1 (* Copyright (C) 2002, 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.
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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/.
26 let rewrite_tac ~direction ~pattern equality =
27 let rewrite_tac ~direction ~pattern:(wanted,hyps_pat,concl_pat) equality status
30 let module U = UriManager in
31 let module PET = ProofEngineTypes in
32 let module PER = ProofEngineReduction in
33 let module PEH = ProofEngineHelpers in
34 let module PT = PrimitiveTactics in
35 assert (wanted = None); (* this should be checked syntactically *)
36 assert (hyps_pat = []); (*CSC: not implemented yet! *)
37 let proof,goal = status in
38 let if_right_to_left a b =
43 let curi, metasenv, pbo, pty = proof in
44 let (metano,context,gty) as conjecture = CicUtil.lookup_meta goal metasenv in
46 CicTypeChecker.type_of_aux' metasenv context equality
47 CicUniv.empty_ugraph in
48 let (ty_eq,metasenv,arguments,fresh_meta) =
49 ProofEngineHelpers.saturate_term
50 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context ty_eq in
52 if List.length arguments = 0 then
55 C.Appl (equality :: arguments) in
56 let eq_ind, ty, t1, t2 =
58 | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2]
59 when LibraryObjects.is_eq_URI uri ->
61 if_right_to_left LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
63 let eq_ind = C.Const (ind_uri uri,[]) in
64 if_right_to_left (eq_ind, ty, t2, t1) (eq_ind, ty, t1, t2)
65 | _ -> raise (PET.Fail "Rewrite: argument is not a proof of an equality") in
66 (* now we always do as if direction was `LeftToRight *)
68 FreshNamesGenerator.mk_fresh_name
69 ~subst:[] metasenv context C.Anonymous ~typ:ty in
70 let lifted_t1 = CicSubstitution.lift 1 t1 in
71 let lifted_gty = CicSubstitution.lift 1 gty in
72 let lifted_conjecture =
73 metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
74 let lifted_pattern = Some lifted_t1,[],CicSubstitution.lift 1 concl_pat in
75 let subst,metasenv,ugraph,_,selected_terms_with_context =
76 ProofEngineHelpers.select
77 ~metasenv ~ugraph ~conjecture:lifted_conjecture ~pattern:lifted_pattern in
78 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
80 (* Note: Rel 1 does not live in the context context_of_t *)
81 (* The replace_lifting_csc_0 function will take care of lifting it *)
84 (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2)
85 selected_terms_with_context ([],[]) in
87 ProofEngineReduction.replace_lifting_csc 0
88 ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
89 let abstr_gty = CicMetaSubst.apply_subst subst abstr_gty in
90 let t1 = CicMetaSubst.apply_subst subst t1 in
91 let t2 = CicMetaSubst.apply_subst subst t2 in
92 let equality = CicMetaSubst.apply_subst subst equality in
93 let gty' = CicSubstitution.subst t2 abstr_gty in
94 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
95 let metasenv' = (fresh_meta,context,gty')::metasenv in
96 let pred = C.Lambda (fresh_name, ty, abstr_gty) in
98 C.Appl [eq_ind ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality]
102 (PT.exact_tac ~term:exact_proof) ((curi,metasenv',pbo,pty),goal)
104 assert (List.length goals = 0) ;
105 (proof',[fresh_meta])
107 ProofEngineTypes.mk_tactic (rewrite_tac ~direction ~pattern equality)
110 let rewrite_simpl_tac ~direction ~pattern equality =
111 let rewrite_simpl_tac ~direction ~pattern equality status =
112 ProofEngineTypes.apply_tactic
114 ~start:(rewrite_tac ~direction ~pattern equality)
116 (ReductionTactics.simpl_tac
117 ~pattern:(ProofEngineTypes.conclusion_pattern None)))
120 ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality)
123 let replace_tac ~pattern ~with_what =
125 let replace_tac ~pattern:(wanted,hyps_pat,concl_pat) ~with_what status =
126 let (proof, goal) = status in
127 let module C = Cic in
128 let module U = UriManager in
129 let module P = PrimitiveTactics in
130 let module T = Tacticals in
131 let _,metasenv,_,_ = proof in
132 let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
133 assert (hyps_pat = []); (*CSC: not implemented yet *)
134 let context_len = List.length context in
135 let _,selected_terms_with_context =
136 ProofEngineHelpers.select ~metasenv ~conjecture ~pattern in
137 let ty_of_with_what,u =
138 CicTypeChecker.type_of_aux'
139 metasenv context with_what CicUniv.empty_ugraph in
141 match selected_terms_with_context with
142 [] -> raise (ProofEngineTypes.Fail "Replace: no term selected")
145 (fun (context_of_t,t) ->
148 let context_of_t_len = List.length context_of_t in
149 if context_of_t_len = context_len then t
151 (let t_in_context,subst,metasenv' =
152 CicMetaSubst.delift_rels [] metasenv
153 (context_of_t_len - context_len) t
156 assert (metasenv = metasenv');
159 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
160 (*CSC: we could implement something stronger by completely changing
161 the semantics of the tactic *)
162 raise (ProofEngineTypes.Fail
163 "Replace: one of the selected terms is not closed") in
164 let ty_of_t_in_context,u = (* TASSI: FIXME *)
165 CicTypeChecker.type_of_aux' metasenv context t_in_context
166 CicUniv.empty_ugraph in
167 let b,u = CicReduction.are_convertible ~metasenv context
168 ty_of_with_what ty_of_t_in_context u in
170 let concl_pat_for_t = ProofEngineHelpers.pattern_of ~term:ty [t] in
171 let pattern_for_t = None,[],concl_pat_for_t in
172 t_in_context,pattern_for_t
175 (ProofEngineTypes.Fail
176 "Replace: one of the selected terms and the term to be replaced with have not convertible types")
178 let rec aux n whats status =
180 [] -> ProofEngineTypes.apply_tactic T.id_tac status
181 | (what,pattern)::tl ->
182 let what = CicSubstitution.lift n what in
183 let with_what = CicSubstitution.lift n with_what in
184 let ty_of_with_what = CicSubstitution.lift n ty_of_with_what in
185 ProofEngineTypes.apply_tactic
190 (C.MutInd (LibraryObjects.eq_URI (), 0, [])) ;
197 rewrite_tac ~direction:`LeftToRight ~pattern (C.Rel 1))
201 ProofEngineTypes.mk_tactic
202 (function ((proof,goal) as status) ->
203 let _,metasenv,_,_ = proof in
204 let _,context,_ = CicUtil.lookup_meta goal metasenv in
207 match List.hd context with
208 Some (Cic.Name name,_) -> name
210 with (Failure "hd") -> assert false
212 ProofEngineTypes.apply_tactic
213 (ProofEngineStructuralRules.clear ~hyp) status))
214 ~continuation:(aux_tac (n + 1) tl));
217 and aux_tac n tl = ProofEngineTypes.mk_tactic (aux n tl) in
220 ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what)
225 (* All these tacs do is applying the right constructor/theorem *)
227 let reflexivity_tac =
228 IntroductionTactics.constructor_tac ~n:1
232 let symmetry_tac (proof, goal) =
233 let module C = Cic in
234 let module R = CicReduction in
235 let module U = UriManager in
236 let (_,metasenv,_,_) = proof in
237 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
238 match (R.whd context ty) with
239 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
240 when LibraryObjects.is_eq_URI uri ->
241 ProofEngineTypes.apply_tactic
242 (PrimitiveTactics.apply_tac
243 ~term: (C.Const (LibraryObjects.sym_eq_URI uri, [])))
246 | _ -> raise (ProofEngineTypes.Fail "Symmetry failed")
248 ProofEngineTypes.mk_tactic symmetry_tac
251 let transitivity_tac ~term =
252 let transitivity_tac ~term status =
253 let (proof, goal) = status in
254 let module C = Cic in
255 let module R = CicReduction in
256 let module U = UriManager in
257 let module T = Tacticals in
258 let (_,metasenv,_,_) = proof in
259 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
260 match (R.whd context ty) with
261 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
262 when LibraryObjects.is_eq_URI uri ->
263 ProofEngineTypes.apply_tactic
265 ~start:(PrimitiveTactics.apply_tac
266 ~term: (C.Const (LibraryObjects.trans_eq_URI uri, [])))
268 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
271 | _ -> raise (ProofEngineTypes.Fail "Transitivity failed")
273 ProofEngineTypes.mk_tactic (transitivity_tac ~term)