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
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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.
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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
49 let eq_ind, ty, t1, t2 =
51 | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2]
52 when LibraryObjects.is_eq_URI uri ->
54 if_right_to_left LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
56 let eq_ind = C.Const (ind_uri uri,[]) in
57 if_right_to_left (eq_ind, ty, t2, t1) (eq_ind, ty, t1, t2)
58 | _ -> raise (PET.Fail "Rewrite: argument is not a proof of an equality") in
59 (* now we always do as if direction was `LeftToRight *)
61 FreshNamesGenerator.mk_fresh_name
62 ~subst:[] metasenv context C.Anonymous ~typ:ty in
63 let lifted_t1 = CicSubstitution.lift 1 t1 in
64 let lifted_gty = CicSubstitution.lift 1 gty in
65 let lifted_conjecture =
66 metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
67 let lifted_pattern = Some lifted_t1,[],CicSubstitution.lift 1 concl_pat in
68 let _,selected_terms_with_context =
69 ProofEngineHelpers.select
70 ~metasenv ~conjecture:lifted_conjecture ~pattern:lifted_pattern in
72 (* Note: Rel 1 does not live in the context context_of_t *)
73 (* The replace_lifting_csc_0 function will take care of lifting it *)
76 (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2)
77 selected_terms_with_context ([],[]) in
79 ProofEngineReduction.replace_lifting_csc 0
80 ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
81 let gty' = CicSubstitution.subst t2 abstr_gty in
82 let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
83 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
84 let metasenv' = (fresh_meta,context,gty')::metasenv in
85 let pred = C.Lambda (fresh_name, ty, abstr_gty) in
87 C.Appl [eq_ind ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality]
91 (PT.exact_tac ~term:exact_proof) ((curi,metasenv',pbo,pty),goal)
93 assert (List.length goals = 0) ;
96 ProofEngineTypes.mk_tactic (rewrite_tac ~direction ~pattern equality)
99 let rewrite_simpl_tac ~direction ~pattern equality =
100 let rewrite_simpl_tac ~direction ~pattern equality status =
101 ProofEngineTypes.apply_tactic
103 ~start:(rewrite_tac ~direction ~pattern equality)
105 (ReductionTactics.simpl_tac
106 ~pattern:(ProofEngineTypes.conclusion_pattern None)))
109 ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality)
112 let replace_tac ~pattern ~with_what =
113 let replace_tac ~pattern:(wanted,hyps_pat,concl_pat) ~with_what status =
114 let (proof, goal) = status in
115 let module C = Cic in
116 let module U = UriManager in
117 let module P = PrimitiveTactics in
118 let module T = Tacticals in
119 let _,metasenv,_,_ = proof in
120 let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
121 assert (hyps_pat = []); (*CSC: not implemented yet *)
122 let context_len = List.length context in
123 let _,selected_terms_with_context =
124 ProofEngineHelpers.select ~metasenv ~conjecture ~pattern in
125 let ty_of_with_what,u =
126 CicTypeChecker.type_of_aux'
127 metasenv context with_what CicUniv.empty_ugraph in
129 match selected_terms_with_context with
130 [] -> raise (ProofEngineTypes.Fail "Replace: no term selected")
133 (fun (context_of_t,t) ->
136 let context_of_t_len = List.length context_of_t in
137 if context_of_t_len = context_len then t
139 (let t_in_context,subst,metasenv' =
140 CicMetaSubst.delift_rels [] metasenv
141 (context_of_t_len - context_len) t
144 assert (metasenv = metasenv');
147 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
148 (*CSC: we could implement something stronger by completely changing
149 the semantics of the tactic *)
150 raise (ProofEngineTypes.Fail
151 "Replace: one of the selected terms is not closed") in
152 let ty_of_t_in_context,u = (* TASSI: FIXME *)
153 CicTypeChecker.type_of_aux' metasenv context t_in_context
154 CicUniv.empty_ugraph in
155 let b,u = CicReduction.are_convertible ~metasenv context
156 ty_of_with_what ty_of_t_in_context u in
158 let concl_pat_for_t = ProofEngineHelpers.pattern_of ~term:ty [t] in
159 let pattern_for_t = None,[],concl_pat_for_t in
160 t_in_context,pattern_for_t
163 (ProofEngineTypes.Fail
164 "Replace: one of the selected terms and the term to be replaced with have not convertible types")
166 let rec aux n whats status =
168 [] -> ProofEngineTypes.apply_tactic T.id_tac status
169 | (what,pattern)::tl ->
170 let what = CicSubstitution.lift n what in
171 let with_what = CicSubstitution.lift n with_what in
172 let ty_of_with_what = CicSubstitution.lift n ty_of_with_what in
173 ProofEngineTypes.apply_tactic
178 (C.MutInd (LibraryObjects.eq_URI (), 0, [])) ;
185 rewrite_tac ~direction:`LeftToRight ~pattern (C.Rel 1))
189 ProofEngineTypes.mk_tactic
190 (function ((proof,goal) as status) ->
191 let _,metasenv,_,_ = proof in
192 let _,context,_ = CicUtil.lookup_meta goal metasenv in
195 match List.hd context with
196 Some (Cic.Name name,_) -> name
198 with (Failure "hd") -> assert false
200 ProofEngineTypes.apply_tactic
201 (ProofEngineStructuralRules.clear ~hyp) status))
202 ~continuation:(aux_tac (n + 1) tl));
205 and aux_tac n tl = ProofEngineTypes.mk_tactic (aux n tl) in
208 ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what)
212 (* All these tacs do is applying the right constructor/theorem *)
214 let reflexivity_tac =
215 IntroductionTactics.constructor_tac ~n:1
219 let symmetry_tac (proof, goal) =
220 let module C = Cic in
221 let module R = CicReduction in
222 let module U = UriManager in
223 let (_,metasenv,_,_) = proof in
224 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
225 match (R.whd context ty) with
226 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
227 when LibraryObjects.is_eq_URI uri ->
228 ProofEngineTypes.apply_tactic
229 (PrimitiveTactics.apply_tac
230 ~term: (C.Const (LibraryObjects.sym_eq_URI uri, [])))
233 | _ -> raise (ProofEngineTypes.Fail "Symmetry failed")
235 ProofEngineTypes.mk_tactic symmetry_tac
238 let transitivity_tac ~term =
239 let transitivity_tac ~term status =
240 let (proof, goal) = status in
241 let module C = Cic in
242 let module R = CicReduction in
243 let module U = UriManager in
244 let module T = Tacticals in
245 let (_,metasenv,_,_) = proof in
246 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
247 match (R.whd context ty) with
248 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
249 when LibraryObjects.is_eq_URI uri ->
250 ProofEngineTypes.apply_tactic
252 ~start:(PrimitiveTactics.apply_tac
253 ~term: (C.Const (LibraryObjects.trans_eq_URI uri, [])))
255 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
258 | _ -> raise (ProofEngineTypes.Fail "Transitivity failed")
260 ProofEngineTypes.mk_tactic (transitivity_tac ~term)