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;
60 (* helpers ******************************************************************)
62 let split2_last l1 l2 =
64 let n = pred (List.length l1) in
65 let before1, after1 = HEL.split_nth n l1 in
66 let before2, after2 = HEL.split_nth n l2 in
67 before1, before2, List.hd after1, List.hd after2
68 with Invalid_argument _ -> failwith "A2P.split2_last"
70 let string_of_head = function
72 | C.AConst _ -> "const"
73 | C.AMutInd _ -> "mutind"
74 | C.AMutConstruct _ -> "mutconstruct"
78 | C.ALambda _ -> "lambda"
79 | C.ALetIn _ -> "letin"
81 | C.ACoFix _ -> "cofix"
84 | C.AMutCase _ -> "mutcase"
86 | C.AImplicit _ -> "implict"
88 let clear st = {st with intros = []}
90 let next st = {(clear st) with depth = succ st.depth}
92 let add st entry intro =
93 {st with context = entry :: st.context; intros = intro :: st.intros}
95 let push st = {st with case = 1 :: st.case}
98 {st with case = match st.case with
100 | hd :: tl -> succ hd :: tl
104 let case = String.concat "." (List.rev_map string_of_int st.case) in
105 Printf.sprintf "case %s: %s" case str
109 let msg = Printf.sprintf "Depth %u: " st.depth in
110 match st.max_depth with
112 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
113 with Invalid_argument _ -> failwith "A2P.test_depth"
115 let is_rewrite_right = function
116 | C.AConst (_, uri, []) ->
117 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
120 let is_rewrite_left = function
121 | C.AConst (_, uri, []) ->
122 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
125 let is_fwd_rewrite_right hd tl =
126 if is_rewrite_right hd then match List.nth tl 3 with
131 let is_fwd_rewrite_left hd tl =
132 if is_rewrite_left hd then match List.nth tl 3 with
137 let get_inner_types st v =
139 let id = Ut.id_of_annterm v in
140 try match Hashtbl.find st.types id with
141 | {A.annsynthesized = st; A.annexpected = Some et} -> Some (st, et)
142 | {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
143 with Not_found -> None
144 with Invalid_argument _ -> failwith "A2P.get_inner_types"
146 let get_inner_sort st v =
148 let id = Ut.id_of_annterm v in
149 try Hashtbl.find st.sorts id
150 with Not_found -> `Type (CicUniv.fresh())
151 with Invalid_argument _ -> failwith "A2P.get_sort"
153 let get_type msg st bo =
155 let ty, _ = TC.type_of_aux' [] st.context (H.cic bo) Un.empty_ugraph in
157 with e -> failwith (msg ^ ": " ^ Printexc.to_string e)
159 let get_entry st id =
160 let rec aux = function
162 | Some (C.Name name, e) :: _ when name = id -> e
167 let get_ind_names uri tno =
169 let ts = match E.get_obj Un.empty_ugraph uri with
170 | C.InductiveDefinition (ts, _, _, _), _ -> ts
173 match List.nth ts tno with
174 | (_, _, _, cs) -> List.map fst cs
175 with Invalid_argument _ -> failwith "A2P.get_ind_names"
177 (* proof construction *******************************************************)
179 let used_premise = C.Name "USED"
181 let mk_exp_args hd tl classes synth =
182 let meta id = C.AImplicit (id, None) in
184 if I.overlaps synth cl && b then v else meta ""
186 let rec aux = function
188 | hd :: tl -> if hd = meta "" then aux tl else List.rev (hd :: tl)
190 let args = T.list_rev_map2 map tl classes in
191 let args = aux args in
192 if args = [] then hd else C.AAppl ("", hd :: args)
194 let convert st ?name v =
195 match get_inner_types st v with
198 let e = Cn.hole "" in
199 let csty, cety = H.cic sty, H.cic ety in
200 if Ut.alpha_equivalence csty cety then [] else
202 | None -> [T.Change (sty, ety, None, e, "")]
204 begin match get_entry st id with
205 | C.Def _ -> [T.ClearBody (id, "")]
207 let w = S.lift i w in
208 if Ut.alpha_equivalence csty w then []
210 [T.Note (Pp.ppterm csty); T.Note (Pp.ppterm w);
211 T.Change (sty, ety, Some (id, Some id), e, "")]
214 let get_intro = function
215 | C.Anonymous -> None
218 let mk_intros st what script =
219 let intros st script =
220 if st.intros = [] then script else
221 let count = List.length st.intros in
222 T.Intros (Some count, List.rev st.intros, "") :: script
224 let clears st script =
225 if true (* st.clears = [] *) then script else T.Clear (st.clears, st.clears_note) :: script
227 intros st (clears st (convert st what @ script))
229 let mk_arg st = function
230 | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
233 let mk_fwd_rewrite st dtext name tl direction =
234 assert (List.length tl = 6);
235 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
236 let e = Cn.mk_pattern 1 predicate in
238 | C.ARel (_, _, _, premise) ->
239 let script = mk_arg st what in
240 let where = Some (premise, name) in
241 let st = {st with context = Cn.clear st.context premise} in
242 st, T.Rewrite (direction, what, where, e, dtext) :: script
245 let mk_rewrite st dtext what qs tl direction =
246 assert (List.length tl = 5);
247 let predicate = List.nth tl 2 in
248 let e = Cn.mk_pattern 1 predicate in
249 [T.Rewrite (direction, what, None, e, dtext); T.Branch (qs, "")]
251 let rec proc_lambda st name v t =
252 let dno = DTI.does_not_occur 1 (H.cic t) in
253 let dno = dno && match get_inner_types st t with
256 DTI.does_not_occur 1 (H.cic it) && DTI.does_not_occur 1 (H.cic et)
258 let name = match dno, name with
259 | true, _ -> C.Anonymous
260 | false, C.Anonymous -> H.mk_fresh_name st.context used_premise
261 | false, name -> name
263 let entry = Some (name, C.Decl (H.cic v)) in
264 let intro = get_intro name in
265 proc_proof (add st entry intro) t
267 and proc_letin st what name v t =
268 let intro = get_intro name in
269 let proceed, dtext = test_depth st in
270 let script = if proceed then
271 let st, hyp, rqv = match get_inner_types st v with
273 let st, rqv = match v with
274 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
275 mk_fwd_rewrite st dtext intro tl true
276 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
277 mk_fwd_rewrite st dtext intro tl false
279 let qs = [proc_proof (next st) v; [T.Id ""]] in
280 st, [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
282 st, C.Decl (H.cic ity), rqv
284 st, C.Def (H.cic v, None), [T.LetIn (intro, v, dtext)]
286 let entry = Some (name, hyp) in
287 let qt = proc_proof (next (add st entry intro)) t in
288 List.rev_append rqv qt
290 [T.Apply (what, dtext)]
292 mk_intros st what script
294 and proc_rel st what =
295 let _, dtext = test_depth st in
296 let text = "assumption" in
297 let script = [T.Apply (what, dtext ^ text)] in
298 mk_intros st what script
300 and proc_mutconstruct st what =
301 let _, dtext = test_depth st in
302 let script = [T.Apply (what, dtext)] in
303 mk_intros st what script
305 and proc_appl st what hd tl =
306 let proceed, dtext = test_depth st in
307 let script = if proceed then
308 let ty = get_type "TC2" st hd in
309 let classes, rc = Cl.classify st.context ty in
310 let goal_arity = match get_inner_types st what with
312 | Some (ity, _) -> snd (PEH.split_with_whd (st.context, H.cic ity))
314 let parsno, argsno = List.length classes, List.length tl in
315 let decurry = parsno - argsno in
316 let diff = goal_arity - decurry in
317 if diff < 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (H.cic hd)));
318 let rec mk_synth a n =
319 if n < 0 then a else mk_synth (I.S.add n a) (pred n)
321 let synth = mk_synth I.S.empty decurry in
322 let text = "" (* Printf.sprintf "%u %s" parsno (Cl.to_string h) *) in
323 let script = List.rev (mk_arg st hd) in
325 | Some (i, j, uri, tyno) ->
326 let classes, tl, _, where = split2_last classes tl in
327 let script = List.rev (mk_arg st where) @ script in
328 let synth = I.S.add 1 synth in
329 let names = get_ind_names uri tyno in
330 let qs = proc_bkd_proofs (next st) synth names classes tl in
331 if is_rewrite_right hd then
332 script @ mk_rewrite st dtext where qs tl false
333 else if is_rewrite_left hd then
334 script @ mk_rewrite st dtext where qs tl true
336 let predicate = List.nth tl (parsno - i) in
337 let e = Cn.mk_pattern j predicate in
338 let using = Some hd in
340 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
342 let qs = proc_bkd_proofs (next st) synth [] classes tl in
343 let hd = mk_exp_args hd tl classes synth in
344 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
346 [T.Apply (what, dtext)]
348 mk_intros st what script
350 and proc_other st what =
351 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
352 let script = [T.Note text] in
353 mk_intros st what script
355 and proc_proof st t =
357 let xtypes, note = match get_inner_types st t with
358 | Some (it, et) -> Some (H.cic it, H.cic et),
359 (Printf.sprintf "\nInferred: %s\nExpected: %s"
360 (Pp.ppterm (H.cic it)) (Pp.ppterm (H.cic et)))
361 | None -> None, "\nNo types"
363 let context, clears = Cn.get_clears st.context (H.cic t) xtypes in
364 let note = Pp.ppcontext st.context ^ note in
365 {st with context = context; clears = clears; clears_note = note}
368 | C.ALambda (_, name, w, t) -> proc_lambda st name w t
369 | C.ALetIn (_, name, v, t) as what -> proc_letin (f st) what name v t
370 | C.ARel _ as what -> proc_rel (f st) what
371 | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
372 | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
373 | what -> proc_other (f st) what
375 and proc_bkd_proofs st synth names classes ts =
378 let names = ref (names, push st) in
381 | [], st -> fun _ -> f st
382 | "" :: tl, st -> names := tl, st; fun _ -> f st
384 let note = case st hd in
386 fun b -> if b then T.Note note :: f st else f st
388 let _, dtext = test_depth st in
390 if I.overlaps synth inv then None else
391 if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
392 Some (fun _ -> [T.Apply (v, dtext ^ "dependent")])
394 let ps = T.list_map2_filter aux classes ts in
395 let b = List.length ps > 1 in
396 List.rev_map (fun f -> f b) ps
398 with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
400 (* object costruction *******************************************************)
402 let is_theorem pars =
403 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
404 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
406 let proc_obj st = function
407 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
408 let ast = proc_proof st v in
409 let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in
410 let text = Printf.sprintf "tactics: %u\nnodes: %u" steps nodes in
411 T.Theorem (Some s, t, "") :: ast @ [T.Qed text]
413 failwith "not a theorem"
415 (* interface functions ******************************************************)
417 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth prefix aobj =
419 sorts = ids_to_inner_sorts;
420 types = ids_to_inner_types;
430 HLog.debug "Procedural: level 2 transformation";
431 let steps = proc_obj st aobj in
432 HLog.debug "Procedural: grafite rendering";
433 List.rev (T.render_steps [] steps)