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
42 module Cl = ProceduralClassify
43 module T = ProceduralTypes
44 module Cn = ProceduralConversion
47 sorts : (C.id, A.sort_kind) Hashtbl.t;
48 types : (C.id, A.anntypes) Hashtbl.t;
50 max_depth: int option;
57 (* helpers ******************************************************************)
59 let cic = D.deannotate_term
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 clear st = {st with intros = []}
89 let next st = {(clear st) with depth = succ st.depth}
91 let add st entry intro =
92 {st with context = entry :: st.context; intros = intro :: st.intros}
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 (cic bo) Un.empty_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.empty_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 unused_premise = "UNUSED"
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 convert st ?name v =
194 match get_inner_types st v with
197 let e = Cn.hole "" in
198 let csty, cety = cic sty, cic ety in
199 if Ut.alpha_equivalence csty cety then [] else
201 | None -> [T.Change (sty, ety, None, e, "")]
203 begin match get_entry st id with
204 | C.Def _ -> [T.ClearBody (id, "")]
206 let w = S.lift i w in
207 if Ut.alpha_equivalence csty w then []
209 [T.Note (Pp.ppterm csty); T.Note (Pp.ppterm w);
210 T.Change (sty, ety, Some (id, id), e, "")]
213 let get_intro = function
214 | C.Anonymous -> unused_premise
217 let mk_intros st script =
218 if st.intros = [] then script else
219 let count = List.length st.intros in
220 T.Intros (Some count, List.rev st.intros, "") :: script
222 let mk_arg st = function
223 | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
226 let mk_fwd_rewrite st dtext name tl direction =
227 assert (List.length tl = 6);
228 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
229 let e = Cn.mk_pattern 1 predicate in
231 | C.ARel (_, _, _, premise) ->
232 let script = mk_arg st what in
233 let where = Some (premise, name) in
234 T.Rewrite (direction, what, where, e, dtext) :: script
237 let mk_rewrite st dtext what qs tl direction =
238 assert (List.length tl = 5);
239 let predicate = List.nth tl 2 in
240 let e = Cn.mk_pattern 1 predicate in
241 [T.Rewrite (direction, what, None, e, dtext); T.Branch (qs, "")]
243 let rec proc_lambda st name v t =
244 let entry = Some (name, C.Decl (cic v)) in
245 let intro = get_intro name in
246 proc_proof (add st entry intro) t
248 and proc_letin st what name v t =
249 let intro = get_intro name in
250 let proceed, dtext = test_depth st in
251 let script = if proceed then
252 let hyp, rqv = match get_inner_types st v with
254 let rqv = match v with
255 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
256 mk_fwd_rewrite st dtext intro tl true
257 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
258 mk_fwd_rewrite st dtext intro tl false
260 let qs = [proc_proof (next st) v; [T.Id ""]] in
261 [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
263 C.Decl (cic ity), rqv
265 C.Def (cic v, None), [T.LetIn (intro, v, dtext)]
267 let entry = Some (name, hyp) in
268 let qt = proc_proof (next (add st entry intro)) t in
269 List.rev_append rqv qt
271 [T.Apply (what, dtext)]
275 and proc_rel st what =
276 let _, dtext = test_depth st in
277 let text = "assumption" in
278 let script = [T.Apply (what, dtext ^ text)] in
281 and proc_mutconstruct st what =
282 let _, dtext = test_depth st in
283 let script = [T.Apply (what, dtext)] in
286 and proc_appl st what hd tl =
287 let proceed, dtext = test_depth st in
288 let script = if proceed then
289 let ty = get_type "TC2" st hd in
290 let classes, rc = Cl.classify st.context ty in
291 let goal_arity = match get_inner_types st what with
293 | Some (ity, _) -> snd (PEH.split_with_whd (st.context, cic ity))
295 let parsno, argsno = List.length classes, List.length tl in
296 let decurry = parsno - argsno in
297 let diff = goal_arity - decurry in
298 if diff < 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (cic hd)));
299 let rec mk_synth a n =
300 if n < 0 then a else mk_synth (I.S.add n a) (pred n)
302 let synth = mk_synth I.S.empty decurry in
303 let text = "" (* Printf.sprintf "%u %s" parsno (Cl.to_string h) *) in
304 let script = List.rev (mk_arg st hd) @ convert st what in
306 | Some (i, j, uri, tyno) ->
307 let classes, tl, _, where = split2_last classes tl in
308 let script = List.rev (mk_arg st where) @ script in
309 let synth = I.S.add 1 synth in
310 let names = get_ind_names uri tyno in
311 let qs = proc_bkd_proofs (next st) synth names classes tl in
312 if is_rewrite_right hd then
313 script @ mk_rewrite st dtext where qs tl false
314 else if is_rewrite_left hd then
315 script @ mk_rewrite st dtext where qs tl true
317 let predicate = List.nth tl (parsno - i) in
318 let e = Cn.mk_pattern j predicate in
319 let using = Some hd in
321 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
323 let qs = proc_bkd_proofs (next st) synth [] classes tl in
324 let hd = mk_exp_args hd tl classes synth in
325 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
327 [T.Apply (what, dtext)]
331 and proc_other st what =
332 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
333 let script = [T.Note text] in
336 and proc_proof st = function
337 | C.ALambda (_, name, w, t) -> proc_lambda st name w t
338 | C.ALetIn (_, name, v, t) as what -> proc_letin st what name v t
339 | C.ARel _ as what -> proc_rel st what
340 | C.AMutConstruct _ as what -> proc_mutconstruct st what
341 | C.AAppl (_, hd :: tl) as what -> proc_appl st what hd tl
342 | what -> proc_other st what
344 and proc_bkd_proofs st synth names classes ts =
347 let names = ref (names, push st) in
350 | [], st -> fun _ -> f st
351 | "" :: tl, st -> names := tl, st; fun _ -> f st
353 let note = case st hd in
355 fun b -> if b then T.Note note :: f st else f st
357 let _, dtext = test_depth st in
359 if I.overlaps synth inv then None else
360 if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
361 Some (fun _ -> [T.Apply (v, dtext ^ "dependent")])
363 let ps = T.list_map2_filter aux classes ts in
364 let b = List.length ps > 1 in
365 List.rev_map (fun f -> f b) ps
367 with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
369 (* object costruction *******************************************************)
371 let is_theorem pars =
372 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
373 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
375 let proc_obj st = function
376 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
377 let ast = proc_proof st v in
378 let count = T.count_steps 0 ast in
379 let text = Printf.sprintf "tactics: %u" count in
380 T.Theorem (s, t, "") :: ast @ [T.Qed text]
382 failwith "not a theorem"
384 (* interface functions ******************************************************)
386 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth prefix aobj =
388 sorts = ids_to_inner_sorts;
389 types = ids_to_inner_types;
397 HLog.debug "Procedural: level 2 transformation";
398 let steps = proc_obj st aobj in
399 HLog.debug "Procedural: grafite rendering";
400 List.rev (T.render_steps [] steps)