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;
59 skip_initial_lambdas : 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 clear st = {st with intros = []}
92 let next st = {(clear st) with depth = succ st.depth}
94 let add st entry intro =
95 {st with context = entry :: st.context; intros = intro :: st.intros}
97 let push st = {st with case = 1 :: st.case}
100 {st with case = match st.case with
102 | hd :: tl -> succ hd :: tl
106 let case = String.concat "." (List.rev_map string_of_int st.case) in
107 Printf.sprintf "case %s: %s" case str
111 let msg = Printf.sprintf "Depth %u: " st.depth in
112 match st.max_depth with
114 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
115 with Invalid_argument _ -> failwith "A2P.test_depth"
117 let is_rewrite_right = function
118 | C.AConst (_, uri, []) ->
119 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
122 let is_rewrite_left = function
123 | C.AConst (_, uri, []) ->
124 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
127 let is_fwd_rewrite_right hd tl =
128 if is_rewrite_right hd then match List.nth tl 3 with
133 let is_fwd_rewrite_left hd tl =
134 if is_rewrite_left hd then match List.nth tl 3 with
139 let get_inner_types st v =
141 let id = Ut.id_of_annterm v in
142 try match Hashtbl.find st.types id with
143 | {A.annsynthesized = st; A.annexpected = Some et} -> Some (st, et)
144 | {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
145 with Not_found -> None
146 with Invalid_argument _ -> failwith "A2P.get_inner_types"
148 let get_inner_sort st v =
150 let id = Ut.id_of_annterm v in
151 try Hashtbl.find st.sorts id
152 with Not_found -> `Type (CicUniv.fresh())
153 with Invalid_argument _ -> failwith "A2P.get_sort"
155 let get_type msg st bo =
157 let ty, _ = TC.type_of_aux' [] st.context (H.cic bo) Un.empty_ugraph in
159 with e -> failwith (msg ^ ": " ^ Printexc.to_string e)
161 let get_entry st id =
162 let rec aux = function
164 | Some (C.Name name, e) :: _ when name = id -> e
169 let get_ind_names uri tno =
171 let ts = match E.get_obj Un.empty_ugraph uri with
172 | C.InductiveDefinition (ts, _, _, _), _ -> ts
175 match List.nth ts tno with
176 | (_, _, _, cs) -> List.map fst cs
177 with Invalid_argument _ -> failwith "A2P.get_ind_names"
179 (* proof construction *******************************************************)
181 let used_premise = C.Name "USED"
183 let mk_exp_args hd tl classes synth =
184 let meta id = C.AImplicit (id, None) in
186 if I.overlaps synth cl && b then v else meta ""
188 let rec aux = function
190 | hd :: tl -> if hd = meta "" then aux tl else List.rev (hd :: tl)
192 let args = T.list_rev_map2 map tl classes in
193 let args = aux args in
194 if args = [] then hd else C.AAppl ("", hd :: args)
196 let mk_convert st ?name sty ety note =
197 let e = Cn.hole "" in
198 let csty, cety = H.cic sty, H.cic ety in
199 let _note = Printf.sprintf "%s\nSINTH: %s\nEXP: %s"
200 note (Pp.ppterm csty) (Pp.ppterm cety)
202 if Ut.alpha_equivalence csty cety then [(* T.Note note *)] else
204 | None -> [T.Change (sty, ety, None, e, ""(*note*))]
206 begin match get_entry st id with
207 | C.Def _ -> assert false (* [T.ClearBody (id, note)] *)
208 | C.Decl _ -> [T.Change (ety, sty, Some (id, Some id), e, "" (* note *))]
211 let convert st ?name v =
212 match get_inner_types st v with
213 | None -> [(*T.Note "NORMAL: NO INNER TYPES"*)]
214 | Some (sty, ety) -> mk_convert st ?name sty ety "NORMAL"
216 let convert_elim st ?name t v pattern =
217 match t, get_inner_types st t, get_inner_types st v with
219 | _, _, None -> [(* T.Note "ELIM: NO INNER TYPES"*)]
220 | C.AAppl (_, hd :: tl), Some (tsty, _), Some (vsty, _) ->
221 let where = List.hd (List.rev tl) in
222 let cty = Cn.elim_inferred_type
223 st.context (H.cic vsty) (H.cic where) (H.cic hd) (H.cic pattern)
225 mk_convert st ?name (Cn.fake_annotate "" st.context cty) tsty "ELIM"
226 | _, Some _, Some _ -> assert false
228 let get_intro = function
229 | C.Anonymous -> None
232 let mk_intros st what script =
233 let intros st script =
234 if st.intros = [] then script else
235 let count = List.length st.intros in
236 T.Intros (Some count, List.rev st.intros, "") :: script
238 let clears st script =
239 if true (* st.clears = [] *) then script else T.Clear (st.clears, st.clears_note) :: script
241 intros st (clears st (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 t =
248 assert (List.length tl = 6);
249 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
250 let e = Cn.mk_pattern 1 predicate in
252 | C.ARel (_, _, i, premise) as v ->
253 let where = Some (premise, name) in
254 (* let _script = convert_elim st ~name:(premise, i) t v e in *)
255 let script = mk_arg st what @ mk_arg st v (* @ script *) in
256 let st = {st with context = Cn.clear st.context premise} in
257 st, T.Rewrite (direction, what, where, e, dtext) :: script
260 let mk_rewrite st dtext where qs tl direction t =
261 assert (List.length tl = 5);
262 let predicate = List.nth tl 2 in
263 let e = Cn.mk_pattern 1 predicate in
264 let script = [] (* convert_elim st t t e *) in
265 script @ [T.Rewrite (direction, where, None, e, dtext); T.Branch (qs, "")]
267 let rec proc_lambda st name v t =
268 let dno = DTI.does_not_occur 1 (H.cic t) in
269 let dno = dno && match get_inner_types st t with
272 DTI.does_not_occur 1 (H.cic it) && DTI.does_not_occur 1 (H.cic et)
274 let name = match dno, name with
275 | true, _ -> C.Anonymous
276 | false, C.Anonymous -> H.mk_fresh_name st.context used_premise
277 | false, name -> name
279 let entry = Some (name, C.Decl (H.cic v)) in
280 let intro = get_intro name in
281 proc_proof (add st entry intro) t
283 and proc_letin st what name v t =
284 let intro = get_intro name in
285 let proceed, dtext = test_depth st in
286 let script = if proceed then
287 let st, hyp, rqv = match get_inner_types st v with
289 let st, rqv = match v with
290 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
291 mk_fwd_rewrite st dtext intro tl true v
292 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
293 mk_fwd_rewrite st dtext intro tl false v
295 let qs = [proc_proof (next st) v; [T.Id ""]] in
296 st, [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
298 st, C.Decl (H.cic ity), rqv
300 st, C.Def (H.cic v, None), [T.LetIn (intro, v, dtext)]
302 let entry = Some (name, hyp) in
303 let qt = proc_proof (next (add st entry intro)) t in
304 List.rev_append rqv qt
306 [T.Apply (what, dtext)]
308 mk_intros st what script
310 and proc_rel st what =
311 let _, dtext = test_depth st in
312 let text = "assumption" in
313 let script = [T.Apply (what, dtext ^ text)] in
314 mk_intros st what script
316 and proc_mutconstruct st what =
317 let _, dtext = test_depth st in
318 let script = [T.Apply (what, dtext)] in
319 mk_intros st what script
321 and proc_appl st what hd tl =
322 let proceed, dtext = test_depth st in
323 let script = if proceed then
324 let ty = get_type "TC2" st hd in
325 let classes, rc = Cl.classify st.context ty in
326 let goal_arity = match get_inner_types st what with
328 | Some (ity, _) -> snd (PEH.split_with_whd (st.context, H.cic ity))
330 let parsno, argsno = List.length classes, List.length tl in
331 let decurry = parsno - argsno in
332 let diff = goal_arity - decurry in
333 if diff < 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (H.cic hd)));
334 let rec mk_synth a n =
335 if n < 0 then a else mk_synth (I.S.add n a) (pred n)
337 let synth = mk_synth I.S.empty decurry in
338 let text = "" (* Printf.sprintf "%u %s" parsno (Cl.to_string h) *) in
339 let script = List.rev (mk_arg st hd) in
341 | Some (i, j, uri, tyno) ->
342 let classes, tl, _, where = split2_last classes tl in
343 let script = List.rev (mk_arg st where) @ script in
344 let synth = I.S.add 1 synth in
345 let names = get_ind_names uri tyno in
346 let qs = proc_bkd_proofs (next st) synth names classes tl in
347 if is_rewrite_right hd then
348 script @ mk_rewrite st dtext where qs tl false what
349 else if is_rewrite_left hd then
350 script @ mk_rewrite st dtext where qs tl true what
352 let predicate = List.nth tl (parsno - i) in
353 let e = Cn.mk_pattern j predicate in
354 let using = Some hd in
355 (* convert_elim st what what e @ *) script @
356 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
358 let qs = proc_bkd_proofs (next st) synth [] classes tl in
359 let hd = mk_exp_args hd tl classes synth in
360 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
362 [T.Apply (what, dtext)]
364 mk_intros st what script
366 and proc_other st what =
367 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
368 let script = [T.Note text] in
369 mk_intros st what script
371 and proc_proof st t =
373 let xtypes, note = match get_inner_types st t with
374 | Some (it, et) -> Some (H.cic it, H.cic et),
375 (Printf.sprintf "\nInferred: %s\nExpected: %s"
376 (Pp.ppterm (H.cic it)) (Pp.ppterm (H.cic et)))
377 | None -> None, "\nNo types"
379 let context, clears =
380 if st.skip_initial_lambdas then
383 Cn.get_clears st.context (H.cic t) xtypes
385 let note = Pp.ppcontext st.context ^ note in
386 {st with context = context; clears = clears; clears_note = note; }
389 | C.ALambda (_, name, w, t) -> proc_lambda st name w t
390 | C.ALetIn (_, name, v, t) as what -> proc_letin (f st) what name v t
391 | C.ARel _ as what -> proc_rel (f st) what
392 | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
393 | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
394 | what -> proc_other (f st) what
396 and proc_bkd_proofs st synth names classes ts =
399 let names = ref (names, push st) in
402 | [], st -> fun _ -> f st
403 | "" :: tl, st -> names := tl, st; fun _ -> f st
405 let note = case st hd in
407 fun b -> if b then T.Note note :: f st else f st
409 let _, dtext = test_depth st in
411 if I.overlaps synth inv then None else
412 if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
413 Some (fun _ -> [T.Apply (v, dtext ^ "dependent")])
415 let ps = T.list_map2_filter aux classes ts in
416 let b = List.length ps > 1 in
417 List.rev_map (fun f -> f b) ps
419 with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
421 (* object costruction *******************************************************)
423 let is_theorem pars =
424 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
425 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
427 let proc_obj st = function
428 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
429 let ast = proc_proof st v in
430 let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in
431 let text = Printf.sprintf "tactics: %u\nnodes: %u" steps nodes in
433 if st.skip_initial_lambdas then
435 | T.Intros _::tl -> tl
439 if st.skip_thm_and_qed then ast
440 else T.Theorem (Some s, t, "") :: ast @ [T.Qed text]
442 failwith "not a theorem"
444 (* interface functions ******************************************************)
446 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth
447 ?(skip_thm_and_qed=false) ?(skip_initial_lambdas=false) prefix aobj =
449 sorts = ids_to_inner_sorts;
450 types = ids_to_inner_types;
459 skip_thm_and_qed = skip_thm_and_qed;
460 skip_initial_lambdas = skip_initial_lambdas;
462 HLog.debug "Procedural: level 2 transformation";
463 let steps = proc_obj st aobj in
464 HLog.debug "Procedural: grafite rendering";
465 List.rev (T.render_steps [] steps)