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
41 module NU = CicNotationUtil
43 module Cl = ProceduralClassify
44 module T = ProceduralTypes
45 module Cn = ProceduralConversion
46 module H = ProceduralHelpers
49 sorts : (C.id, A.sort_kind) Hashtbl.t;
50 types : (C.id, A.anntypes) Hashtbl.t;
51 max_depth: int option;
59 (* helpers ******************************************************************)
61 let split2_last l1 l2 =
63 let n = pred (List.length l1) in
64 let before1, after1 = HEL.split_nth n l1 in
65 let before2, after2 = HEL.split_nth n l2 in
66 before1, before2, List.hd after1, List.hd after2
67 with Invalid_argument _ -> failwith "A2P.split2_last"
69 let string_of_head = function
71 | C.AConst _ -> "const"
72 | C.AMutInd _ -> "mutind"
73 | C.AMutConstruct _ -> "mutconstruct"
77 | C.ALambda _ -> "lambda"
78 | C.ALetIn _ -> "letin"
80 | C.ACoFix _ -> "cofix"
83 | C.AMutCase _ -> "mutcase"
85 | C.AImplicit _ -> "implict"
87 let next st = {st with depth = succ st.depth}
89 let add st entry = {st with context = entry :: st.context}
91 let push st = {st with case = 1 :: st.case}
94 {st with case = match st.case with
96 | hd :: tl -> succ hd :: tl
100 let case = String.concat "." (List.rev_map string_of_int st.case) in
101 Printf.sprintf "case %s: %s" case str
105 let msg = Printf.sprintf "Depth %u: " st.depth in
106 match st.max_depth with
108 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
109 with Invalid_argument _ -> failwith "A2P.test_depth"
111 let is_rewrite_right = function
112 | C.AConst (_, uri, []) ->
113 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
116 let is_rewrite_left = function
117 | C.AConst (_, uri, []) ->
118 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
121 let is_fwd_rewrite_right hd tl =
122 if is_rewrite_right hd then match List.nth tl 3 with
127 let is_fwd_rewrite_left hd tl =
128 if is_rewrite_left hd then match List.nth tl 3 with
133 let get_inner_types st v =
135 let id = Ut.id_of_annterm v in
136 try match Hashtbl.find st.types id with
137 | {A.annsynthesized = st; A.annexpected = Some et} -> Some (st, et)
138 | {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
139 with Not_found -> None
140 with Invalid_argument _ -> failwith "A2P.get_inner_types"
142 let get_inner_sort st v =
144 let id = Ut.id_of_annterm v in
145 try Hashtbl.find st.sorts id
146 with Not_found -> `Type (CicUniv.fresh())
147 with Invalid_argument _ -> failwith "A2P.get_sort"
149 let get_entry st id =
150 let rec aux = function
152 | Some (C.Name name, e) :: _ when name = id -> e
157 let string_of_atomic = function
158 | C.ARel (_, _, _, s) -> s
159 | C.AVar (_, uri, _) -> H.name_of_uri uri None None
160 | C.AConst (_, uri, _) -> H.name_of_uri uri None None
161 | C.AMutInd (_, uri, i, _) -> H.name_of_uri uri (Some i) None
162 | C.AMutConstruct (_, uri, i, j, _) -> H.name_of_uri uri (Some i) (Some j)
165 let get_sub_names head l =
166 let s = string_of_atomic head in
167 if s = "" then [] else
168 let map (names, i) _ =
169 let name = Printf.sprintf "%s_%u" s i in name :: names, succ i
171 let names, _ = List.fold_left map ([], 1) l in
174 let get_type msg st t = H.get_type msg st.context (H.cic t)
176 (* proof construction *******************************************************)
178 let anonymous_premise = C.Name "PREMISE"
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 st.context csty);
206 assert (Ut.is_sober st.context 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 convert st what @ script
243 let mk_arg st = function
244 | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
247 let mk_fwd_rewrite st dtext name tl direction v t ity =
248 let compare premise = function
250 | Some s -> s = premise
252 assert (List.length tl = 6);
253 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
254 let e = Cn.mk_pattern 1 predicate in
255 if (Cn.does_not_occur e) then st, [] else
257 | C.ARel (_, _, i, premise) as w ->
258 (* let _script = convert_elim st ~name:(premise, i) v w e in *)
260 let where = Some (premise, name) in
261 let script = mk_arg st what @ mk_arg st w (* @ script *) in
262 T.Rewrite (direction, what, where, e, dtext) :: script
264 if DTI.does_not_occur (succ i) (H.cic t) || compare premise name then
265 {st with context = Cn.clear st.context premise}, script name
267 assert (Ut.is_sober st.context (H.cic ity));
268 let ity = H.acic_bc st.context ity in
269 let br1 = [T.Id ""] in
270 let br2 = List.rev (T.Apply (w, "assumption") :: script None) in
271 let text = "non linear rewrite" in
272 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 name = match name with
287 | C.Anonymous -> H.mk_fresh_name st.context anonymous_premise
290 let entry = Some (name, C.Decl (H.cic v)) in
291 let intro = get_intro name in
292 let script = proc_proof (add st entry) t in
293 let script = T.Intros (Some 1, [intro], "") :: script in
294 mk_preamble st what script
296 and proc_letin st what name v w t =
297 let intro = get_intro name in
298 let proceed, dtext = test_depth st in
299 let script = if proceed then
300 let st, hyp, rqv = match get_inner_types st v with
302 let st, rqv = match v with
303 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
304 mk_fwd_rewrite st dtext intro tl true v t ity
305 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
306 mk_fwd_rewrite st dtext intro tl false v t ity
308 assert (Ut.is_sober st.context (H.cic ity));
309 let ity = H.acic_bc st.context ity in
310 let qs = [proc_proof (next st) v; [T.Id ""]] in
311 st, [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
313 st, C.Decl (H.cic ity), rqv
315 st, C.Def (H.cic v, H.cic w), [T.LetIn (intro, v, dtext)]
317 let entry = Some (name, hyp) in
318 let qt = proc_proof (next (add st entry)) t in
319 List.rev_append rqv qt
321 [T.Apply (what, dtext)]
323 mk_preamble st what script
325 and proc_rel st what =
326 let _, dtext = test_depth st in
327 let text = "assumption" in
328 let script = [T.Apply (what, dtext ^ text)] in
329 mk_preamble st what script
331 and proc_mutconstruct st what =
332 let _, dtext = test_depth st in
333 let script = [T.Apply (what, dtext)] in
334 mk_preamble st what script
336 and proc_const st what =
337 let _, dtext = test_depth st in
338 let script = [T.Apply (what, dtext)] in
339 mk_preamble st what script
341 and proc_appl st what hd tl =
342 let proceed, dtext = test_depth st in
343 let script = if proceed then
344 let ty = get_type "TC2" st hd in
345 let classes, rc = Cl.classify st.context ty in
346 let goal_arity, goal = match get_inner_types st what with
349 snd (PEH.split_with_whd (st.context, H.cic ity)), Some (H.cic ety)
351 let parsno, argsno = List.length classes, List.length tl in
352 let decurry = parsno - argsno in
353 let diff = goal_arity - decurry in
354 if diff < 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (H.cic hd)));
355 let classes = Cl.adjust st.context tl ?goal classes in
356 let rec mk_synth a n =
357 if n < 0 then a else mk_synth (I.S.add n a) (pred n)
359 let synth = mk_synth I.S.empty decurry in
360 let text = "" (* Printf.sprintf "%u %s" parsno (Cl.to_string h) *) in
361 let script = List.rev (mk_arg st hd) in
363 | Some (i, j, uri, tyno) ->
364 let classes2, tl2, _, where = split2_last classes tl in
365 let script2 = List.rev (mk_arg st where) @ script in
366 let synth2 = I.S.add 1 synth in
367 let names = H.get_ind_names uri tyno in
368 let qs = proc_bkd_proofs (next st) synth2 names classes2 tl2 in
369 if List.length qs <> List.length names then
370 let qs = proc_bkd_proofs (next st) synth [] classes tl in
371 let hd = mk_exp_args hd tl classes synth in
372 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
373 else if is_rewrite_right hd then
374 script2 @ mk_rewrite st dtext where qs tl2 false what
375 else if is_rewrite_left hd then
376 script2 @ mk_rewrite st dtext where qs tl2 true what
378 let predicate = List.nth tl2 (parsno - i) in
379 let e = Cn.mk_pattern j predicate in
380 let using = Some hd in
381 (* convert_elim st what what e @ *) script2 @
382 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
384 let names = get_sub_names hd tl in
385 let qs = proc_bkd_proofs (next st) synth names classes tl in
386 let hd = mk_exp_args hd tl classes synth in
387 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
389 [T.Apply (what, dtext)]
391 mk_preamble st what script
393 and proc_other st what =
394 let _, dtext = test_depth st in
395 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
396 let script = [T.Apply (what, dtext ^ text)] in
397 mk_preamble st what script
399 and proc_proof st t =
401 let xtypes, note = match get_inner_types st t with
402 | Some (it, et) -> Some (H.cic it, H.cic et),
403 (Printf.sprintf "\nInferred: %s\nExpected: %s"
404 (Pp.ppterm (H.cic it)) (Pp.ppterm (H.cic et)))
405 | None -> None, "\nNo types"
407 let context, _clears = Cn.get_clears st.context (H.cic t) xtypes in
408 {st with context = context}
411 | C.ALambda (_, name, w, t) as what -> proc_lambda (f st) what name w t
412 | C.ALetIn (_, name, v, w, t) as what -> proc_letin (f st) what name v w t
413 | C.ARel _ as what -> proc_rel (f st) what
414 | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
415 | C.AConst _ as what -> proc_const (f st) what
416 | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
417 | what -> proc_other (f st) what
419 and proc_bkd_proofs st synth names classes ts =
421 let get_names b = ref (names, if b then push st else st) in
422 let get_note f b names =
425 | "" :: tl, st -> names := tl, st; f st
427 let note = case st hd in
429 if b then T.Note note :: f st else f st
431 let _, dtext = test_depth st in
433 if I.overlaps synth inv then None else
434 if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
435 Some (get_note (fun _ -> [T.Apply (v, dtext ^ "dependent")]))
437 let ps = T.list_map2_filter aux classes ts in
438 let b = List.length ps > 1 in
439 let names = get_names b in
440 List.rev_map (fun f -> f b names) ps
442 with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
444 (* object costruction *******************************************************)
446 let th_flavours = [`Theorem; `Lemma; `Remark; `Fact]
448 let def_flavours = [`Definition]
450 let get_flavour ?flavour attrs =
451 let rec aux = function
452 | [] -> List.hd th_flavours
453 | `Flavour fl :: _ -> fl
460 let proc_obj ?flavour st = function
461 | C.AConstant (_, _, s, Some v, t, [], attrs) ->
462 begin match get_flavour ?flavour attrs with
463 | flavour when List.mem flavour th_flavours ->
464 let ast = proc_proof st v in
465 let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in
466 let text = Printf.sprintf "tactics: %u\nnodes: %u" steps nodes in
467 T.Statement (flavour, Some s, t, None, "") :: ast @ [T.Qed text]
468 | flavour when List.mem flavour def_flavours ->
469 [T.Statement (flavour, Some s, t, Some v, "")]
471 failwith "not a theorem, definition, axiom or inductive type"
473 | C.AConstant (_, _, s, None, t, [], attrs) ->
474 [T.Statement (`Axiom, Some s, t, None, "")]
475 | C.AInductiveDefinition (_, types, [], lpsno, attrs) ->
476 [T.Inductive (types, lpsno, "")]
478 failwith "not a theorem, definition, axiom or inductive type"
480 (* interface functions ******************************************************)
482 let procedural_of_acic_object ~ids_to_inner_sorts ~ids_to_inner_types ?depth
483 ?flavour prefix anobj =
485 sorts = ids_to_inner_sorts;
486 types = ids_to_inner_types;
492 HLog.debug "Procedural: level 2 transformation";
493 let steps = proc_obj st ?flavour anobj in
494 HLog.debug "Procedural: grafite rendering";
495 List.rev (T.render_steps [] steps)
497 let procedural_of_acic_term ~ids_to_inner_sorts ~ids_to_inner_types ?depth
498 prefix context annterm =
500 sorts = ids_to_inner_sorts;
501 types = ids_to_inner_types;
507 HLog.debug "Procedural: level 2 transformation";
508 let steps = proc_proof st annterm in
509 HLog.debug "Procedural: grafite rendering";
510 List.rev (T.render_steps [] steps)