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
38 module PEH = ProofEngineHelpers
41 module Cl = ProceduralClassify
42 module T = ProceduralTypes
43 module Cn = ProceduralConversion
46 sorts : (C.id, A.sort_kind) Hashtbl.t;
47 types : (C.id, A.anntypes) Hashtbl.t;
49 max_depth: int option;
55 (* helpers ******************************************************************)
57 let cic = D.deannotate_term
59 let split2_last l1 l2 =
61 let n = pred (List.length l1) in
62 let before1, after1 = T.list_split n l1 in
63 let before2, after2 = T.list_split n l2 in
64 before1, before2, List.hd after1, List.hd after2
65 with Invalid_argument _ -> failwith "A2P.split2_last"
67 let string_of_head = function
69 | C.AConst _ -> "const"
70 | C.AMutInd _ -> "mutind"
71 | C.AMutConstruct _ -> "mutconstruct"
75 | C.ALambda _ -> "lambda"
76 | C.ALetIn _ -> "letin"
78 | C.ACoFix _ -> "cofix"
81 | C.AMutCase _ -> "mutcase"
83 | C.AImplicit _ -> "implict"
85 let clear st = {st with intros = []}
87 let next st = {(clear st) with depth = succ st.depth}
89 let add st entry intro =
90 {st with context = entry :: st.context; intros = intro :: st.intros}
94 let msg = Printf.sprintf "Depth %u: " st.depth in
95 match st.max_depth with
97 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
98 with Invalid_argument _ -> failwith "A2P.test_depth"
100 let is_rewrite_right = function
101 | C.AConst (_, uri, []) ->
102 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
105 let is_rewrite_left = function
106 | C.AConst (_, uri, []) ->
107 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
110 let is_fwd_rewrite_right hd tl =
111 if is_rewrite_right hd then match List.nth tl 3 with
116 let is_fwd_rewrite_left hd tl =
117 if is_rewrite_left hd then match List.nth tl 3 with
122 let get_ind_name uri tno xcno =
124 let ts = match E.get_obj Un.empty_ugraph uri with
125 | C.InductiveDefinition (ts, _, _,_), _ -> ts
128 let tname, cs = match List.nth ts tno with
129 | (name, _, _, cs) -> name, cs
133 | Some cno -> fst (List.nth cs (pred cno))
134 with Invalid_argument _ -> failwith "A2P.get_ind_name"
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 (* proof construction *******************************************************)
168 let unused_premise = "UNUSED"
170 let mk_exp_args hd tl classes =
171 let meta id = C.AImplicit (id, None) in
173 if I.S.mem 0 cl && b then v else meta ""
175 let rec aux = function
177 | hd :: tl -> if hd = meta "" then aux tl else List.rev (hd :: tl)
179 let args = List.rev_map2 map tl classes in
180 let args = aux args in
181 if args = [] then hd else C.AAppl ("", hd :: args)
183 let convert st ?name v =
184 match get_inner_types st v with
187 let e = Cn.mk_pattern 0 (T.mk_arel 1 "") in
188 let csty, cety = cic sty, cic ety in
189 if Ut.alpha_equivalence csty cety then [] else
191 | None -> [T.Change (sty, ety, None, e, "")]
193 begin match get_entry st id with
194 | C.Def _ -> [T.ClearBody (id, "")]
196 let w = S.lift i w in
197 if Ut.alpha_equivalence csty w then []
199 [T.Note (Pp.ppterm csty); T.Note (Pp.ppterm w);
200 T.Change (sty, ety, Some (id, id), e, "")]
203 let get_intro = function
204 | C.Anonymous -> unused_premise
207 let mk_intros st script =
208 if st.intros = [] then script else
209 let count = List.length st.intros in
210 T.Intros (Some count, List.rev st.intros, "") :: script
212 let mk_arg st = function
213 | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
216 let mk_fwd_rewrite st dtext name tl direction =
217 assert (List.length tl = 6);
218 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
219 let e = Cn.mk_pattern 1 predicate in
221 | C.ARel (_, _, _, premise) ->
222 let script = mk_arg st what in
223 let where = Some (premise, name) in
224 T.Rewrite (direction, what, where, e, dtext) :: script
227 let mk_rewrite st dtext what qs tl direction =
228 assert (List.length tl = 5);
229 let predicate = List.nth tl 2 in
230 let e = Cn.mk_pattern 1 predicate in
231 [T.Rewrite (direction, what, None, e, dtext); T.Branch (qs, "")]
233 let rec proc_lambda st name v t =
234 let entry = Some (name, C.Decl (cic v)) in
235 let intro = get_intro name in
236 proc_proof (add st entry intro) t
238 and proc_letin st what name v t =
239 let intro = get_intro name in
240 let proceed, dtext = test_depth st in
241 let script = if proceed then
242 let hyp, rqv = match get_inner_types st v with
244 let rqv = match v with
245 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
246 mk_fwd_rewrite st dtext intro tl true
247 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
248 mk_fwd_rewrite st dtext intro tl false
250 let qs = [[T.Id ""]; proc_proof (next st) v] in
251 [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
253 C.Decl (cic ity), rqv
255 C.Def (cic v, None), [T.LetIn (intro, v, dtext)]
257 let entry = Some (name, hyp) in
258 let qt = proc_proof (next (add st entry intro)) t in
259 List.rev_append rqv qt
261 [T.Apply (what, dtext)]
265 and proc_rel st what =
266 let _, dtext = test_depth st in
267 let text = "assumption" in
268 let script = [T.Apply (what, dtext ^ text)] in
271 and proc_mutconstruct st what =
272 let _, dtext = test_depth st in
273 let script = [T.Apply (what, dtext)] in
276 and proc_appl st what hd tl =
277 let proceed, dtext = test_depth st in
278 let script = if proceed then
279 let ty = get_type "TC2" st hd in
280 let (classes, rc) as h = Cl.classify st.context ty in
281 let argsno = List.length classes in
282 let diff = argsno - List.length tl in
283 if diff <> 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (cic hd)));
284 let synth = I.S.singleton 0 in
285 let text = Printf.sprintf "%u %s" argsno (Cl.to_string h) in
286 let script = List.rev (mk_arg st hd) @ convert st what in
289 let classes, tl, _, where = split2_last classes tl in
290 let script = List.rev (mk_arg st where) @ script in
291 let synth = I.S.add 1 synth in
292 let qs = proc_bkd_proofs (next st) synth classes tl in
293 if is_rewrite_right hd then
294 script @ mk_rewrite st dtext where qs tl false
295 else if is_rewrite_left hd then
296 script @ mk_rewrite st dtext where qs tl true
298 let predicate = List.nth tl (argsno - i) in
299 let e = Cn.mk_pattern 0 (T.mk_arel 1 "") (* j predicate *) in
300 let using = Some hd in
302 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
304 let qs = proc_bkd_proofs (next st) synth classes tl in
305 let hd = mk_exp_args hd tl classes in
306 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
308 [T.Apply (what, dtext)]
312 and proc_other st what =
313 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
314 let script = [T.Note text] in
318 and proc_proof st = function
319 | C.ALambda (_, name, w, t) -> proc_lambda st name w t
320 | C.ALetIn (_, name, v, t) as what -> proc_letin st what name v t
321 | C.ARel _ as what -> proc_rel st what
322 | C.AMutConstruct _ as what -> proc_mutconstruct st what
323 | C.AAppl (_, hd :: tl) as what -> proc_appl st what hd tl
324 | what -> proc_other st what
326 and proc_bkd_proofs st synth classes ts =
328 let _, dtext = test_depth st in
330 if I.overlaps synth inv then None else
331 if I.S.is_empty inv then Some (proc_proof st v) else
332 Some [T.Apply (v, dtext ^ "dependent")]
334 T.list_map2_filter aux classes ts
335 with Invalid_argument _ -> failwith "A2P.proc_bkd_proofs"
337 (* object costruction *******************************************************)
339 let is_theorem pars =
340 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
341 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
343 let proc_obj st = function
344 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
345 let ast = proc_proof st v in
346 let count = T.count_steps 0 ast in
347 let text = Printf.sprintf "tactics: %u" count in
348 T.Theorem (s, t, text) :: ast @ [T.Qed ""]
350 failwith "not a theorem"
352 (* interface functions ******************************************************)
354 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth prefix aobj =
356 sorts = ids_to_inner_sorts;
357 types = ids_to_inner_types;
364 HLog.debug "Procedural: level 2 transformation";
365 let steps = proc_obj st aobj in
366 HLog.debug "Procedural: grafite rendering";
367 List.rev (T.render_steps [] steps)