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 Cl = ProceduralClassify
41 module M = ProceduralMode
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;
56 (* helpers ******************************************************************)
60 let comp f g x = f (g x)
62 let cic = D.deannotate_term
64 let split2_last l1 l2 =
66 let n = pred (List.length l1) in
67 let before1, after1 = T.list_split n l1 in
68 let before2, after2 = T.list_split n l2 in
69 before1, before2, List.hd after1, List.hd after2
70 with Invalid_argument _ -> failwith "A2P.split2_last"
72 let string_of_head = function
74 | C.AConst _ -> "const"
75 | C.AMutInd _ -> "mutind"
76 | C.AMutConstruct _ -> "mutconstruct"
80 | C.ALambda _ -> "lambda"
81 | C.ALetIn _ -> "letin"
83 | C.ACoFix _ -> "cofix"
86 | C.AMutCase _ -> "mutcase"
88 | C.AImplicit _ -> "implict"
90 let clear st = {st with intros = []; ety = None}
92 let next st = {(clear st) with depth = succ st.depth}
95 if st.ety = None then {st with ety = ety} else st
97 let add st entry intro ety =
98 let st = set_ety st ety in
99 {st with context = entry :: st.context; intros = intro :: st.intros}
103 let msg = Printf.sprintf "Depth %u: " st.depth in
104 match st.max_depth with
106 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
107 with Invalid_argument _ -> failwith "A2P.test_depth"
109 let is_rewrite_right = function
110 | C.AConst (_, uri, []) ->
111 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
114 let is_rewrite_left = function
115 | C.AConst (_, uri, []) ->
116 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
119 let is_fwd_rewrite_right hd tl =
120 if is_rewrite_right hd then match List.nth tl 3 with
125 let is_fwd_rewrite_left hd tl =
126 if is_rewrite_left hd then match List.nth tl 3 with
131 let get_ind_name uri tno xcno =
133 let ts = match E.get_obj Un.empty_ugraph uri with
134 | C.InductiveDefinition (ts, _, _,_), _ -> ts
137 let tname, cs = match List.nth ts tno with
138 | (name, _, _, cs) -> name, cs
142 | Some cno -> fst (List.nth cs (pred cno))
143 with Invalid_argument _ -> failwith "A2P.get_ind_name"
145 let get_inner_types st v =
147 let id = Ut.id_of_annterm v in
148 try match Hashtbl.find st.types id with
149 | {A.annsynthesized = st; A.annexpected = Some et} -> Some (st, et)
150 | {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
151 with Not_found -> None
152 with Invalid_argument _ -> failwith "A2P.get_inner_types"
154 let get_inner_sort st v =
156 let id = Ut.id_of_annterm v in
157 try Hashtbl.find st.sorts id
158 with Not_found -> `Type (CicUniv.fresh())
159 with Invalid_argument _ -> failwith "A2P.get_sort"
161 (* proof construction *******************************************************)
163 let unused_premise = "UNUSED"
165 let defined_premise = "DEFINED"
167 let assumed_premise = "ASSUMED"
169 let expanded_premise = "EXPANDED"
171 let convert st ?name v =
172 match get_inner_types st v with
175 let cst, cet = cic st, cic et in
176 if PER.alpha_equivalence cst cet then [] else
178 | None -> [T.Change (st, et, None, "")]
179 | Some id -> [T.Change (st, et, Some (id, id), ""); T.ClearBody (id, "")]
182 let id = Ut.id_of_annterm t in
183 let ty = C.AImplicit ("", None) in
184 let name i = Printf.sprintf "%s%u" expanded_premise i in
185 let lambda i t = C.ALambda (id, C.Name (name i), ty, t) in
186 let arg i n = T.mk_arel (n - i) (name i) in
188 if i >= n then f, a else aux (succ i) (comp f (lambda i)) (arg i n :: a)
190 let absts, args = aux 0 identity [] in
191 match Cn.lift 1 n t with
192 | C.AAppl (id, ts) -> absts (C.AAppl (id, ts @ args))
193 | t -> absts (C.AAppl ("", t :: args))
195 let appl_expand n = function
196 | C.AAppl (id, ts) ->
197 let before, after = T.list_split (List.length ts + n) ts in
198 C.AAppl ("", C.AAppl (id, before) :: after)
201 let get_intro name t =
204 | C.Anonymous -> unused_premise
206 if DTI.does_not_occur 1 (cic t) then unused_premise else s
207 with Invalid_argument _ -> failwith "A2P.get_intro"
209 let mk_intros st script =
211 if st.intros = [] then script else
212 let count = List.length st.intros in
213 let p0 = T.Whd (count, "") in
214 let p1 = T.Intros (Some count, List.rev st.intros, "") in
216 | Some ety when Cn.need_whd count ety -> p0 :: p1 :: script
218 with Invalid_argument _ -> failwith "A2P.mk_intros"
220 let rec mk_atomic st dtext what =
221 if T.is_atomic what then
223 | C.ARel (_, _, _, name) -> convert st ~name what, what
226 let name = defined_premise in
227 let script = convert st ~name what in
228 script @ mk_fwd_proof st dtext name what, T.mk_arel 0 name
230 and mk_fwd_rewrite st dtext name tl direction =
231 let what, where = List.nth tl 5, List.nth tl 3 in
232 let rewrite premise =
233 let script, what = mk_atomic st dtext what in
234 T.Rewrite (direction, what, Some (premise, name), dtext) :: script
237 | C.ARel (_, _, _, binder) -> rewrite binder
241 assert (get_inner_sort st where = `Prop);
242 let pred, old = List.nth tl 2, List.nth tl 1 in
243 let pred_name = defined_premise in
244 let pred_text = "extracted" in
245 let p1 = T.LetIn (pred_name, pred, pred_text) in
246 let cut_name = assumed_premise in
247 let cut_type = C.AAppl ("", [T.mk_arel 0 pred_name; old]) in
249 let p2 = T.Cut (cut_name, cut_type, cut_text) in
250 let qs = [rewrite cut_name; mk_proof (next st) where] in
251 [T.Branch (qs, ""); p2; p1]
253 and mk_fwd_proof st dtext name = function
254 | C.AAppl (_, hd :: tl) as v ->
255 if is_fwd_rewrite_right hd tl then mk_fwd_rewrite st dtext name tl true else
256 if is_fwd_rewrite_left hd tl then mk_fwd_rewrite st dtext name tl false else
257 let ty, _ = TC.type_of_aux' [] st.context (cic hd) Un.empty_ugraph in
258 begin match get_inner_types st v with
259 | Some (ity, _) when M.bkd st.context ty ->
260 let qs = [[T.Id ""]; mk_proof (next st) v] in
261 [T.Branch (qs, ""); T.Cut (name, ity, dtext)]
263 let (classes, rc) as h = Cl.classify st.context ty in
264 let text = Printf.sprintf "%u %s" (List.length classes) (Cl.to_string h) in
265 [T.LetIn (name, v, dtext ^ text)]
267 | C.AMutCase (id, uri, tyno, outty, arg, cases) as v ->
268 begin match Cn.mk_ind st.context id uri tyno outty arg cases with
269 | None -> [T.LetIn (name, v, dtext)]
270 | Some v -> mk_fwd_proof st dtext name v
273 [T.LetIn (name, v, dtext)]
275 and mk_proof st = function
276 | C.ALambda (_, name, v, t) as what ->
277 let entry = Some (name, C.Decl (cic v)) in
278 let intro = get_intro name t in
279 let ety = match get_inner_types st what with
280 | Some (_, ety) -> Some ety
283 mk_proof (add st entry intro ety) t
284 | C.ALetIn (_, name, v, t) as what ->
285 let proceed, dtext = test_depth st in
286 let script = if proceed then
287 let entry = Some (name, C.Def (cic v, None)) in
288 let intro = get_intro name t in
289 let q = mk_proof (next (add st entry intro None)) t in
290 List.rev_append (mk_fwd_proof st dtext intro v) q
292 [T.Apply (what, dtext)]
295 | C.ARel _ as what ->
296 let _, dtext = test_depth st in
297 let text = "assumption" in
298 let script = [T.Apply (what, dtext ^ text)] in
300 | C.AMutConstruct _ as what ->
301 let _, dtext = test_depth st in
302 let script = [T.Apply (what, dtext)] in
304 | C.AAppl (_, hd :: tl) as t ->
305 let proceed, dtext = test_depth st in
306 let script = if proceed then
307 let ty, _ = TC.type_of_aux' [] st.context (cic hd) Un.empty_ugraph in
308 let (classes, rc) as h = Cl.classify st.context ty in
309 let premises, _ = Cl.split st.context ty in
310 let decurry = List.length classes - List.length tl in
311 if decurry < 0 then mk_proof (clear st) (appl_expand decurry t) else
312 if decurry > 0 then mk_proof (clear st) (eta_expand decurry t) else
313 let synth = I.S.singleton 0 in
314 let text = Printf.sprintf "%u %s" (List.length classes) (Cl.to_string h) in
316 | Some (i, j) when i > 1 && i <= List.length classes && M.is_eliminator premises ->
317 let classes, tl, _, what = split2_last classes tl in
318 let script, what = mk_atomic st dtext what in
319 let synth = I.S.add 1 synth in
320 let qs = mk_bkd_proofs (next st) synth classes tl in
321 if is_rewrite_right hd then
322 List.rev script @ convert st t @
323 [T.Rewrite (false, what, None, dtext); T.Branch (qs, "")]
324 else if is_rewrite_left hd then
325 List.rev script @ convert st t @
326 [T.Rewrite (true, what, None, dtext); T.Branch (qs, "")]
328 let using = Some hd in
329 List.rev script @ convert st t @
330 [T.Elim (what, using, dtext ^ text); T.Branch (qs, "")]
332 let qs = mk_bkd_proofs (next st) synth classes tl in
333 let script, hd = mk_atomic st dtext hd in
334 List.rev script @ convert st t @
335 [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
340 | C.AMutCase (id, uri, tyno, outty, arg, cases) ->
341 begin match Cn.mk_ind st.context id uri tyno outty arg cases with
343 let text = Printf.sprintf "%s" "UNEXPANDED: mutcase" in
344 let script = [T.Note text] in
346 (* | Some t -> mk_proof st t *)
349 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head t) in
350 let script = [T.Note text] in
353 and mk_bkd_proofs st synth classes ts =
355 let _, dtext = test_depth st in
357 if I.overlaps synth inv then None else
358 if I.S.is_empty inv then Some (mk_proof st v) else
359 Some [T.Apply (v, dtext ^ "dependent")]
361 T.list_map2_filter aux classes ts
362 with Invalid_argument _ -> failwith "A2P.mk_bkd_proofs"
364 (* object costruction *******************************************************)
366 let is_theorem pars =
367 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
368 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
370 let mk_obj st = function
371 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
372 let ast = mk_proof (set_ety st (Some t)) v in
373 let count = T.count_steps 0 ast in
374 let text = Printf.sprintf "tactics: %u" count in
375 T.Theorem (s, t, text) :: ast @ [T.Qed ""]
377 failwith "not a theorem"
379 (* interface functions ******************************************************)
381 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth prefix aobj =
383 sorts = ids_to_inner_sorts;
384 types = ids_to_inner_types;
392 HLog.debug "Level 2 transformation";
393 let steps = mk_obj st aobj in
394 HLog.debug "grafite rendering";
395 List.rev (T.render_steps [] steps)