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
41 module NU = CicNotationUtil
43 module Cl = ProceduralClassify
44 module T = ProceduralTypes
45 module Cn = ProceduralConversion
46 module H = ProceduralHelpers
49 sorts : (C.id, A.sort_kind) Hashtbl.t;
50 types : (C.id, A.anntypes) Hashtbl.t;
51 max_depth: int option;
59 (* helpers ******************************************************************)
61 let split2_last l1 l2 =
63 let n = pred (List.length l1) in
64 let before1, after1 = HEL.split_nth n l1 in
65 let before2, after2 = HEL.split_nth n l2 in
66 before1, before2, List.hd after1, List.hd after2
67 with Invalid_argument _ -> failwith "A2P.split2_last"
69 let string_of_head = function
71 | C.AConst _ -> "const"
72 | C.AMutInd _ -> "mutind"
73 | C.AMutConstruct _ -> "mutconstruct"
77 | C.ALambda _ -> "lambda"
78 | C.ALetIn _ -> "letin"
80 | C.ACoFix _ -> "cofix"
83 | C.AMutCase _ -> "mutcase"
85 | C.AImplicit _ -> "implict"
87 let next st = {st with depth = succ st.depth}
89 let add st entry = {st with context = entry :: st.context}
91 let push st = {st with case = 1 :: st.case}
94 {st with case = match st.case with
96 | hd :: tl -> succ hd :: tl
100 let case = String.concat "." (List.rev_map string_of_int st.case) in
101 Printf.sprintf "case %s: %s" case str
105 let msg = Printf.sprintf "Depth %u: " st.depth in
106 match st.max_depth with
108 | Some d -> if st.depth < d then true, msg else false, "DEPTH EXCEDED: "
109 with Invalid_argument _ -> failwith "A2P.test_depth"
111 let is_rewrite_right = function
112 | C.AConst (_, uri, []) ->
113 UM.eq uri HObj.Logic.eq_ind_r_URI || Obj.is_eq_ind_r_URI uri
116 let is_rewrite_left = function
117 | C.AConst (_, uri, []) ->
118 UM.eq uri HObj.Logic.eq_ind_URI || Obj.is_eq_ind_URI uri
121 let is_fwd_rewrite_right hd tl =
122 if is_rewrite_right hd then match List.nth tl 3 with
127 let is_fwd_rewrite_left hd tl =
128 if is_rewrite_left hd then match List.nth tl 3 with
133 let get_inner_types st v =
135 let id = Ut.id_of_annterm v in
136 try match Hashtbl.find st.types id with
137 | {A.annsynthesized = st; A.annexpected = Some et} -> Some (st, et)
138 | {A.annsynthesized = st; A.annexpected = None} -> Some (st, st)
139 with Not_found -> None
140 with Invalid_argument _ -> failwith "A2P.get_inner_types"
142 let get_inner_sort st v =
144 let id = Ut.id_of_annterm v in
145 try Hashtbl.find st.sorts id
146 with Not_found -> `Type (CicUniv.fresh())
147 with Invalid_argument _ -> failwith "A2P.get_sort"
149 let get_type msg st bo =
151 let ty, _ = TC.type_of_aux' [] st.context (H.cic bo) Un.oblivion_ugraph in
153 with e -> failwith (msg ^ ": " ^ Printexc.to_string e)
155 let get_entry st id =
156 let rec aux = function
158 | Some (C.Name name, e) :: _ when name = id -> e
163 let get_ind_names uri tno =
165 let ts = match E.get_obj Un.oblivion_ugraph uri with
166 | C.InductiveDefinition (ts, _, _, _), _ -> ts
169 match List.nth ts tno with
170 | (_, _, _, cs) -> List.map fst cs
171 with Invalid_argument _ -> failwith "A2P.get_ind_names"
173 let string_of_atomic = function
174 | C.ARel (_, _, _, s) -> s
175 | C.AVar (_, uri, _) -> H.name_of_uri uri None None
176 | C.AConst (_, uri, _) -> H.name_of_uri uri None None
177 | C.AMutInd (_, uri, i, _) -> H.name_of_uri uri (Some i) None
178 | C.AMutConstruct (_, uri, i, j, _) -> H.name_of_uri uri (Some i) (Some j)
181 let get_sub_names head l =
182 let s = string_of_atomic head in
183 if s = "" then [] else
184 let map (names, i) _ =
185 let name = Printf.sprintf "%s_%u" s i in name :: names, succ i
187 let names, _ = List.fold_left map ([], 1) l in
190 (* proof construction *******************************************************)
192 let anonymous_premise = C.Name "PREMISE"
194 let mk_exp_args hd tl classes synth =
195 let meta id = C.AImplicit (id, None) in
197 if I.overlaps synth cl && b then v else meta ""
199 let rec aux = function
201 | hd :: tl -> if hd = meta "" then aux tl else List.rev (hd :: tl)
203 let args = T.list_rev_map2 map tl classes in
204 let args = aux args in
205 if args = [] then hd else C.AAppl ("", hd :: args)
207 let mk_convert st ?name sty ety note =
208 let e = Cn.hole "" in
209 let csty, cety = H.cic sty, H.cic ety in
212 let sname = match name with None -> "" | Some (id, _) -> id in
213 let note = Printf.sprintf "%s: %s\nSINTH: %s\nEXP: %s"
214 note sname (Pp.ppterm csty) (Pp.ppterm cety)
219 assert (Ut.is_sober st.context csty);
220 assert (Ut.is_sober st.context cety);
221 if Ut.alpha_equivalence csty cety then script else
222 let sty, ety = H.acic_bc st.context sty, H.acic_bc st.context ety in
224 | None -> T.Change (sty, ety, None, e, "") :: script
226 begin match get_entry st id with
227 | C.Def _ -> assert false (* T.ClearBody (id, "") :: script *)
229 T.Change (ety, sty, Some (id, Some id), e, "") :: script
232 let convert st ?name v =
233 match get_inner_types st v with
235 if debug then [T.Note "NORMAL: NO INNER TYPES"] else []
236 | Some (sty, ety) -> mk_convert st ?name sty ety "NORMAL"
238 let convert_elim st ?name t v pattern =
239 match t, get_inner_types st t, get_inner_types st v with
241 | _, _, None -> [(* T.Note "ELIM: NO INNER TYPES"*)]
242 | C.AAppl (_, hd :: tl), Some (tsty, _), Some (vsty, _) ->
243 let where = List.hd (List.rev tl) in
244 let cty = Cn.elim_inferred_type
245 st.context (H.cic vsty) (H.cic where) (H.cic hd) (H.cic pattern)
247 mk_convert st ?name (Cn.fake_annotate "" st.context cty) tsty "ELIM"
248 | _, Some _, Some _ -> assert false
250 let get_intro = function
251 | C.Anonymous -> None
254 let mk_preamble st what script =
255 convert st what @ script
257 let mk_arg st = function
258 | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
261 let mk_fwd_rewrite st dtext name tl direction v t ity =
262 let compare premise = function
264 | Some s -> s = premise
266 assert (List.length tl = 6);
267 let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
268 let e = Cn.mk_pattern 1 predicate in
269 if (Cn.does_not_occur e) then st, [] else
271 | C.ARel (_, _, i, premise) as w ->
272 (* let _script = convert_elim st ~name:(premise, i) v w e in *)
274 let where = Some (premise, name) in
275 let script = mk_arg st what @ mk_arg st w (* @ script *) in
276 T.Rewrite (direction, what, where, e, dtext) :: script
278 if DTI.does_not_occur (succ i) (H.cic t) || compare premise name then
279 {st with context = Cn.clear st.context premise}, script name
281 assert (Ut.is_sober st.context (H.cic ity));
282 let ity = H.acic_bc st.context ity in
283 let br1 = [T.Id ""] in
284 let br2 = List.rev (T.Apply (w, "assumption") :: script None) in
285 let text = "non linear rewrite" in
286 st, [T.Branch ([br2; br1], ""); T.Cut (name, ity, text)]
290 let mk_rewrite st dtext where qs tl direction t =
291 assert (List.length tl = 5);
292 let predicate = List.nth tl 2 in
293 let e = Cn.mk_pattern 1 predicate in
294 let script = [T.Branch (qs, "")] in
295 if (Cn.does_not_occur e) then script else
296 (* let script = convert_elim st t t e in *)
297 T.Rewrite (direction, where, None, e, dtext) :: script
299 let rec proc_lambda st what name v t =
300 let name = match name with
301 | C.Anonymous -> H.mk_fresh_name st.context anonymous_premise
304 let entry = Some (name, C.Decl (H.cic v)) in
305 let intro = get_intro name in
306 let script = proc_proof (add st entry) t in
307 let script = T.Intros (Some 1, [intro], "") :: script in
308 mk_preamble st what script
310 and proc_letin st what name v w t =
311 let intro = get_intro name in
312 let proceed, dtext = test_depth st in
313 let script = if proceed then
314 let st, hyp, rqv = match get_inner_types st v with
316 let st, rqv = match v with
317 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
318 mk_fwd_rewrite st dtext intro tl true v t ity
319 | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl ->
320 mk_fwd_rewrite st dtext intro tl false v t ity
322 assert (Ut.is_sober st.context (H.cic ity));
323 let ity = H.acic_bc st.context ity in
324 let qs = [proc_proof (next st) v; [T.Id ""]] in
325 st, [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
327 st, C.Decl (H.cic ity), rqv
329 st, C.Def (H.cic v, H.cic w), [T.LetIn (intro, v, dtext)]
331 let entry = Some (name, hyp) in
332 let qt = proc_proof (next (add st entry)) t in
333 List.rev_append rqv qt
335 [T.Apply (what, dtext)]
337 mk_preamble st what script
339 and proc_rel st what =
340 let _, dtext = test_depth st in
341 let text = "assumption" in
342 let script = [T.Apply (what, dtext ^ text)] in
343 mk_preamble st what script
345 and proc_mutconstruct st what =
346 let _, dtext = test_depth st in
347 let script = [T.Apply (what, dtext)] in
348 mk_preamble st what script
350 and proc_const st what =
351 let _, dtext = test_depth st in
352 let script = [T.Apply (what, dtext)] in
353 mk_preamble st what script
355 and proc_appl st what hd tl =
356 let proceed, dtext = test_depth st in
357 let script = if proceed then
358 let ty = get_type "TC2" st hd in
359 let classes, rc = Cl.classify st.context ty in
360 let goal_arity, goal = match get_inner_types st what with
363 snd (PEH.split_with_whd (st.context, H.cic ity)), Some (H.cic ety)
365 let parsno, argsno = List.length classes, List.length tl in
366 let decurry = parsno - argsno in
367 let diff = goal_arity - decurry in
368 if diff < 0 then failwith (Printf.sprintf "NOT TOTAL: %i %s |--- %s" diff (Pp.ppcontext st.context) (Pp.ppterm (H.cic hd)));
369 let classes = Cl.adjust st.context tl ?goal classes in
370 let rec mk_synth a n =
371 if n < 0 then a else mk_synth (I.S.add n a) (pred n)
373 let synth = mk_synth I.S.empty decurry in
374 let text = "" (* Printf.sprintf "%u %s" parsno (Cl.to_string h) *) in
375 let script = List.rev (mk_arg st hd) in
377 | Some (i, j, uri, tyno) ->
378 let classes2, tl2, _, where = split2_last classes tl in
379 let script2 = List.rev (mk_arg st where) @ script in
380 let synth2 = I.S.add 1 synth in
381 let names = get_ind_names uri tyno in
382 let qs = proc_bkd_proofs (next st) synth2 names classes2 tl2 in
383 if List.length qs <> List.length names then
384 let qs = proc_bkd_proofs (next st) synth [] classes tl in
385 let hd = mk_exp_args hd tl classes synth in
386 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
387 else if is_rewrite_right hd then
388 script2 @ mk_rewrite st dtext where qs tl2 false what
389 else if is_rewrite_left hd then
390 script2 @ mk_rewrite st dtext where qs tl2 true what
392 let predicate = List.nth tl2 (parsno - i) in
393 let e = Cn.mk_pattern j predicate in
394 let using = Some hd in
395 (* convert_elim st what what e @ *) script2 @
396 [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
398 let names = get_sub_names hd tl in
399 let qs = proc_bkd_proofs (next st) synth names classes tl in
400 let hd = mk_exp_args hd tl classes synth in
401 script @ [T.Apply (hd, dtext ^ text); T.Branch (qs, "")]
403 [T.Apply (what, dtext)]
405 mk_preamble st what script
407 and proc_other st what =
408 let _, dtext = test_depth st in
409 let text = Printf.sprintf "%s: %s" "UNEXPANDED" (string_of_head what) in
410 let script = [T.Apply (what, dtext ^ text)] in
411 mk_preamble st what script
413 and proc_proof st t =
415 let xtypes, note = match get_inner_types st t with
416 | Some (it, et) -> Some (H.cic it, H.cic et),
417 (Printf.sprintf "\nInferred: %s\nExpected: %s"
418 (Pp.ppterm (H.cic it)) (Pp.ppterm (H.cic et)))
419 | None -> None, "\nNo types"
421 let context, _clears = Cn.get_clears st.context (H.cic t) xtypes in
422 {st with context = context}
425 | C.ALambda (_, name, w, t) as what -> proc_lambda (f st) what name w t
426 | C.ALetIn (_, name, v, w, t) as what -> proc_letin (f st) what name v w t
427 | C.ARel _ as what -> proc_rel (f st) what
428 | C.AMutConstruct _ as what -> proc_mutconstruct (f st) what
429 | C.AConst _ as what -> proc_const (f st) what
430 | C.AAppl (_, hd :: tl) as what -> proc_appl (f st) what hd tl
431 | what -> proc_other (f st) what
433 and proc_bkd_proofs st synth names classes ts =
435 let get_names b = ref (names, if b then push st else st) in
436 let get_note f b names =
439 | "" :: tl, st -> names := tl, st; f st
441 let note = case st hd in
443 if b then T.Note note :: f st else f st
445 let _, dtext = test_depth st in
447 if I.overlaps synth inv then None else
448 if I.S.is_empty inv then Some (get_note (fun st -> proc_proof st v)) else
449 Some (get_note (fun _ -> [T.Apply (v, dtext ^ "dependent")]))
451 let ps = T.list_map2_filter aux classes ts in
452 let b = List.length ps > 1 in
453 let names = get_names b in
454 List.rev_map (fun f -> f b names) ps
456 with Invalid_argument s -> failwith ("A2P.proc_bkd_proofs: " ^ s)
458 (* object costruction *******************************************************)
460 let th_flavours = [`Theorem; `Lemma; `Remark; `Fact]
462 let def_flavours = [`Definition]
464 let get_flavour ?flavour attrs =
465 let rec aux = function
466 | [] -> List.hd th_flavours
467 | `Flavour fl :: _ -> fl
474 let proc_obj ?flavour st = function
475 | C.AConstant (_, _, s, Some v, t, [], attrs) ->
476 begin match get_flavour ?flavour attrs with
477 | flavour when List.mem flavour th_flavours ->
478 let ast = proc_proof st v in
479 let steps, nodes = T.count_steps 0 ast, T.count_nodes 0 ast in
480 let text = Printf.sprintf "tactics: %u\nnodes: %u" steps nodes in
481 T.Statement (flavour, Some s, t, None, "") :: ast @ [T.Qed text]
482 | flavour when List.mem flavour def_flavours ->
483 [T.Statement (flavour, Some s, t, Some v, "")]
485 failwith "not a theorem, definition, axiom or inductive type"
487 | C.AConstant (_, _, s, None, t, [], attrs) ->
488 [T.Statement (`Axiom, Some s, t, None, "")]
489 | C.AInductiveDefinition (_, types, [], lpsno, attrs) ->
490 [T.Inductive (types, lpsno, "")]
492 failwith "not a theorem, definition, axiom or inductive type"
494 (* interface functions ******************************************************)
496 let procedural_of_acic_object ~ids_to_inner_sorts ~ids_to_inner_types ?depth
497 ?flavour prefix anobj =
499 sorts = ids_to_inner_sorts;
500 types = ids_to_inner_types;
506 HLog.debug "Procedural: level 2 transformation";
507 let steps = proc_obj st ?flavour anobj in
508 HLog.debug "Procedural: grafite rendering";
509 List.rev (T.render_steps [] steps)
511 let procedural_of_acic_term ~ids_to_inner_sorts ~ids_to_inner_types ?depth
512 prefix context annterm =
514 sorts = ids_to_inner_sorts;
515 types = ids_to_inner_types;
521 HLog.debug "Procedural: level 2 transformation";
522 let steps = proc_proof st annterm in
523 HLog.debug "Procedural: grafite rendering";
524 List.rev (T.render_steps [] steps)