* http://cs.unibo.it/helm/.
*)
-
-let rewrite_tac ~term:equality (proof,goal) =
- let module C = Cic in
- let module U = UriManager in
- let curi,metasenv,pbo,pty = proof in
- let metano,context,gty = CicUtil.lookup_meta goal metasenv in
- let eq_ind_r,ty,t1,t2 =
- match CicTypeChecker.type_of_aux' metasenv context equality with
- C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
- when U.eq uri HelmLibraryObjects.Logic.eq_URI ->
- let eq_ind_r =
- C.Const
- (HelmLibraryObjects.Logic.eq_ind_r_URI,[])
- in
- eq_ind_r,ty,t1,t2
- | _ ->
- raise
- (ProofEngineTypes.Fail
- "Rewrite: the argument is not a proof of an equality")
- in
- let pred =
- let gty' = CicSubstitution.lift 1 gty in
- let t1' = CicSubstitution.lift 1 t1 in
- let gty'' =
- ProofEngineReduction.replace_lifting
- ~equality:ProofEngineReduction.alpha_equivalence
- ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty'
- in
- C.Lambda
- (FreshNamesGenerator.mk_fresh_name metasenv context C.Anonymous ty,
- ty, gty'')
+let rewrite_tac ~term:equality =
+ let rewrite_tac ~term:equality (proof,goal) =
+ let module C = Cic in
+ let module U = UriManager in
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,gty = CicUtil.lookup_meta goal metasenv in
+ let eq_ind_r,ty,t1,t2 =
+ match CicTypeChecker.type_of_aux' metasenv context equality with
+ C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
+ when U.eq uri HelmLibraryObjects.Logic.eq_URI ->
+ let eq_ind_r =
+ C.Const
+ (HelmLibraryObjects.Logic.eq_ind_r_URI,[])
+ in
+ eq_ind_r,ty,t1,t2
+ | _ ->
+ raise
+ (ProofEngineTypes.Fail
+ "Rewrite: the argument is not a proof of an equality")
in
- let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
- let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
- let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
-
- let (proof',goals) =
- PrimitiveTactics.exact_tac
- ~term:(C.Appl
- [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
- ((curi,metasenv',pbo,pty),goal)
+ let pred =
+ let gty' = CicSubstitution.lift 1 gty in
+ let t1' = CicSubstitution.lift 1 t1 in
+ let gty'' =
+ ProofEngineReduction.replace_lifting
+ ~equality:ProofEngineReduction.alpha_equivalence
+ ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty'
+ in
+ C.Lambda
+ (FreshNamesGenerator.mk_fresh_name metasenv context C.Anonymous ty,
+ ty, gty'')
in
- assert (List.length goals = 0) ;
- (proof',[fresh_meta])
+ let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
+ let irl =CicMkImplicit.identity_relocation_list_for_metavariable context in
+ let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
+
+ let (proof',goals) =
+ ProofEngineTypes.apply_tactic
+ (PrimitiveTactics.exact_tac
+ ~term:(C.Appl
+ [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])) ((curi,metasenv',pbo,pty),goal)
+ in
+ assert (List.length goals = 0) ;
+ (proof',[fresh_meta])
+ in
+ ProofEngineTypes.mk_tactic (rewrite_tac ~term:equality)
;;
-let rewrite_simpl_tac ~term status =
- Tacticals.then_
- ~start:(rewrite_tac ~term)
- ~continuation:
- (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None)
- status
+let rewrite_simpl_tac ~term =
+ let rewrite_simpl_tac ~term status =
+ ProofEngineTypes.apply_tactic
+ (Tacticals.then_
+ ~start:(rewrite_tac ~term)
+ ~continuation:
+ (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None))
+ status
+ in
+ ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~term)
;;
-let rewrite_back_tac ~term:equality (proof,goal) =
- let module C = Cic in
- let module U = UriManager in
- let curi,metasenv,pbo,pty = proof in
- let metano,context,gty = CicUtil.lookup_meta goal metasenv in
- let eq_ind_r,ty,t1,t2 =
- match CicTypeChecker.type_of_aux' metasenv context equality with
- C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
- when U.eq uri HelmLibraryObjects.Logic.eq_URI ->
- let eq_ind_r =
- C.Const (HelmLibraryObjects.Logic.eq_ind_URI,[])
- in
- eq_ind_r,ty,t2,t1
- | _ ->
- raise
- (ProofEngineTypes.Fail
- "Rewrite: the argument is not a proof of an equality")
- in
- let pred =
- let gty' = CicSubstitution.lift 1 gty in
- let t1' = CicSubstitution.lift 1 t1 in
- let gty'' =
- ProofEngineReduction.replace_lifting
- ~equality:ProofEngineReduction.alpha_equivalence
- ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty'
- in
- C.Lambda
- (FreshNamesGenerator.mk_fresh_name metasenv context C.Anonymous ty,
- ty, gty'')
+let rewrite_back_tac ~term:equality =
+ let rewrite_back_tac equality (proof,goal) =
+ let module C = Cic in
+ let module U = UriManager in
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,gty = CicUtil.lookup_meta goal metasenv in
+ let eq_ind_r,ty,t1,t2 =
+ match CicTypeChecker.type_of_aux' metasenv context equality with
+ C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
+ when U.eq uri HelmLibraryObjects.Logic.eq_URI ->
+ let eq_ind_r =
+ C.Const (HelmLibraryObjects.Logic.eq_ind_URI,[])
+ in
+ eq_ind_r,ty,t2,t1
+ | _ ->
+ raise
+ (ProofEngineTypes.Fail
+ "Rewrite: the argument is not a proof of an equality")
in
- let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
- let irl =
- CicMkImplicit.identity_relocation_list_for_metavariable context in
- let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
-
- let (proof',goals) =
- PrimitiveTactics.exact_tac
- ~term:(C.Appl
- [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
- ((curi,metasenv',pbo,pty),goal)
+ let pred =
+ let gty' = CicSubstitution.lift 1 gty in
+ let t1' = CicSubstitution.lift 1 t1 in
+ let gty'' =
+ ProofEngineReduction.replace_lifting
+ ~equality:ProofEngineReduction.alpha_equivalence
+ ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty'
+ in
+ C.Lambda
+ (FreshNamesGenerator.mk_fresh_name metasenv context C.Anonymous ty,
+ ty, gty'')
in
- assert (List.length goals = 0) ;
- (proof',[fresh_meta])
-
+ let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context in
+ let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
+
+ let (proof',goals) =
+ ProofEngineTypes.apply_tactic
+ (PrimitiveTactics.exact_tac
+ ~term:(C.Appl
+ [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality]))
+ ((curi,metasenv',pbo,pty),goal)
+ in
+ assert (List.length goals = 0) ;
+ (proof',[fresh_meta])
+ in
+ ProofEngineTypes.mk_tactic (rewrite_back_tac equality)
;;
-let rewrite_back_simpl_tac ~term status =
- Tacticals.then_
- ~start:(rewrite_back_tac ~term)
- ~continuation:
- (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None)
- status
+let rewrite_back_simpl_tac ~term =
+ let rewrite_back_simpl_tac ~term status =
+ ProofEngineTypes.apply_tactic
+ (Tacticals.then_
+ ~start:(rewrite_back_tac ~term)
+ ~continuation:
+ (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None))
+ status
+ in
+ ProofEngineTypes.mk_tactic (rewrite_back_simpl_tac ~term)
;;
-
-let replace_tac ~what ~with_what status =
+let replace_tac ~what ~with_what =
+ let replace_tac ~what ~with_what status =
let (proof, goal) = status in
let module C = Cic in
let module U = UriManager in
try
if (wty = (CicTypeChecker.type_of_aux' metasenv context with_what))
then
- T.thens
+ ProofEngineTypes.apply_tactic
+ (T.thens
~start:(
P.cut_tac
(C.Appl [
~continuation:(
ProofEngineStructuralRules.clear
~hyp:(List.hd context)) ;
- T.id_tac]
+ T.id_tac])
status
else raise (ProofEngineTypes.Fail "Replace: terms not replaceable")
- with (Failure "hd") -> raise (ProofEngineTypes.Fail "Replace: empty context")
+ with (Failure "hd") ->
+ raise (ProofEngineTypes.Fail "Replace: empty context")
+ in
+ ProofEngineTypes.mk_tactic (replace_tac ~what ~with_what)
;;
IntroductionTactics.constructor_tac ~n:1
;;
-
-let symmetry_tac (proof, goal) =
+let symmetry_tac =
+ let symmetry_tac (proof, goal) =
let module C = Cic in
let module R = CicReduction in
let module U = UriManager in
let (_,metasenv,_,_) = proof in
let metano,context,ty = CicUtil.lookup_meta goal metasenv in
match (R.whd context ty) with
- (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (U.eq uri HelmLibraryObjects.Logic.eq_URI) ->
- PrimitiveTactics.apply_tac (proof,goal)
- ~term: (C.Const (HelmLibraryObjects.Logic.sym_eq_URI, []))
+ (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
+ when (U.eq uri HelmLibraryObjects.Logic.eq_URI) ->
+ ProofEngineTypes.apply_tactic
+ (PrimitiveTactics.apply_tac
+ ~term: (C.Const (HelmLibraryObjects.Logic.sym_eq_URI, [])))
+ (proof,goal)
| _ -> raise (ProofEngineTypes.Fail "Symmetry failed")
+ in
+ ProofEngineTypes.mk_tactic symmetry_tac
;;
-
-let transitivity_tac ~term status =
+let transitivity_tac ~term =
+ let transitivity_tac ~term status =
let (proof, goal) = status in
let module C = Cic in
let module R = CicReduction in
let (_,metasenv,_,_) = proof in
let metano,context,ty = CicUtil.lookup_meta goal metasenv in
match (R.whd context ty) with
- (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (uri = HelmLibraryObjects.Logic.eq_URI) ->
- T.thens
+ (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
+ when (uri = HelmLibraryObjects.Logic.eq_URI) ->
+ ProofEngineTypes.apply_tactic
+ (T.thens
~start:(PrimitiveTactics.apply_tac
~term: (C.Const (HelmLibraryObjects.Logic.trans_eq_URI, [])))
~continuations:
- [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac]
+ [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
status
| _ -> raise (ProofEngineTypes.Fail "Transitivity failed")
+ in
+ ProofEngineTypes.mk_tactic (transitivity_tac ~term)
;;
projects / helm.git / blobdiff