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 ******************************************************************)
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 = []}
92 let next st = {(clear st) with depth = succ st.depth}
94 let add st entry intro =
95 {st with context = entry :: st.context; intros = intro :: st.intros}
99 let msg = Printf.sprintf "Depth %u: " st.depth in
100 match st.max_depth with
102 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
103 with Invalid_argument _ -> failwith "A2P.test_depth"
105 let is_rewrite_right = function
106 | C.AConst (_, uri, []) ->
107 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
110 let is_rewrite_left = function
111 | C.AConst (_, uri, []) ->
112 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
115 let is_fwd_rewrite_right hd tl =
116 if is_rewrite_right hd then match List.nth tl 3 with
121 let is_fwd_rewrite_left hd tl =
122 if is_rewrite_left hd then match List.nth tl 3 with
127 let get_ind_name uri tno xcno =
129 let ts = match E.get_obj Un.empty_ugraph uri with
130 | C.InductiveDefinition (ts, _, _,_), _ -> ts
133 let tname, cs = match List.nth ts tno with
134 | (name, _, _, cs) -> name, cs
138 | Some cno -> fst (List.nth cs (pred cno))
139 with Invalid_argument _ -> failwith "A2P.get_ind_name"
141 let get_inner_types st v =
143 let id = Ut.id_of_annterm v in
144 try match Hashtbl.find st.types id with
145 | {A.annsynthesized = st; A.annexpected = Some et} -> Some (st, et)
146 | {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
147 with Not_found -> None
148 with Invalid_argument _ -> failwith "A2P.get_inner_types"
150 let get_inner_sort st v =
152 let id = Ut.id_of_annterm v in
153 try Hashtbl.find st.sorts id
154 with Not_found -> `Type (CicUniv.fresh())
155 with Invalid_argument _ -> failwith "A2P.get_sort"
157 let get_type msg st bo =
159 let ty, _ = TC.type_of_aux' [] st.context (cic bo) Un.empty_ugraph in
161 with e -> failwith (msg ^ ": " ^ Printexc.to_string e)
163 (* proof construction *******************************************************)
165 let unused_premise = "UNUSED"
167 let defined_premise = "DEFINED"
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
177 let e = Cn.mk_pattern [] (T.mk_arel 1 "") in
179 | None -> [T.Change (st, et, None, e, "")]
180 | Some id -> [T.Change (st, et, Some (id, id), e, ""); T.ClearBody (id, "")]
183 let id = Ut.id_of_annterm t in
184 let ty = C.AImplicit ("", None) in
185 let name i = Printf.sprintf "%s%u" expanded_premise i in
186 let lambda i t = C.ALambda (id, C.Name (name i), ty, t) in
187 let arg i n = T.mk_arel ((* n - *) succ i) (name (n - i - 1)) in
189 if i >= n then f, a else aux (succ i) (comp f (lambda i)) (arg i n :: a)
191 let absts, args = aux 0 identity [] in
192 match Cn.lift 1 n t with
193 | C.AAppl (id, ts) -> absts (C.AAppl (id, ts @ args))
194 | t -> absts (C.AAppl ("", t :: args))
196 let appl_expand n = function
197 | C.AAppl (id, ts) ->
198 let before, after = T.list_split (List.length ts + n) ts in
199 C.AAppl (id, C.AAppl ("", before) :: after)
202 let get_intro name t =
205 | C.Anonymous -> unused_premise
207 if DTI.does_not_occur 1 (cic t) then unused_premise else s
208 with Invalid_argument _ -> failwith "A2P.get_intro"
210 let mk_intros st script =
212 if st.intros = [] then script else
213 let count = List.length st.intros in
214 T.Intros (Some count, List.rev st.intros, "") :: script
215 with Invalid_argument _ -> failwith "A2P.mk_intros"
217 let rec mk_atomic st dtext what =
218 if T.is_atomic what then
220 | C.ARel (_, _, _, name) -> convert st ~name what, what
223 let name = defined_premise in
224 let script = convert st ~name what in
225 script @ mk_fwd_proof st dtext name what, T.mk_arel 0 name
227 and mk_fwd_rewrite st dtext name tl direction =
228 assert (List.length tl = 6);
229 let what, where = List.nth tl 5, List.nth tl 3 in
230 let rps, predicate = [List.nth tl 4], List.nth tl 2 in
231 let e = Cn.mk_pattern rps predicate in
233 | C.ARel (_, _, _, premise) ->
234 let script, what = mk_atomic st dtext what in
235 T.Rewrite (direction, what, Some (premise, name), e, dtext) :: script
238 and mk_rewrite st dtext script t what qs tl direction =
239 assert (List.length tl = 5);
240 let rps, predicate = [List.nth tl 4], List.nth tl 2 in
241 let e = Cn.mk_pattern rps predicate in
242 List.rev script @ convert st t @
243 [T.Rewrite (direction, what, None, e, dtext); T.Branch (qs, "")]
245 and mk_fwd_proof st dtext name = function
246 | C.ALetIn (_, n, v, t) ->
247 let entry = Some (n, C.Def (cic v, None)) in
248 let intro = get_intro n t in
249 let qt = mk_fwd_proof (add st entry intro) dtext name t in
250 let qv = mk_fwd_proof st "" intro v in
252 | C.AAppl (_, hd :: tl) as v ->
253 if is_fwd_rewrite_right hd tl then mk_fwd_rewrite st dtext name tl true else
254 if is_fwd_rewrite_left hd tl then mk_fwd_rewrite st dtext name tl false else
255 let ty = get_type "TC1" st hd in
256 begin match get_inner_types st v with
257 | Some (ity, _) when M.bkd st.context ty ->
258 let qs = [[T.Id ""]; mk_proof (next st) v] in
259 [T.Branch (qs, ""); T.Cut (name, ity, dtext)]
261 let (classes, rc) as h = Cl.classify st.context ty in
262 let text = Printf.sprintf "%u %s" (List.length classes) (Cl.to_string h) in
263 [T.LetIn (name, v, dtext ^ text)]
265 (* | C.AMutCase (id, uri, tyno, outty, arg, cases) as v ->
266 begin match Cn.mk_ind st.context id uri tyno outty arg cases with
267 | None -> [T.LetIn (name, v, dtext)]
268 | Some v -> mk_fwd_proof st dtext name v
270 *) | C.ACast (_, v, _) ->
271 mk_fwd_proof st dtext name v
273 match get_inner_types st v with
275 let qs = [[T.Id ""]; mk_proof (next st) v] in
276 [T.Branch (qs, ""); T.Cut (name, ity, dtext)]
278 [T.LetIn (name, v, dtext)]
280 and mk_proof st = function
281 | C.ALambda (_, name, v, t) ->
282 let entry = Some (name, C.Decl (cic v)) in
283 let intro = get_intro name t in
284 mk_proof (add st entry intro) t
285 | C.ALetIn (_, name, v, t) as what ->
286 let proceed, dtext = test_depth st in
287 let script = if proceed then
288 let entry = Some (name, C.Def (cic v, None)) in
289 let intro = get_intro name t in
290 let q = mk_proof (next (add st entry intro)) t in
291 List.rev_append (mk_fwd_proof st dtext intro v) q
293 [T.Apply (what, dtext)]
296 | C.ARel _ as what ->
297 let _, dtext = test_depth st in
298 let text = "assumption" in
299 let script = [T.Apply (what, dtext ^ text)] in
301 | C.AMutConstruct _ as what ->
302 let _, dtext = test_depth st in
303 let script = [T.Apply (what, dtext)] in
305 | C.AAppl (_, hd :: tl) as t ->
306 let proceed, dtext = test_depth st in
307 let script = if proceed then
308 let ty = get_type "TC2" st hd in
309 let (classes, rc) as h = Cl.classify st.context ty in
310 let premises, _ = P.split st.context ty in
311 let decurry = List.length classes - List.length tl in
313 Printf.eprintf "DECURRY: %u %s\n" decurry (CicPp.ppterm (cic t));
314 assert (decurry = 0);
315 if decurry < 0 then mk_proof (clear st) (appl_expand decurry t) else
316 if decurry > 0 then mk_proof (clear st) (eta_expand decurry t) else
317 let synth = I.S.singleton 0 in
318 let text = Printf.sprintf "%u %s" (List.length classes) (Cl.to_string h) in
320 | Some (i, j) when i > 1 && i <= List.length classes && M.is_eliminator premises ->
321 let classes, tl, _, what = split2_last classes tl in
322 let script, what = mk_atomic st dtext what in
323 let synth = I.S.add 1 synth in
324 let qs = mk_bkd_proofs (next st) synth classes tl in
325 if is_rewrite_right hd then
326 mk_rewrite st dtext script t what qs tl false
327 else if is_rewrite_left hd then
328 mk_rewrite st dtext script t what qs tl true
330 let using = Some hd in
331 List.rev script @ convert st t @
332 [T.Elim (what, using, dtext ^ text); T.Branch (qs, "")]
334 let qs = mk_bkd_proofs (next st) synth classes tl in
335 let script, hd = mk_atomic st dtext hd in
336 List.rev script @ convert st t @
337 [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
342 | C.AMutCase (id, uri, tyno, outty, arg, cases) as t ->
343 begin match Cn.mk_ind st.context id uri tyno outty arg cases with
345 let text = Printf.sprintf "%s" "UNEXPANDED: mutcase" in
346 let script = [T.Note text] in
348 (* | Some t -> mk_proof st t *)
350 | C.ACast (_, t, _) ->
353 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head t) in
354 let script = [T.Note text] in
357 and mk_bkd_proofs st synth classes ts =
359 let _, dtext = test_depth st in
361 if I.overlaps synth inv then None else
362 if I.S.is_empty inv then Some (mk_proof st v) else
363 Some [T.Apply (v, dtext ^ "dependent")]
365 T.list_map2_filter aux classes ts
366 with Invalid_argument _ -> failwith "A2P.mk_bkd_proofs"
368 (* object costruction *******************************************************)
370 let is_theorem pars =
371 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
372 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
374 let mk_obj st = function
375 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
376 let ast = mk_proof st v in
377 let count = T.count_steps 0 ast in
378 let text = Printf.sprintf "tactics: %u" count in
379 T.Theorem (s, t, text) :: ast @ [T.Qed ""]
381 failwith "not a theorem"
383 (* interface functions ******************************************************)
385 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth prefix aobj =
387 sorts = ids_to_inner_sorts;
388 types = ids_to_inner_types;
395 HLog.debug "Level 2 transformation";
396 let steps = mk_obj st aobj in
397 HLog.debug "grafite rendering";
398 List.rev (T.render_steps [] steps)