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;
57 skip_thm_and_qed : bool;
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 = function
115 | C.AConst (_, uri, []) ->
116 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
119 let is_rewrite_left = function
120 | C.AConst (_, uri, []) ->
121 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
124 let is_fwd_rewrite_right hd tl =
125 if is_rewrite_right hd then match List.nth tl 3 with
130 let is_fwd_rewrite_left hd tl =
131 if is_rewrite_left 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 = st; A.annexpected = Some et} -> Some (st, et)
141 | {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
142 with Not_found -> None
143 with Invalid_argument _ -> failwith "A2P.get_inner_types"
145 let get_inner_sort st v =
147 let id = Ut.id_of_annterm v in
148 try Hashtbl.find st.sorts id
149 with Not_found -> `Type (CicUniv.fresh())
150 with Invalid_argument _ -> failwith "A2P.get_sort"
152 let get_type msg st bo =
154 let ty, _ = TC.type_of_aux' [] st.context (H.cic bo) Un.oblivion_ugraph in
156 with e -> failwith (msg ^ ": " ^ Printexc.to_string e)
158 let get_entry st id =
159 let rec aux = function
161 | Some (C.Name name, e) :: _ when name = id -> e
166 let get_ind_names uri tno =
168 let ts = match E.get_obj Un.oblivion_ugraph uri with
169 | C.InductiveDefinition (ts, _, _, _), _ -> ts
172 match List.nth ts tno with
173 | (_, _, _, cs) -> List.map fst cs
174 with Invalid_argument _ -> failwith "A2P.get_ind_names"
176 (* proof construction *******************************************************)
178 let used_premise = C.Name "USED"
180 let mk_exp_args hd tl classes synth =
181 let meta id = C.AImplicit (id, None) in
183 if I.overlaps synth cl && b then v else meta ""
185 let rec aux = function
187 | hd :: tl -> if hd = meta "" then aux tl else List.rev (hd :: tl)
189 let args = T.list_rev_map2 map tl classes in
190 let args = aux args in
191 if args = [] then hd else C.AAppl ("", hd :: args)
193 let mk_convert st ?name sty ety note =
194 let e = Cn.hole "" in
195 let csty, cety = H.cic sty, H.cic ety in
198 let sname = match name with None -> "" | Some (id, _) -> id in
199 let note = Printf.sprintf "%s: %s\nSINTH: %s\nEXP: %s"
200 note sname (Pp.ppterm csty) (Pp.ppterm cety)
205 assert (Ut.is_sober csty);
206 assert (Ut.is_sober cety);
207 if Ut.alpha_equivalence csty cety then script else
208 let sty, ety = H.acic_bc st.context sty, H.acic_bc st.context ety in
210 | None -> T.Change (sty, ety, None, e, "") :: script
212 begin match get_entry st id with
213 | C.Def _ -> assert false (* T.ClearBody (id, "") :: script *)
215 T.Change (ety, sty, Some (id, Some id), e, "") :: script
218 let convert st ?name v =
219 match get_inner_types st v with
221 if debug then [T.Note "NORMAL: NO INNER TYPES"] else []
222 | Some (sty, ety) -> mk_convert st ?name sty ety "NORMAL"
224 let convert_elim st ?name t v pattern =
225 match t, get_inner_types st t, get_inner_types st v with
227 | _, _, None -> [(* T.Note "ELIM: NO INNER TYPES"*)]
228 | C.AAppl (_, hd :: tl), Some (tsty, _), Some (vsty, _) ->
229 let where = List.hd (List.rev tl) in
230 let cty = Cn.elim_inferred_type
231 st.context (H.cic vsty) (H.cic where) (H.cic hd) (H.cic pattern)
233 mk_convert st ?name (Cn.fake_annotate "" st.context cty) tsty "ELIM"
234 | _, Some _, Some _ -> assert false
236 let get_intro = function
237 | C.Anonymous -> None
240 let mk_preamble st what script =
241 let clears st script =
242 if true (* st.clears = [] *) then script else T.Clear (st.clears, st.clears_note) :: script
244 clears st (convert st what @ script)
246 let mk_arg st = function
247 | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
250 let mk_fwd_rewrite st dtext name tl direction v t ity =
251 let compare premise = function
253 | Some s -> s = premise
255 assert (List.length tl = 6);
256 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
257 let e = Cn.mk_pattern 1 predicate in
258 if (Cn.does_not_occur e) then st, [] else
260 | C.ARel (_, _, i, premise) as w ->
261 (* let _script = convert_elim st ~name:(premise, i) v w e in *)
263 let where = Some (premise, name) in
264 let script = mk_arg st what @ mk_arg st w (* @ script *) in
265 T.Rewrite (direction, what, where, e, dtext) :: script
267 if DTI.does_not_occur (succ i) (H.cic t) || compare premise name then
268 {st with context = Cn.clear st.context premise}, script name
270 let br1 = [T.Id ""] in
271 let br2 = List.rev (T.Apply (w, "assumption") :: script None) in
272 let text = "non linear rewrite" in
273 st, [T.Branch ([br2; br1], ""); T.Cut (name, ity, text)]
276 let mk_rewrite st dtext where qs tl direction t =
277 assert (List.length tl = 5);
278 let predicate = List.nth tl 2 in
279 let e = Cn.mk_pattern 1 predicate in
280 let script = [T.Branch (qs, "")] in
281 if (Cn.does_not_occur e) then script else
282 (* let script = convert_elim st t t e in *)
283 T.Rewrite (direction, where, None, e, dtext) :: script
285 let rec proc_lambda st what name v t =
286 let dno = match get_inner_types st t with
289 let sty, ety = H.cic sty, H.cic ety in
290 DTI.does_not_occur 1 sty && DTI.does_not_occur 1 ety
292 let dno = dno && DTI.does_not_occur 1 (H.cic t) in
293 let name = match dno, name with
294 | true, _ -> C.Anonymous
295 | false, C.Anonymous -> H.mk_fresh_name st.context used_premise
296 | false, name -> name
298 let entry = Some (name, C.Decl (H.cic v)) in
299 let intro = get_intro name in
300 let script = proc_proof (add st entry) t in
301 let script = T.Intros (Some 1, [intro], "") :: script in
302 mk_preamble st what script
304 and proc_letin st what name v w t =
305 let intro = get_intro name in
306 let proceed, dtext = test_depth st in
307 let script = if proceed then
308 let st, hyp, rqv = match get_inner_types st v with
310 let st, rqv = match v with
311 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
312 mk_fwd_rewrite st dtext intro tl true v t ity
313 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
314 mk_fwd_rewrite st dtext intro tl false v t ity
316 let qs = [proc_proof (next st) v; [T.Id ""]] in
317 let ity = H.acic_bc st.context ity in
318 st, [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
320 st, C.Decl (H.cic ity), rqv
322 st, C.Def (H.cic v, H.cic w), [T.LetIn (intro, v, dtext)]
324 let entry = Some (name, hyp) in
325 let qt = proc_proof (next (add st entry)) t in
326 List.rev_append rqv qt
328 [T.Apply (what, dtext)]
330 mk_preamble st what script
332 and proc_rel st what =
333 let _, dtext = test_depth st in
334 let text = "assumption" in
335 let script = [T.Apply (what, dtext ^ text)] in
336 mk_preamble st what script
338 and proc_mutconstruct st what =
339 let _, dtext = test_depth st in
340 let script = [T.Apply (what, dtext)] in
341 mk_preamble st what script
343 and proc_const st what =
344 let _, dtext = test_depth st in
345 let script = [T.Apply (what, dtext)] in
346 mk_preamble st what script
348 and proc_appl st what hd tl =
349 let proceed, dtext = test_depth st in
350 let script = if proceed then
351 let ty = get_type "TC2" st hd in
352 let classes, rc = Cl.classify st.context ty in
353 let goal_arity, goal = match get_inner_types st what with
356 snd (PEH.split_with_whd (st.context, H.cic ity)), Some (H.cic ety)
358 let parsno, argsno = List.length classes, List.length tl in
359 let decurry = parsno - argsno in
360 let diff = goal_arity - decurry in
361 if diff < 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (H.cic hd)));
362 let classes = Cl.adjust st.context tl ?goal classes in
363 let rec mk_synth a n =
364 if n < 0 then a else mk_synth (I.S.add n a) (pred n)
366 let synth = mk_synth I.S.empty decurry in
367 let text = "" (* Printf.sprintf "%u %s" parsno (Cl.to_string h) *) in
368 let script = List.rev (mk_arg st hd) in
370 | Some (i, j, uri, tyno) ->
371 let classes2, tl2, _, where = split2_last classes tl in
372 let script2 = List.rev (mk_arg st where) @ script in
373 let synth2 = I.S.add 1 synth in
374 let names = get_ind_names uri tyno in
375 let qs = proc_bkd_proofs (next st) synth2 names classes2 tl2 in
376 if List.length qs <> List.length names then
377 let qs = proc_bkd_proofs (next st) synth [] classes tl in
378 let hd = mk_exp_args hd tl classes synth in
379 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
380 else if is_rewrite_right hd then
381 script2 @ mk_rewrite st dtext where qs tl2 false what
382 else if is_rewrite_left hd then
383 script2 @ mk_rewrite st dtext where qs tl2 true what
385 let predicate = List.nth tl2 (parsno - i) in
386 let e = Cn.mk_pattern j predicate in
387 let using = Some hd in
388 (* convert_elim st what what e @ *) script2 @
389 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
391 let qs = proc_bkd_proofs (next st) synth [] classes tl in
392 let hd = mk_exp_args hd tl classes synth in
393 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
395 [T.Apply (what, dtext)]
397 mk_preamble st what script
399 and proc_other st what =
400 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
401 let script = [T.Note text] in
402 mk_preamble st what script
404 and proc_proof st t =
406 let xtypes, note = match get_inner_types st t with
407 | Some (it, et) -> Some (H.cic it, H.cic et),
408 (Printf.sprintf "\nInferred: %s\nExpected: %s"
409 (Pp.ppterm (H.cic it)) (Pp.ppterm (H.cic et)))
410 | None -> None, "\nNo types"
412 let context, clears = Cn.get_clears st.context (H.cic t) xtypes in
413 let note = Pp.ppcontext st.context ^ note in
414 {st with context = context; clears = clears; clears_note = note; }
417 | C.ALambda (_, name, w, t) as what -> proc_lambda (f st) what name w t
418 | C.ALetIn (_, name, v, w, t) as what -> proc_letin (f st) what name v w t
419 | C.ARel _ as what -> proc_rel (f st) what
420 | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
421 | C.AConst _ as what -> proc_const (f st) what
422 | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
423 | what -> proc_other (f st) what
425 and proc_bkd_proofs st synth names classes ts =
428 let names = ref (names, push st) in
431 | [], st -> fun _ -> f st
432 | "" :: tl, st -> names := tl, st; fun _ -> f st
434 let note = case st hd in
436 fun b -> if b then T.Note note :: f st else f st
438 let _, dtext = test_depth st in
440 if I.overlaps synth inv then None else
441 if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
442 Some (fun _ -> [T.Apply (v, dtext ^ "dependent")])
444 let ps = T.list_map2_filter aux classes ts in
445 let b = List.length ps > 1 in
446 List.rev_map (fun f -> f b) ps
448 with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
450 (* object costruction *******************************************************)
452 let is_theorem pars =
454 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
455 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
457 let proc_obj st = function
458 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
459 let ast = proc_proof st v in
460 let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in
461 let text = Printf.sprintf "tactics: %u\nnodes: %u" steps nodes in
462 if st.skip_thm_and_qed then ast
463 else T.Theorem (Some s, t, "") :: ast @ [T.Qed text]
465 failwith "not a theorem"
467 (* interface functions ******************************************************)
469 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth
470 ?(skip_thm_and_qed=false) prefix aobj =
472 sorts = ids_to_inner_sorts;
473 types = ids_to_inner_types;
481 skip_thm_and_qed = skip_thm_and_qed;
483 HLog.debug "Procedural: level 2 transformation";
484 let steps = proc_obj st aobj in
485 HLog.debug "Procedural: grafite rendering";
486 List.rev (T.render_steps [] steps)