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/.
28 module DTI = DoubleTypeInference
29 module TC = CicTypeChecker
31 module UM = UriManager
32 module Obj = LibraryObjects
33 module HObj = HelmLibraryObjects
36 module E = CicEnvironment
37 module PER = ProofEngineReduction
39 module Cl = ProceduralClassify
40 module M = ProceduralMode
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;
55 (* helpers ******************************************************************)
59 let comp f g x = f (g x)
61 let cic = D.deannotate_term
63 let split2_last l1 l2 =
65 let n = pred (List.length l1) in
66 let before1, after1 = T.list_split n l1 in
67 let before2, after2 = T.list_split n l2 in
68 before1, before2, List.hd after1, List.hd after2
69 with Invalid_argument _ -> failwith "A2P.split2_last"
71 let string_of_head = function
73 | C.AConst _ -> "const"
74 | C.AMutInd _ -> "mutind"
75 | C.AMutConstruct _ -> "mutconstruct"
79 | C.ALambda _ -> "lambda"
80 | C.ALetIn _ -> "letin"
82 | C.ACoFix _ -> "cofix"
85 | C.AMutCase _ -> "mutcase"
87 | C.AImplicit _ -> "implict"
89 let clear st = {st with intros = []; ety = None}
91 let next st = {(clear st) with depth = succ st.depth}
94 if st.ety = None then {st with ety = ety} else st
96 let add st entry intro ety =
97 let st = set_ety st ety in
98 {st with context = entry :: st.context; intros = intro :: st.intros}
102 let msg = Printf.sprintf "Depth %u: " st.depth in
103 match st.max_depth with
105 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
106 with Invalid_argument _ -> failwith "A2P.test_depth"
108 let is_rewrite_right = function
109 | C.AConst (_, uri, []) ->
110 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
113 let is_rewrite_left = function
114 | C.AConst (_, uri, []) ->
115 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
118 let get_ind_name uri tno xcno =
120 let ts = match E.get_obj Un.empty_ugraph uri with
121 | C.InductiveDefinition (ts, _, _,_), _ -> ts
124 let tname, cs = match List.nth ts tno with
125 | (name, _, _, cs) -> name, cs
129 | Some cno -> fst (List.nth cs (pred cno))
130 with Invalid_argument _ -> failwith "A2P.get_ind_name"
132 let get_inner_types st v =
134 let id = Ut.id_of_annterm v in
135 try match Hashtbl.find st.types id with
136 | {A.annsynthesized = st; A.annexpected = Some et} -> Some (st, et)
137 | {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
138 with Not_found -> None
139 with Invalid_argument _ -> failwith "A2P.get_inner_types"
141 let get_inner_sort st v =
143 let id = Ut.id_of_annterm v in
144 try Hashtbl.find st.sorts id
145 with Not_found -> `Type (CicUniv.fresh())
146 with Invalid_argument _ -> failwith "A2P.get_sort"
148 (* proof construction *******************************************************)
150 let unused_premise = "UNUSED"
152 let defined_premise = "DEFINED"
154 let assumed_premise = "ASSUMED"
156 let expanded_premise = "EXPANDED"
159 match get_inner_types st v with
161 let cst, cet = cic st, cic et in
162 if PER.alpha_equivalence cst cet then [] else
163 [T.Change (st, et, "")]
167 let ty = C.AImplicit ("", None) in
168 let name i = Printf.sprintf "%s%u" expanded_premise i in
169 let lambda i t = C.ALambda ("", C.Name (name i), ty, t) in
170 let arg i n = T.mk_arel (n - i) (name i) in
172 if i >= n then f, a else aux (succ i) (comp f (lambda i)) (arg i n :: a)
174 let absts, args = aux 0 id [] in
175 match Cn.lift 1 n t with
176 | C.AAppl (id, ts) -> absts (C.AAppl (id, ts @ args))
177 | t -> absts (C.AAppl ("", t :: args))
179 let appl_expand n = function
180 | C.AAppl (id, ts) ->
181 let before, after = T.list_split (List.length ts + n) ts in
182 C.AAppl ("", C.AAppl (id, before) :: after)
185 let get_intro name t =
188 | C.Anonymous -> unused_premise
190 if DTI.does_not_occur 1 (cic t) then unused_premise else s
191 with Invalid_argument _ -> failwith "A2P.get_intro"
193 let mk_intros st script =
195 if st.intros = [] then script else
196 let count = List.length st.intros in
197 let p0 = T.Whd (count, "") in
198 let p1 = T.Intros (Some count, List.rev st.intros, "") in
200 | Some ety when Cn.need_whd count ety -> p0 :: p1 :: script
202 with Invalid_argument _ -> failwith "A2P.mk_intros"
204 let rec mk_atomic st dtext what =
205 if T.is_atomic what then [], what else
206 let name = defined_premise in
207 mk_fwd_proof st dtext name what, T.mk_arel 0 name
209 and mk_fwd_rewrite st dtext name tl direction =
210 let what, where = List.nth tl 5, List.nth tl 3 in
211 let rewrite premise =
212 let script, what = mk_atomic st dtext what in
213 T.Rewrite (direction, what, Some (premise, name), dtext) :: script
216 | C.ARel (_, _, _, binder) -> rewrite binder
218 assert (get_inner_sort st where = `Prop);
219 let pred, old = List.nth tl 2, List.nth tl 1 in
220 let pred_name = defined_premise in
221 let pred_text = "extracted" in
222 let p1 = T.LetIn (pred_name, pred, pred_text) in
223 let cut_name = assumed_premise in
224 let cut_type = C.AAppl ("", [T.mk_arel 0 pred_name; old]) in
226 let p2 = T.Cut (cut_name, cut_type, cut_text) in
227 let qs = [rewrite cut_name; mk_proof (next st) where] in
228 [T.Branch (qs, ""); p2; p1]
230 and mk_fwd_proof st dtext name = function
231 | C.AAppl (_, hd :: tl) as v ->
232 if is_rewrite_right hd then mk_fwd_rewrite st dtext name tl true else
233 if is_rewrite_left hd then mk_fwd_rewrite st dtext name tl false else
234 let ty, _ = TC.type_of_aux' [] st.context (cic hd) Un.empty_ugraph in
235 begin match get_inner_types st v with
236 | Some (ity, _) when M.bkd st.context ty ->
237 let qs = [[T.Id ""]; mk_proof (next st) v] in
238 [T.Branch (qs, ""); T.Cut (name, ity, dtext)]
240 let (classes, rc) as h = Cl.classify st.context ty in
241 let text = Printf.sprintf "%u %s" (List.length classes) (Cl.to_string h) in
242 [T.LetIn (name, v, dtext ^ text)]
245 [T.LetIn (name, v, dtext)]
247 and mk_proof st = function
248 | C.ALambda (_, name, v, t) as what ->
249 let entry = Some (name, C.Decl (cic v)) in
250 let intro = get_intro name t in
251 let ety = match get_inner_types st what with
252 | Some (_, ety) -> Some ety
255 mk_proof (add st entry intro ety) t
256 | C.ALetIn (_, name, v, t) as what ->
257 let proceed, dtext = test_depth st in
258 let script = if proceed then
259 let entry = Some (name, C.Def (cic v, None)) in
260 let intro = get_intro name t in
261 let q = mk_proof (next (add st entry intro None)) t in
262 List.rev_append (mk_fwd_proof st dtext intro v) q
264 [T.Apply (what, dtext)]
267 | C.ARel _ as what ->
268 let _, dtext = test_depth st in
269 let text = "assumption" in
270 let script = [T.Apply (what, dtext ^ text)] in
272 | C.AMutConstruct _ as what ->
273 let _, dtext = test_depth st in
274 let script = [T.Apply (what, dtext)] in
276 | C.AAppl (_, hd :: tl) as t ->
277 let proceed, dtext = test_depth st in
278 let script = if proceed then
279 let ty, _ = TC.type_of_aux' [] st.context (cic hd) Un.empty_ugraph in
280 let (classes, rc) as h = Cl.classify st.context ty in
281 let decurry = List.length classes - List.length tl in
282 if decurry < 0 then mk_proof (clear st) (appl_expand decurry t) else
283 if decurry > 0 then mk_proof (clear st) (eta_expand decurry t) else
284 let synth = Cl.S.singleton 0 in
285 let text = Printf.sprintf "%u %s" (List.length classes) (Cl.to_string h) in
287 | Some (i, j) when i > 1 && i <= List.length classes ->
288 let classes, tl, _, what = split2_last classes tl in
289 let script, what = mk_atomic st dtext what in
290 let synth = Cl.S.add 1 synth in
291 let qs = mk_bkd_proofs (next st) synth classes tl in
292 if is_rewrite_right hd then
293 List.rev script @ convert st t @
294 [T.Rewrite (false, what, None, dtext); T.Branch (qs, "")]
295 else if is_rewrite_left hd then
296 List.rev script @ convert st t @
297 [T.Rewrite (true, what, None, dtext); T.Branch (qs, "")]
299 let using = Some hd in
300 List.rev script @ convert st t @
301 [T.Elim (what, using, dtext ^ text); T.Branch (qs, "")]
303 let qs = mk_bkd_proofs (next st) synth classes tl in
304 let script, hd = mk_atomic st dtext hd in
305 List.rev script @ convert st t @
306 [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
312 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head t) in
313 let script = [T.Note text] in
316 and mk_bkd_proofs st synth classes ts =
318 let _, dtext = test_depth st in
320 if Cl.overlaps synth inv then None else
321 if Cl.S.is_empty inv then Some (mk_proof st v) else
322 Some [T.Apply (v, dtext ^ "dependent")]
324 T.list_map2_filter aux classes ts
325 with Invalid_argument _ -> failwith "A2P.mk_bkd_proofs"
327 (* object costruction *******************************************************)
329 let is_theorem pars =
330 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
331 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
333 let mk_obj st = function
334 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
335 let ast = mk_proof (set_ety st (Some t)) v in
336 let count = T.count_steps 0 ast in
337 let text = Printf.sprintf "tactics: %u" count in
338 T.Theorem (s, t, text) :: ast @ [T.Qed ""]
340 failwith "not a theorem"
342 (* interface functions ******************************************************)
344 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth prefix aobj =
346 sorts = ids_to_inner_sorts;
347 types = ids_to_inner_types;
355 HLog.debug "Level 2 transformation";
356 let steps = mk_obj st aobj in
357 HLog.debug "grafite rendering";
358 List.rev (T.render_steps [] steps)