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 TC = CicTypeChecker
31 module UM = UriManager
32 module Obj = LibraryObjects
33 module HObj = HelmLibraryObjects
36 module E = CicEnvironment
37 module PEH = ProofEngineHelpers
40 module Cl = ProceduralClassify
41 module T = ProceduralTypes
42 module Cn = ProceduralConversion
45 sorts : (C.id, A.sort_kind) Hashtbl.t;
46 types : (C.id, A.anntypes) Hashtbl.t;
48 max_depth: int option;
54 (* helpers ******************************************************************)
56 let cic = D.deannotate_term
58 let split2_last l1 l2 =
60 let n = pred (List.length l1) in
61 let before1, after1 = T.list_split n l1 in
62 let before2, after2 = T.list_split n l2 in
63 before1, before2, List.hd after1, List.hd after2
64 with Invalid_argument _ -> failwith "A2P.split2_last"
66 let string_of_head = function
68 | C.AConst _ -> "const"
69 | C.AMutInd _ -> "mutind"
70 | C.AMutConstruct _ -> "mutconstruct"
74 | C.ALambda _ -> "lambda"
75 | C.ALetIn _ -> "letin"
77 | C.ACoFix _ -> "cofix"
80 | C.AMutCase _ -> "mutcase"
82 | C.AImplicit _ -> "implict"
84 let clear st = {st with intros = []}
86 let next st = {(clear st) with depth = succ st.depth}
88 let add st entry intro =
89 {st with context = entry :: st.context; intros = intro :: st.intros}
93 let msg = Printf.sprintf "Depth %u: " st.depth in
94 match st.max_depth with
96 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
97 with Invalid_argument _ -> failwith "A2P.test_depth"
99 let is_rewrite_right = function
100 | C.AConst (_, uri, []) ->
101 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
104 let is_rewrite_left = function
105 | C.AConst (_, uri, []) ->
106 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
109 let is_fwd_rewrite_right hd tl =
110 if is_rewrite_right hd then match List.nth tl 3 with
115 let is_fwd_rewrite_left hd tl =
116 if is_rewrite_left hd then match List.nth tl 3 with
121 let get_ind_name uri tno xcno =
123 let ts = match E.get_obj Un.empty_ugraph uri with
124 | C.InductiveDefinition (ts, _, _,_), _ -> ts
127 let tname, cs = match List.nth ts tno with
128 | (name, _, _, cs) -> name, cs
132 | Some cno -> fst (List.nth cs (pred cno))
133 with Invalid_argument _ -> failwith "A2P.get_ind_name"
135 let get_inner_types st v =
137 let id = Ut.id_of_annterm v in
138 try match Hashtbl.find st.types id with
139 | {A.annsynthesized = st; A.annexpected = Some et} -> Some (st, et)
140 | {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
141 with Not_found -> None
142 with Invalid_argument _ -> failwith "A2P.get_inner_types"
144 let get_inner_sort st v =
146 let id = Ut.id_of_annterm v in
147 try Hashtbl.find st.sorts id
148 with Not_found -> `Type (CicUniv.fresh())
149 with Invalid_argument _ -> failwith "A2P.get_sort"
151 let get_type msg st bo =
153 let ty, _ = TC.type_of_aux' [] st.context (cic bo) Un.empty_ugraph in
155 with e -> failwith (msg ^ ": " ^ Printexc.to_string e)
157 let get_entry st id =
158 let rec aux = function
160 | Some (C.Name name, e) :: _ when name = id -> e
165 (* proof construction *******************************************************)
167 let unused_premise = "UNUSED"
169 let mk_exp_args hd tl classes =
170 let meta id = C.AImplicit (id, None) in
172 if I.S.mem 0 cl && b then v else meta ""
174 let rec aux = function
176 | hd :: tl -> if hd = meta "" then aux tl else List.rev (hd :: tl)
178 let args = List.rev_map2 map tl classes in
179 let args = aux args in
180 if args = [] then hd else C.AAppl ("", hd :: args)
182 let convert st ?name v =
183 match get_inner_types st v with
186 let csty, cety = cic sty, cic ety in
187 if Ut.alpha_equivalence csty cety then [] else
188 let e = Cn.mk_pattern 0 (T.mk_arel 1 "") in
190 | None -> [T.Change (sty, ety, None, e, "")]
192 begin match get_entry st id with
193 | C.Def _ -> [T.ClearBody (id, "")]
195 if Ut.alpha_equivalence csty w then []
196 else [T.Change (sty, ety, Some (id, id), e, "")]
199 let get_intro = function
200 | C.Anonymous -> unused_premise
203 let mk_intros st script =
204 if st.intros = [] then script else
205 let count = List.length st.intros in
206 T.Intros (Some count, List.rev st.intros, "") :: script
208 let mk_arg st = function
209 | C.ARel (_, _, _, name) as what -> convert st ~name what
212 let mk_fwd_rewrite st dtext name tl direction =
213 assert (List.length tl = 6);
214 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
215 let e = Cn.mk_pattern 1 predicate in
217 | C.ARel (_, _, _, premise) ->
218 let script = mk_arg st what in
219 let where = Some (premise, name) in
220 T.Rewrite (direction, what, where, e, dtext) :: script
223 let mk_rewrite st dtext what qs tl direction =
224 assert (List.length tl = 5);
225 let predicate = List.nth tl 2 in
226 let e = Cn.mk_pattern 1 predicate in
227 [T.Rewrite (direction, what, None, e, dtext); T.Branch (qs, "")]
229 let rec proc_lambda st name v t =
230 let entry = Some (name, C.Decl (cic v)) in
231 let intro = get_intro name in
232 proc_proof (add st entry intro) t
234 and proc_letin st what name v t =
235 let intro = get_intro name in
236 let proceed, dtext = test_depth st in
237 let script = if proceed then
238 let hyp, rqv = match get_inner_types st v with
240 let rqv = match v with
241 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
242 mk_fwd_rewrite st dtext intro tl true
243 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
244 mk_fwd_rewrite st dtext intro tl false
246 let qs = [[T.Id ""]; proc_proof (next st) v] in
247 [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
249 C.Decl (cic ity), rqv
251 C.Def (cic v, None), [T.LetIn (intro, v, dtext)]
253 let entry = Some (name, hyp) in
254 let qt = proc_proof (next (add st entry intro)) t in
255 List.rev_append rqv qt
257 [T.Apply (what, dtext)]
261 and proc_rel st what =
262 let _, dtext = test_depth st in
263 let text = "assumption" in
264 let script = [T.Apply (what, dtext ^ text)] in
267 and proc_mutconstruct st what =
268 let _, dtext = test_depth st in
269 let script = [T.Apply (what, dtext)] in
272 and proc_appl st what hd tl =
273 let proceed, dtext = test_depth st in
274 let script = if proceed then
275 let ty = get_type "TC2" st hd in
276 let (classes, rc) as h = Cl.classify st.context ty in
277 let argsno = List.length classes in
278 let diff = argsno - List.length tl in
279 if diff <> 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (cic hd)));
280 let synth = I.S.singleton 0 in
281 let text = Printf.sprintf "%u %s" argsno (Cl.to_string h) in
282 let script = List.rev (mk_arg st hd) @ convert st what in
285 let classes, tl, _, where = split2_last classes tl in
286 let script = List.rev (mk_arg st where) @ script in
287 let synth = I.S.add 1 synth in
288 let qs = proc_bkd_proofs (next st) synth classes tl in
289 if is_rewrite_right hd then
290 script @ mk_rewrite st dtext where qs tl false
291 else if is_rewrite_left hd then
292 script @ mk_rewrite st dtext where qs tl true
294 let predicate = List.nth tl (argsno - i) in
295 let e = Cn.mk_pattern 0 (T.mk_arel 1 "") (* j predicate *) in
296 let using = Some hd in
298 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
300 let qs = proc_bkd_proofs (next st) synth classes tl in
301 let hd = mk_exp_args hd tl classes in
302 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
304 [T.Apply (what, dtext)]
308 and proc_other st what =
309 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
310 let script = [T.Note text] in
314 and proc_proof st = function
315 | C.ALambda (_, name, w, t) -> proc_lambda st name w t
316 | C.ALetIn (_, name, v, t) as what -> proc_letin st what name v t
317 | C.ARel _ as what -> proc_rel st what
318 | C.AMutConstruct _ as what -> proc_mutconstruct st what
319 | C.AAppl (_, hd :: tl) as what -> proc_appl st what hd tl
320 | what -> proc_other st what
322 and proc_bkd_proofs st synth classes ts =
324 let _, dtext = test_depth st in
326 if I.overlaps synth inv then None else
327 if I.S.is_empty inv then Some (proc_proof st v) else
328 Some [T.Apply (v, dtext ^ "dependent")]
330 T.list_map2_filter aux classes ts
331 with Invalid_argument _ -> failwith "A2P.proc_bkd_proofs"
333 (* object costruction *******************************************************)
335 let is_theorem pars =
336 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
337 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
339 let proc_obj st = function
340 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
341 let ast = proc_proof st v in
342 let count = T.count_steps 0 ast in
343 let text = Printf.sprintf "tactics: %u" count in
344 T.Theorem (s, t, text) :: ast @ [T.Qed ""]
346 failwith "not a theorem"
348 (* interface functions ******************************************************)
350 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth prefix aobj =
352 sorts = ids_to_inner_sorts;
353 types = ids_to_inner_types;
360 HLog.debug "Procedural: level 2 transformation";
361 let steps = proc_obj st aobj in
362 HLog.debug "Procedural: grafite rendering";
363 List.rev (T.render_steps [] steps)