note) :: script
253 intros st (clears st (convert st what @ script))
255 let mk_arg st = function
256 | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
259 let mk_fwd_rewrite st dtext name tl direction v t ity =
260 let compare premise = function
262 | Some s -> s = premise
264 assert (List.length tl = 6);
265 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
266 let e = Cn.mk_pattern 1 predicate in
268 | C.ARel (_, _, i, premise) as w ->
269 (* let _script = convert_elim st ~name:(premise, i) v w e in *)
271 let where = Some (premise, name) in
272 let script = mk_arg st what @ mk_arg st w (* @ script *) in
273 T.Rewrite (direction, what, where, e, dtext) :: script
275 if DTI.does_not_occur (succ i) (H.cic t) || compare premise name then
276 {st with context = Cn.clear st.context premise}, script name
278 let br1 = [T.Id ""] in
279 let br2 = List.rev (T.Apply (w, "assumption") :: script None) in
280 let text = "non linear rewrite" in
281 st, [T.Branch ([br2; br1], ""); T.Cut (name, ity, text)]
284 let mk_rewrite st dtext where qs tl direction t =
285 assert (List.length tl = 5);
286 let predicate = List.nth tl 2 in
287 let e = Cn.mk_pattern 1 predicate in
288 let script = [] (* convert_elim st t t e *) in
289 script @ [T.Rewrite (direction, where, None, e, dtext); T.Branch (qs, "")]
291 let rec proc_lambda st what name v t =
292 let dno, ae = match get_inner_types st t with
293 | None -> false, true
295 let sty, ety = H.cic sty, H.cic ety in
296 DTI.does_not_occur 1 sty && DTI.does_not_occur 1 ety,
297 Ut.alpha_equivalence sty ety
299 let dno = dno && DTI.does_not_occur 1 (H.cic t) in
300 let name = match dno, name with
301 | true, _ -> C.Anonymous
302 | false, C.Anonymous -> H.mk_fresh_name st.context used_premise
303 | false, name -> name
305 let entry = Some (name, C.Decl (H.cic v)) in
306 let intro = get_intro name in
307 let st = (add st entry intro) in
308 if ae then proc_proof st t else
309 let script = proc_proof (clear st) t in
310 mk_intros st t script
312 and proc_letin st what name v w t =
313 let intro = get_intro name in
314 let proceed, dtext = test_depth st in
315 let script = if proceed then
316 let st, hyp, rqv = match get_inner_types st v with
318 let st, rqv = match v with
319 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
320 mk_fwd_rewrite st dtext intro tl true v t ity
321 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
322 mk_fwd_rewrite st dtext intro tl false v t ity
324 let qs = [proc_proof (next st) v; [T.Id ""]] in
325 let ity = H.acic_bc st.context ity in
326 st, [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
328 st, C.Decl (H.cic ity), rqv
330 st, C.Def (H.cic v, H.cic w), [T.LetIn (intro, v, dtext)]
332 let entry = Some (name, hyp) in
333 let qt = proc_proof (next (add st entry intro)) t in
334 List.rev_append rqv qt
336 [T.Apply (what, dtext)]
338 mk_intros st what script
340 and proc_rel st what =
341 let _, dtext = test_depth st in
342 let text = "assumption" in
343 let script = [T.Apply (what, dtext ^ text)] in
344 mk_intros st what script
346 and proc_mutconstruct st what =
347 let _, dtext = test_depth st in
348 let script = [T.Apply (what, dtext)] in
349 mk_intros st what script
351 and proc_const st what =
352 let _, dtext = test_depth st in
353 let script = [T.Apply (what, dtext)] in
354 mk_intros st what script
356 and proc_appl st what hd tl =
357 let proceed, dtext = test_depth st in
358 let script = if proceed then
359 let ty = get_type "TC2" st hd in
360 let classes, rc = Cl.classify st.context ty in
361 let goal_arity, goal = match get_inner_types st what with
364 snd (PEH.split_with_whd (st.context, H.cic ity)), Some (H.cic ety)
366 let parsno, argsno = List.length classes, List.length tl in
367 let decurry = parsno - argsno in
368 let diff = goal_arity - decurry in
369 if diff < 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (H.cic hd)));
370 let classes = Cl.adjust st.context tl ?goal classes in
371 let rec mk_synth a n =
372 if n < 0 then a else mk_synth (I.S.add n a) (pred n)
374 let synth = mk_synth I.S.empty decurry in
375 let text = "" (* Printf.sprintf "%u %s" parsno (Cl.to_string h) *) in
376 let script = List.rev (mk_arg st hd) in
378 | Some (i, j, uri, tyno) ->
379 let classes2, tl2, _, where = split2_last classes tl in
380 let script2 = List.rev (mk_arg st where) @ script in
381 let synth2 = I.S.add 1 synth in
382 let names = get_ind_names uri tyno in
383 let qs = proc_bkd_proofs (next st) synth2 names classes2 tl2 in
384 if List.length qs <> List.length names then
385 let qs = proc_bkd_proofs (next st) synth [] classes tl in
386 let hd = mk_exp_args hd tl classes synth in
387 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
388 else if is_rewrite_right hd then
389 script2 @ mk_rewrite st dtext where qs tl2 false what
390 else if is_rewrite_left hd then
391 script2 @ mk_rewrite st dtext where qs tl2 true what
393 let predicate = List.nth tl2 (parsno - i) in
394 let e = Cn.mk_pattern j predicate in
395 let using = Some hd in
396 (* convert_elim st what what e @ *) script2 @
397 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
399 let qs = proc_bkd_proofs (next st) synth [] classes tl in
400 let hd = mk_exp_args hd tl classes synth in
401 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
403 [T.Apply (what, dtext)]
405 mk_intros st what script
407 and proc_other st what =
408 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
409 let script = [T.Note text] in
410 mk_intros st what script
412 and proc_proof st t =
414 let xtypes, note = match get_inner_types st t with
415 | Some (it, et) -> Some (H.cic it, H.cic et),
416 (Printf.sprintf "\nInferred: %s\nExpected: %s"
417 (Pp.ppterm (H.cic it)) (Pp.ppterm (H.cic et)))
418 | None -> None, "\nNo types"
420 let context, clears = Cn.get_clears st.context (H.cic t) xtypes in
421 let note = Pp.ppcontext st.context ^ note in
422 {st with context = context; clears = clears; clears_note = note; }
425 | C.ALambda (_, name, w, t) as what -> proc_lambda (f st) what name w t
426 | C.ALetIn (_, name, v, w, t) as what -> proc_letin (f st) what name v w t
427 | C.ARel _ as what -> proc_rel (f st) what
428 | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
429 | C.AConst _ as what -> proc_const (f st) what
430 | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
431 | what -> proc_other (f st) what
433 and proc_bkd_proofs st synth names classes ts =
436 let names = ref (names, push st) in
439 | [], st -> fun _ -> f st
440 | "" :: tl, st -> names := tl, st; fun _ -> f st
442 let note = case st hd in
444 fun b -> if b then T.Note note :: f st else f st
446 let _, dtext = test_depth st in
448 if I.overlaps synth inv then None else
449 if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
450 Some (fun _ -> [T.Apply (v, dtext ^ "dependent")])
452 let ps = T.list_map2_filter aux classes ts in
453 let b = List.length ps > 1 in
454 List.rev_map (fun f -> f b) ps
456 with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
458 (* object costruction *******************************************************)
460 let is_theorem pars =
462 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
463 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
465 let proc_obj st = function
466 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
467 let ast = proc_proof st v in
468 let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in
469 let text = Printf.sprintf "tactics: %u\nnodes: %u" steps nodes in
470 if st.skip_thm_and_qed then ast
471 else T.Theorem (Some s, t, "") :: ast @ [T.Qed text]
473 failwith "not a theorem"
475 (* interface functions ******************************************************)
477 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth
478 ?(skip_thm_and_qed=false) prefix aobj =
480 sorts = ids_to_inner_sorts;
481 types = ids_to_inner_types;
490 skip_thm_and_qed = skip_thm_and_qed;
492 HLog.debug "Procedural: level 2 transformation";
493 let steps = proc_obj st aobj in
494 HLog.debug "Procedural: grafite rendering";
495 List.rev (T.render_steps [] steps)