1 (* Copyright (C) 2002, HELM Team.
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4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
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27 let rewrite_tac ~term:equality ~status:(proof,goal) =
29 let module U = UriManager in
30 let curi,metasenv,pbo,pty = proof in
31 let metano,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in
32 let eq_ind_r,ty,t1,t2 =
33 match CicTypeChecker.type_of_aux' metasenv context equality with
34 C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
35 when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind") ->
38 (U.uri_of_string "cic:/Coq/Init/Logic/eq_ind_r.con",[])
41 | C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
42 when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") ->
45 (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind_r.con",[])
50 (ProofEngineTypes.Fail
51 "Rewrite: the argument is not a proof of an equality")
54 let gty' = CicSubstitution.lift 1 gty in
55 let t1' = CicSubstitution.lift 1 t1 in
57 ProofEngineReduction.replace_lifting
58 ~equality:ProofEngineReduction.alpha_equivalence
59 ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty'
62 (ProofEngineHelpers.mk_fresh_name context C.Anonymous ty, ty, gty'')
64 let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
65 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
66 let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
69 PrimitiveTactics.exact_tac
71 [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
72 ~status:((curi,metasenv',pbo,pty),goal)
74 assert (List.length goals = 0) ;
79 let rewrite_simpl_tac ~term ~status =
81 ~start:(rewrite_tac ~term)
83 (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None)
88 let rewrite_back_tac ~term:equality ~status:(proof,goal) =
90 let module U = UriManager in
91 let curi,metasenv,pbo,pty = proof in
92 let metano,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in
93 let eq_ind_r,ty,t1,t2 =
94 match CicTypeChecker.type_of_aux' metasenv context equality with
95 C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
96 when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind") ->
99 (U.uri_of_string "cic:/Coq/Init/Logic/eq_ind.con",[])
102 | C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
103 when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") ->
106 (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind.con",[])
111 (ProofEngineTypes.Fail
112 "Rewrite: the argument is not a proof of an equality")
115 let gty' = CicSubstitution.lift 1 gty in
116 let t1' = CicSubstitution.lift 1 t1 in
118 ProofEngineReduction.replace_lifting
119 ~equality:ProofEngineReduction.alpha_equivalence
120 ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty'
123 (ProofEngineHelpers.mk_fresh_name context C.Anonymous ty, ty, gty'')
125 let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
127 CicMkImplicit.identity_relocation_list_for_metavariable context in
128 let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
131 PrimitiveTactics.exact_tac
133 [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
134 ~status:((curi,metasenv',pbo,pty),goal)
136 assert (List.length goals = 0) ;
137 (proof',[fresh_meta])
142 let rewrite_back_simpl_tac ~term ~status =
144 ~start:(rewrite_back_tac ~term)
146 (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None)
151 let replace_tac ~what ~with_what ~status:((proof, goal) as status) =
152 let module C = Cic in
153 let module U = UriManager in
154 let module P = PrimitiveTactics in
155 let module T = Tacticals in
156 let _,metasenv,_,_ = proof in
157 let _,context,_ = List.find (function (m,_,_) -> m=goal) metasenv in
158 let wty = CicTypeChecker.type_of_aux' metasenv context what in
160 if (wty = (CicTypeChecker.type_of_aux' metasenv context with_what))
163 match CicTypeChecker.type_of_aux' metasenv context wty with
164 C.Sort C.Set -> "cic:/Coq/Init/Logic/eq.ind"
167 | C.Sort C.Prop -> "cic:/Coq/Init/Logic_Type/eqT.ind"
174 (C.MutInd ((U.uri_of_string equality), 0, [])) ;
180 ~start:(rewrite_simpl_tac ~term:(C.Rel 1))
182 ProofEngineStructuralRules.clear
183 ~hyp:(List.hd context)) ;
186 else raise (ProofEngineTypes.Fail "Replace: terms not replaceable")
187 with (Failure "hd") -> raise (ProofEngineTypes.Fail "Replace: empty context")
191 (* All these tacs do is applying the right constructor/theorem *)
193 let reflexivity_tac =
194 IntroductionTactics.constructor_tac ~n:1
198 let symmetry_tac ~status:(proof, goal) =
199 let module C = Cic in
200 let module R = CicReduction in
201 let module U = UriManager in
202 let (_,metasenv,_,_) = proof in
203 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
204 match (R.whd context ty) with
205 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
206 PrimitiveTactics.apply_tac ~status:(proof,goal)
207 ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic/sym_eq.con", []))
209 | (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
210 PrimitiveTactics.apply_tac ~status:(proof,goal)
211 ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic_Type/sym_eqT.con", []))
213 | _ -> raise (ProofEngineTypes.Fail "Symmetry failed")
217 let transitivity_tac ~term ~status:((proof, goal) as status) =
218 let module C = Cic in
219 let module R = CicReduction in
220 let module U = UriManager in
221 let module T = Tacticals in
222 let (_,metasenv,_,_) = proof in
223 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
224 match (R.whd context ty) with
225 (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
227 ~start:(PrimitiveTactics.apply_tac
228 ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic/trans_eq.con", [])))
230 [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac]
233 | (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
235 ~start:(PrimitiveTactics.apply_tac
236 ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic_Type/trans_eqT.con", [])))
238 [T.id_tac ; T.id_tac ; PrimitiveTactics.exact_tac ~term]
241 | _ -> raise (ProofEngineTypes.Fail "Transitivity failed")