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 S = CicSubstitution
29 module TC = CicTypeChecker
31 module UM = UriManager
32 module Obj = LibraryObjects
33 module HObj = HelmLibraryObjects
36 module E = CicEnvironment
38 module PEH = ProofEngineHelpers
40 module DTI = DoubleTypeInference
42 module Cl = ProceduralClassify
43 module T = ProceduralTypes
44 module Cn = ProceduralConversion
45 module H = ProceduralHelpers
48 sorts : (C.id, A.sort_kind) Hashtbl.t;
49 types : (C.id, A.anntypes) Hashtbl.t;
51 max_depth: int option;
54 intros: string option list;
58 skip_thm_and_qed : bool;
61 (* helpers ******************************************************************)
63 let split2_last l1 l2 =
65 let n = pred (List.length l1) in
66 let before1, after1 = HEL.split_nth n l1 in
67 let before2, after2 = HEL.split_nth 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 = []}
91 let next st = {(clear st) with depth = succ st.depth}
93 let add st entry intro =
94 {st with context = entry :: st.context; intros = intro :: st.intros}
96 let push st = {st with case = 1 :: st.case}
99 {st with case = match st.case with
101 | hd :: tl -> succ hd :: tl
105 let case = String.concat "." (List.rev_map string_of_int st.case) in
106 Printf.sprintf "case %s: %s" case str
110 let msg = Printf.sprintf "Depth %u: " st.depth in
111 match st.max_depth with
113 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
114 with Invalid_argument _ -> failwith "A2P.test_depth"
116 let is_rewrite_right = function
117 | C.AConst (_, uri, []) ->
118 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
121 let is_rewrite_left = function
122 | C.AConst (_, uri, []) ->
123 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
126 let is_fwd_rewrite_right hd tl =
127 if is_rewrite_right hd then match List.nth tl 3 with
132 let is_fwd_rewrite_left hd tl =
133 if is_rewrite_left hd then match List.nth tl 3 with
138 let get_inner_types st v =
140 let id = Ut.id_of_annterm v in
141 try match Hashtbl.find st.types id with
142 | {A.annsynthesized = st; A.annexpected = Some et} -> Some (st, et)
143 | {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
144 with Not_found -> None
145 with Invalid_argument _ -> failwith "A2P.get_inner_types"
147 let get_inner_sort st v =
149 let id = Ut.id_of_annterm v in
150 try Hashtbl.find st.sorts id
151 with Not_found -> `Type (CicUniv.fresh())
152 with Invalid_argument _ -> failwith "A2P.get_sort"
154 let get_type msg st bo =
156 let ty, _ = TC.type_of_aux' [] st.context (H.cic bo) Un.empty_ugraph in
158 with e -> failwith (msg ^ ": " ^ Printexc.to_string e)
160 let get_entry st id =
161 let rec aux = function
163 | Some (C.Name name, e) :: _ when name = id -> e
168 let get_ind_names uri tno =
170 let ts = match E.get_obj Un.empty_ugraph uri with
171 | C.InductiveDefinition (ts, _, _, _), _ -> ts
174 match List.nth ts tno with
175 | (_, _, _, cs) -> List.map fst cs
176 with Invalid_argument _ -> failwith "A2P.get_ind_names"
178 (* proof construction *******************************************************)
180 let used_premise = C.Name "USED"
182 let mk_exp_args hd tl classes synth =
183 let meta id = C.AImplicit (id, None) in
185 if I.overlaps synth cl && b then v else meta ""
187 let rec aux = function
189 | hd :: tl -> if hd = meta "" then aux tl else List.rev (hd :: tl)
191 let args = T.list_rev_map2 map tl classes in
192 let args = aux args in
193 if args = [] then hd else C.AAppl ("", hd :: args)
195 let mk_convert st ?name sty ety note =
196 let e = Cn.hole "" in
197 let csty, cety = H.cic sty, H.cic ety in
198 let _note = Printf.sprintf "%s\nSINTH: %s\nEXP: %s"
199 note (Pp.ppterm csty) (Pp.ppterm cety)
201 if Ut.alpha_equivalence csty cety then [(* T.Note note *)] else
203 | None -> [T.Change (sty, ety, None, e, ""(*note*))]
205 begin match get_entry st id with
206 | C.Def _ -> assert false (* [T.ClearBody (id, note)] *)
207 | C.Decl _ -> [T.Change (ety, sty, Some (id, Some id), e, "" (* note *))]
210 let convert st ?name v =
211 match get_inner_types st v with
212 | None -> [(*T.Note "NORMAL: NO INNER TYPES"*)]
213 | Some (sty, ety) -> mk_convert st ?name sty ety "NORMAL"
215 let convert_elim st ?name t v pattern =
216 match t, get_inner_types st t, get_inner_types st v with
218 | _, _, None -> [(* T.Note "ELIM: NO INNER TYPES"*)]
219 | C.AAppl (_, hd :: tl), Some (tsty, _), Some (vsty, _) ->
220 let where = List.hd (List.rev tl) in
221 let cty = Cn.elim_inferred_type
222 st.context (H.cic vsty) (H.cic where) (H.cic hd) (H.cic pattern)
224 mk_convert st ?name (Cn.fake_annotate "" st.context cty) tsty "ELIM"
225 | _, Some _, Some _ -> assert false
227 let get_intro = function
228 | C.Anonymous -> None
231 let mk_intros st what script =
232 let intros st script =
233 if st.intros = [] then script else
234 let count = List.length st.intros in
235 T.Intros (Some count, List.rev st.intros, "") :: script
237 let clears st script =
238 if true (* st.clears = [] *) then script else T.Clear (st.clears, st.clears_note) :: script
240 intros st (clears st (convert st what @ script))
242 let mk_arg st = function
243 | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
246 let mk_fwd_rewrite st dtext name tl direction t =
247 assert (List.length tl = 6);
248 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
249 let e = Cn.mk_pattern 1 predicate in
251 | C.ARel (_, _, i, premise) as v ->
252 let where = Some (premise, name) in
253 (* let _script = convert_elim st ~name:(premise, i) t v e in *)
254 let script = mk_arg st what @ mk_arg st v (* @ script *) in
255 let st = {st with context = Cn.clear st.context premise} in
256 st, T.Rewrite (direction, what, where, e, dtext) :: script
259 let mk_rewrite st dtext where qs tl direction t =
260 assert (List.length tl = 5);
261 let predicate = List.nth tl 2 in
262 let e = Cn.mk_pattern 1 predicate in
263 let script = [] (* convert_elim st t t e *) in
264 script @ [T.Rewrite (direction, where, None, e, dtext); T.Branch (qs, "")]
266 let rec proc_lambda st name v t =
267 let dno = DTI.does_not_occur 1 (H.cic t) in
268 let dno = dno && match get_inner_types st t with
271 DTI.does_not_occur 1 (H.cic it) && DTI.does_not_occur 1 (H.cic et)
273 let name = match dno, name with
274 | true, _ -> C.Anonymous
275 | false, C.Anonymous -> H.mk_fresh_name st.context used_premise
276 | false, name -> name
278 let entry = Some (name, C.Decl (H.cic v)) in
279 let intro = get_intro name in
280 proc_proof (add st entry intro) t
282 and proc_letin st what name v t =
283 let intro = get_intro name in
284 let proceed, dtext = test_depth st in
285 let script = if proceed then
286 let st, hyp, rqv = match get_inner_types st v with
288 let st, rqv = match v with
289 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
290 mk_fwd_rewrite st dtext intro tl true v
291 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
292 mk_fwd_rewrite st dtext intro tl false v
294 let qs = [proc_proof (next st) v; [T.Id ""]] in
295 st, [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
297 st, C.Decl (H.cic ity), rqv
299 st, C.Def (H.cic v, None), [T.LetIn (intro, v, dtext)]
301 let entry = Some (name, hyp) in
302 let qt = proc_proof (next (add st entry intro)) t in
303 List.rev_append rqv qt
305 [T.Apply (what, dtext)]
307 mk_intros st what script
309 and proc_rel st what =
310 let _, dtext = test_depth st in
311 let text = "assumption" in
312 let script = [T.Apply (what, dtext ^ text)] in
313 mk_intros st what script
315 and proc_mutconstruct st what =
316 let _, dtext = test_depth st in
317 let script = [T.Apply (what, dtext)] in
318 mk_intros st what script
320 and proc_appl st what hd tl =
321 let proceed, dtext = test_depth st in
322 let script = if proceed then
323 let ty = get_type "TC2" st hd in
324 let classes, rc = Cl.classify st.context ty in
325 let goal_arity = match get_inner_types st what with
327 | Some (ity, _) -> snd (PEH.split_with_whd (st.context, H.cic ity))
329 let parsno, argsno = List.length classes, List.length tl in
330 let decurry = parsno - argsno in
331 let diff = goal_arity - decurry in
332 if diff < 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (H.cic hd)));
333 let rec mk_synth a n =
334 if n < 0 then a else mk_synth (I.S.add n a) (pred n)
336 let synth = mk_synth I.S.empty decurry in
337 let text = "" (* Printf.sprintf "%u %s" parsno (Cl.to_string h) *) in
338 let script = List.rev (mk_arg st hd) in
340 | Some (i, j, uri, tyno) ->
341 let classes, tl, _, where = split2_last classes tl in
342 let script = List.rev (mk_arg st where) @ script in
343 let synth = I.S.add 1 synth in
344 let names = get_ind_names uri tyno in
345 let qs = proc_bkd_proofs (next st) synth names classes tl in
346 if is_rewrite_right hd then
347 script @ mk_rewrite st dtext where qs tl false what
348 else if is_rewrite_left hd then
349 script @ mk_rewrite st dtext where qs tl true what
351 let predicate = List.nth tl (parsno - i) in
352 let e = Cn.mk_pattern j predicate in
353 let using = Some hd in
354 (* convert_elim st what what e @ *) script @
355 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
357 let qs = proc_bkd_proofs (next st) synth [] classes tl in
358 let hd = mk_exp_args hd tl classes synth in
359 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
361 [T.Apply (what, dtext)]
363 mk_intros st what script
365 and proc_other st what =
366 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
367 let script = [T.Note text] in
368 mk_intros st what script
370 and proc_proof st t =
372 let xtypes, note = match get_inner_types st t with
373 | Some (it, et) -> Some (H.cic it, H.cic et),
374 (Printf.sprintf "\nInferred: %s\nExpected: %s"
375 (Pp.ppterm (H.cic it)) (Pp.ppterm (H.cic et)))
376 | None -> None, "\nNo types"
378 let context, clears = Cn.get_clears st.context (H.cic t) xtypes in
379 let note = Pp.ppcontext st.context ^ note in
380 {st with context = context; clears = clears; clears_note = note; }
383 | C.ALambda (_, name, w, t) -> proc_lambda st name w t
384 | C.ALetIn (_, name, v, t) as what -> proc_letin (f st) what name v t
385 | C.ARel _ as what -> proc_rel (f st) what
386 | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
387 | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
388 | what -> proc_other (f st) what
390 and proc_bkd_proofs st synth names classes ts =
393 let names = ref (names, push st) in
396 | [], st -> fun _ -> f st
397 | "" :: tl, st -> names := tl, st; fun _ -> f st
399 let note = case st hd in
401 fun b -> if b then T.Note note :: f st else f st
403 let _, dtext = test_depth st in
405 if I.overlaps synth inv then None else
406 if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
407 Some (fun _ -> [T.Apply (v, dtext ^ "dependent")])
409 let ps = T.list_map2_filter aux classes ts in
410 let b = List.length ps > 1 in
411 List.rev_map (fun f -> f b) ps
413 with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
415 (* object costruction *******************************************************)
417 let is_theorem pars =
418 List.mem (`Flavour `Theorem) pars || List.mem (`Flavour `Fact) pars ||
419 List.mem (`Flavour `Remark) pars || List.mem (`Flavour `Lemma) pars
421 let proc_obj st = function
422 | C.AConstant (_, _, s, Some v, t, [], pars) when is_theorem pars ->
423 let ast = proc_proof st v in
424 let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in
425 let text = Printf.sprintf "tactics: %u\nnodes: %u" steps nodes in
426 if st.skip_thm_and_qed then ast
427 else T.Theorem (Some s, t, "") :: ast @ [T.Qed text]
429 failwith "not a theorem"
431 (* interface functions ******************************************************)
433 let acic2procedural ~ids_to_inner_sorts ~ids_to_inner_types ?depth
434 ?(skip_thm_and_qed=false) prefix aobj =
436 sorts = ids_to_inner_sorts;
437 types = ids_to_inner_types;
446 skip_thm_and_qed = skip_thm_and_qed;
448 HLog.debug "Procedural: level 2 transformation";
449 let steps = proc_obj st aobj in
450 HLog.debug "Procedural: grafite rendering";
451 List.rev (T.render_steps [] steps)