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/.
29 module S = CicSubstitution
30 module TC = CicTypeChecker
32 module UM = UriManager
33 module Obj = LibraryObjects
34 module HObj = HelmLibraryObjects
37 module E = CicEnvironment
39 module PEH = ProofEngineHelpers
41 module DTI = DoubleTypeInference
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;
52 max_depth: int option;
55 intros: string option list;
61 (* helpers ******************************************************************)
63 let cic = D.deannotate_term
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 (cic bo) Un.empty_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.empty_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 convert st ?name v =
198 match get_inner_types st v with
201 let e = Cn.hole "" in
202 let csty, cety = cic sty, cic ety in
203 if Ut.alpha_equivalence csty cety then [] else
205 | None -> [T.Change (sty, ety, None, e, "")]
207 begin match get_entry st id with
208 | C.Def _ -> [T.ClearBody (id, "")]
210 let w = S.lift i w in
211 if Ut.alpha_equivalence csty w then []
213 [T.Note (Pp.ppterm csty); T.Note (Pp.ppterm w);
214 T.Change (sty, ety, Some (id, Some id), e, "")]
217 let get_intro = function
218 | C.Anonymous -> None
221 let mk_intros st script =
222 let intros st script =
223 if st.intros = [] then script else
224 let count = List.length st.intros in
225 T.Intros (Some count, List.rev st.intros, "") :: script
227 let clears st script =
228 if st.clears = [] then script else T.Clear (st.clears, st.clears_note) :: script
230 intros st (clears st script)
232 let mk_arg st = function
233 | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
236 let mk_fwd_rewrite st dtext name tl direction =
237 assert (List.length tl = 6);
238 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
239 let e = Cn.mk_pattern 1 predicate in
241 | C.ARel (_, _, _, premise) ->
242 let script = mk_arg st what in
243 let where = Some (premise, name) in
244 let st = {st with context = Cn.clear st.context premise} in
245 st, T.Rewrite (direction, what, where, e, dtext) :: script
248 let mk_rewrite st dtext what qs tl direction =
249 assert (List.length tl = 5);
250 let predicate = List.nth tl 2 in
251 let e = Cn.mk_pattern 1 predicate in
252 [T.Rewrite (direction, what, None, e, dtext); T.Branch (qs, "")]
254 let rec proc_lambda st name v t =
255 let dno = DTI.does_not_occur 1 (cic t) in
256 let dno = dno && match get_inner_types st t with
259 DTI.does_not_occur 1 (cic it) && DTI.does_not_occur 1 (cic et)
261 let name = match dno, name with
262 | true, _ -> C.Anonymous
263 | false, C.Anonymous -> H.mk_fresh_name st.context used_premise
264 | false, name -> name
266 let entry = Some (name, C.Decl (cic v)) in
267 let intro = get_intro name in
268 proc_proof (add st entry intro) t
270 and proc_letin st what name v t =
271 let intro = get_intro name in
272 let proceed, dtext = test_depth st in
273 let script = if proceed then
274 let st, hyp, rqv = match get_inner_types st v with
276 let st, rqv = match v with
277 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
278 mk_fwd_rewrite st dtext intro tl true
279 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
280 mk_fwd_rewrite st dtext intro tl false
282 let qs = [proc_proof (next st) v; [T.Id ""]] in
283 st, [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
285 st, C.Decl (cic ity), rqv
287 st, C.Def (cic v, None), [T.LetIn (intro, v, dtext)]
289 let entry = Some (name, hyp) in
290 let qt = proc_proof (next (add st entry intro)) t in
291 List.rev_append rqv qt
293 [T.Apply (what, dtext)]
297 and proc_rel st what =
298 let _, dtext = test_depth st in
299 let text = "assumption" in
300 let script = [T.Apply (what, dtext ^ text)] in
303 and proc_mutconstruct st what =
304 let _, dtext = test_depth st in
305 let script = [T.Apply (what, dtext)] in
308 and proc_appl st what hd tl =
309 let proceed, dtext = test_depth st in
310 let script = if proceed then
311 let ty = get_type "TC2" st hd in
312 let classes, rc = Cl.classify st.context ty in
313 let goal_arity = match get_inner_types st what with
315 | Some (ity, _) -> snd (PEH.split_with_whd (st.context, cic ity))
317 let parsno, argsno = List.length classes, List.length tl in
318 let decurry = parsno - argsno in
319 let diff = goal_arity - decurry in
320 if diff < 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (cic hd)));
321 let rec mk_synth a n =
322 if n < 0 then a else mk_synth (I.S.add n a) (pred n)
324 let synth = mk_synth I.S.empty decurry in
325 let text = "" (* Printf.sprintf "%u %s" parsno (Cl.to_string h) *) in
326 let script = List.rev (mk_arg st hd) @ convert st what in
328 | Some (i, j, uri, tyno) ->
329 let classes, tl, _, where = split2_last classes tl in
330 let script = List.rev (mk_arg st where) @ script in
331 let synth = I.S.add 1 synth in
332 let names = get_ind_names uri tyno in
333 let qs = proc_bkd_proofs (next st) synth names classes tl in
334 if is_rewrite_right hd then
335 script @ mk_rewrite st dtext where qs tl false
336 else if is_rewrite_left hd then
337 script @ mk_rewrite st dtext where qs tl true
339 let predicate = List.nth tl (parsno - i) in
340 let e = Cn.mk_pattern j predicate in
341 let using = Some hd in
343 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
345 let qs = proc_bkd_proofs (next st) synth [] classes tl in
346 let hd = mk_exp_args hd tl classes synth in
347 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
349 [T.Apply (what, dtext)]
353 and proc_other st what =
354 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
355 let script = [T.Note text] in
358 and proc_proof st t =
360 let xtypes, note = match get_inner_types st t with
361 | Some (it, et) -> Some (cic it, cic et),
362 (Printf.sprintf "\nInferred: %s\nExpected: %s"
363 (Pp.ppterm (cic it)) (Pp.ppterm (cic et)))
364 | None -> None, "\nNo types"
366 let context, clears = Cn.get_clears st.context (cic t) xtypes in
367 let note = Pp.ppcontext st.context ^ note in
368 {st with context = context; clears = clears; clears_note = note}
371 | C.ALambda (_, name, w, t) -> proc_lambda st name w t
372 | C.ALetIn (_, name, v, t) as what -> proc_letin (f st) what name v t
373 | C.ARel _ as what -> proc_rel (f st) what
374 | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
375 | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
376 | what -> proc_other (f st) what
378 and proc_bkd_proofs st synth names classes ts =
381 let names = ref (names, push st) in
384 | [], st -> fun _ -> f st
385 | "" :: tl, st -> names := tl, st; fun _ -> f st
387 let note = case st hd in
389 fun b -> if b then T.Note note :: f st else f st
391 let _, dtext = test_depth st in
393 if I.overlaps synth inv then None else
394 if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
395 Some (fun _ -> [T.Apply (v, dtext ^ "dependent")])
397 let ps = T.list_map2_filter aux classes ts in
398 let b = List.length ps > 1 in
399 List.rev_map (fun f -> f b) ps
401 with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
403 (* object costruction *******************************************************)
405 let is_theorem pars =
406 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
407 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
409 let proc_obj st = function
410 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
411 let ast = proc_proof st v in
412 let count = T.count_steps 0 ast in
413 let text = Printf.sprintf "tactics: %u" count in
414 T.Theorem (Some s, t, "") :: ast @ [T.Qed text]
416 failwith "not a theorem"
418 (* interface functions ******************************************************)
420 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth prefix aobj =
422 sorts = ids_to_inner_sorts;
423 types = ids_to_inner_types;
433 HLog.debug "Procedural: level 2 transformation";
434 let steps = proc_obj st aobj in
435 HLog.debug "Procedural: grafite rendering";
436 List.rev (T.render_steps [] steps)