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 DTI = DoubleTypeInference
30 module TC = CicTypeChecker
32 module UM = UriManager
33 module Obj = LibraryObjects
34 module HObj = HelmLibraryObjects
37 module E = CicEnvironment
38 module PER = ProofEngineReduction
40 module P = ProceduralPreprocess
41 module Cl = ProceduralClassify
42 module M = ProceduralMode
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;
56 (* helpers ******************************************************************)
58 let cic = D.deannotate_term
60 let split2_last l1 l2 =
62 let n = pred (List.length l1) in
63 let before1, after1 = T.list_split n l1 in
64 let before2, after2 = T.list_split n l2 in
65 before1, before2, List.hd after1, List.hd after2
66 with Invalid_argument _ -> failwith "A2P.split2_last"
68 let string_of_head = function
70 | C.AConst _ -> "const"
71 | C.AMutInd _ -> "mutind"
72 | C.AMutConstruct _ -> "mutconstruct"
76 | C.ALambda _ -> "lambda"
77 | C.ALetIn _ -> "letin"
79 | C.ACoFix _ -> "cofix"
82 | C.AMutCase _ -> "mutcase"
84 | C.AImplicit _ -> "implict"
86 let clear st = {st with intros = []}
88 let next st = {(clear st) with depth = succ st.depth}
90 let add st entry intro =
91 {st with context = entry :: st.context; intros = intro :: st.intros}
95 let msg = Printf.sprintf "Depth %u: " st.depth in
96 match st.max_depth with
98 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
99 with Invalid_argument _ -> failwith "A2P.test_depth"
101 let is_rewrite_right = function
102 | C.AConst (_, uri, []) ->
103 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
106 let is_rewrite_left = function
107 | C.AConst (_, uri, []) ->
108 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
111 let is_fwd_rewrite_right hd tl =
112 if is_rewrite_right hd then match List.nth tl 3 with
117 let is_fwd_rewrite_left hd tl =
118 if is_rewrite_left hd then match List.nth tl 3 with
123 let get_ind_name uri tno xcno =
125 let ts = match E.get_obj Un.empty_ugraph uri with
126 | C.InductiveDefinition (ts, _, _,_), _ -> ts
129 let tname, cs = match List.nth ts tno with
130 | (name, _, _, cs) -> name, cs
134 | Some cno -> fst (List.nth cs (pred cno))
135 with Invalid_argument _ -> failwith "A2P.get_ind_name"
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 (cic bo) Un.empty_ugraph in
157 with e -> failwith (msg ^ ": " ^ Printexc.to_string e)
159 (* proof construction *******************************************************)
161 let unused_premise = "UNUSED"
163 let defined_premise = "DEFINED"
165 let convert st ?name v =
166 match get_inner_types st v with
169 let cst, cet = cic st, cic et in
170 if PER.alpha_equivalence cst cet then [] else
171 let e = Cn.mk_pattern 0 (T.mk_arel 1 "") in
173 | None -> [T.Change (st, et, None, e, "")]
174 | Some id -> [T.Change (st, et, Some (id, id), e, ""); T.ClearBody (id, "")]
176 let get_intro name t =
179 | C.Anonymous -> unused_premise
181 if DTI.does_not_occur 1 (cic t) then unused_premise else s
182 with Invalid_argument _ -> failwith "A2P.get_intro"
184 let mk_intros st script =
186 if st.intros = [] then script else
187 let count = List.length st.intros in
188 T.Intros (Some count, List.rev st.intros, "") :: script
189 with Invalid_argument _ -> failwith "A2P.mk_intros"
191 let rec mk_atomic st dtext what =
192 if T.is_atomic what then
194 | C.ARel (_, _, _, name) -> convert st ~name what, what
197 let name = defined_premise in
198 let script = convert st ~name what in
199 script @ mk_fwd_proof st dtext name what, T.mk_arel 0 name
201 and mk_fwd_rewrite st dtext name tl direction =
202 assert (List.length tl = 6);
203 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
204 let e = Cn.mk_pattern 1 predicate in
206 | C.ARel (_, _, _, premise) ->
207 let script, what = mk_atomic st dtext what in
208 T.Rewrite (direction, what, Some (premise, name), e, dtext) :: script
211 and mk_rewrite st dtext script t what qs tl direction =
212 assert (List.length tl = 5);
213 let predicate = List.nth tl 2 in
214 let e = Cn.mk_pattern 1 predicate in
215 List.rev script @ convert st t @
216 [T.Rewrite (direction, what, None, e, dtext); T.Branch (qs, "")]
218 and mk_fwd_proof st dtext name = function
219 | C.ALetIn (_, n, v, t) ->
220 let entry = Some (n, C.Def (cic v, None)) in
221 let intro = get_intro n t in
222 let qt = mk_fwd_proof (add st entry intro) dtext name t in
223 let qv = mk_fwd_proof st "" intro v in
225 | C.AAppl (_, hd :: tl) as v ->
226 if is_fwd_rewrite_right hd tl then mk_fwd_rewrite st dtext name tl true else
227 if is_fwd_rewrite_left hd tl then mk_fwd_rewrite st dtext name tl false else
228 let ty = get_type "TC1" st hd in
229 begin match get_inner_types st v with
230 | Some (ity, _) when M.bkd st.context ty ->
231 let qs = [[T.Id ""]; mk_proof (next st) v] in
232 [T.Branch (qs, ""); T.Cut (name, ity, dtext)]
234 let (classes, rc) as h = Cl.classify st.context ty in
235 let text = Printf.sprintf "%u %s" (List.length classes) (Cl.to_string h) in
236 [T.LetIn (name, v, dtext ^ text)]
238 | C.AMutCase _ -> assert false
239 | C.ACast _ -> assert false
241 match get_inner_types st v with
243 let qs = [[T.Id ""]; mk_proof (next st) v] in
244 [T.Branch (qs, ""); T.Cut (name, ity, dtext)]
246 [T.LetIn (name, v, dtext)]
248 and mk_proof st = function
249 | C.ALambda (_, name, v, t) ->
250 let entry = Some (name, C.Decl (cic v)) in
251 let intro = get_intro name t in
252 mk_proof (add st entry intro) t
253 | C.ALetIn (_, name, v, t) as what ->
254 let proceed, dtext = test_depth st in
255 let script = if proceed then
256 let entry = Some (name, C.Def (cic v, None)) in
257 let intro = get_intro name t in
258 let q = mk_proof (next (add st entry intro)) t in
259 List.rev_append (mk_fwd_proof st dtext intro v) q
261 [T.Apply (what, dtext)]
264 | C.ARel _ as what ->
265 let _, dtext = test_depth st in
266 let text = "assumption" in
267 let script = [T.Apply (what, dtext ^ text)] in
269 | C.AMutConstruct _ as what ->
270 let _, dtext = test_depth st in
271 let script = [T.Apply (what, dtext)] in
273 | C.AAppl (_, hd :: tl) as t ->
274 let proceed, dtext = test_depth st in
275 let script = if proceed then
276 let ty = get_type "TC2" st hd in
277 let (classes, rc) as h = Cl.classify st.context ty in
278 let premises, _ = P.split st.context ty in
279 assert (List.length classes - List.length tl = 0);
280 let synth = I.S.singleton 0 in
281 let text = Printf.sprintf "%u %s" (List.length classes) (Cl.to_string h) in
283 | Some (i, j) when i > 1 && i <= List.length classes && M.is_eliminator premises ->
284 let classes, tl, _, what = split2_last classes tl in
285 let script, what = mk_atomic st dtext what in
286 let synth = I.S.add 1 synth in
287 let qs = mk_bkd_proofs (next st) synth classes tl in
288 if is_rewrite_right hd then
289 mk_rewrite st dtext script t what qs tl false
290 else if is_rewrite_left hd then
291 mk_rewrite st dtext script t what qs tl true
293 let l = succ (List.length tl) in
294 let predicate = List.nth tl (l - i) in
295 let e = Cn.mk_pattern j predicate in
296 let using = Some hd in
297 List.rev script @ convert st t @
298 [T.Elim (what, using, e, dtext ^ text); T.Branch (qs, "")]
300 let qs = mk_bkd_proofs (next st) synth classes tl in
301 let script, hd = mk_atomic st dtext hd in
302 List.rev script @ convert st t @
303 [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
308 | C.AMutCase _ -> assert false
309 | C.ACast _ -> assert false
311 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head t) in
312 let script = [T.Note text] in
315 and mk_bkd_proofs st synth classes ts =
317 let _, dtext = test_depth st in
319 if I.overlaps synth inv then None else
320 if I.S.is_empty inv then Some (mk_proof st v) else
321 Some [T.Apply (v, dtext ^ "dependent")]
323 T.list_map2_filter aux classes ts
324 with Invalid_argument _ -> failwith "A2P.mk_bkd_proofs"
326 (* object costruction *******************************************************)
328 let is_theorem pars =
329 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
330 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
332 let mk_obj st = function
333 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
334 let ast = mk_proof st v in
335 let count = T.count_steps 0 ast in
336 let text = Printf.sprintf "tactics: %u" count in
337 T.Theorem (s, t, text) :: ast @ [T.Qed ""]
339 failwith "not a theorem"
341 (* interface functions ******************************************************)
343 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth prefix aobj =
345 sorts = ids_to_inner_sorts;
346 types = ids_to_inner_types;
353 HLog.debug "Level 2 transformation";
354 let steps = mk_obj st aobj in
355 HLog.debug "grafite rendering";
356 List.rev (T.render_steps [] steps)