* http://cs.unibo.it/helm/.
*)
-
-let rewrite_tac ~term:equality ~status:(proof,goal) =
- let module C = Cic in
- let module U = UriManager in
- let curi,metasenv,pbo,pty = proof in
- let metano,context,gty = List.find (function (m,_,_) -> m=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 (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind") ->
- let eq_ind_r =
- C.Const
- (U.uri_of_string "cic:/Coq/Init/Logic/eq_ind_r.con",[])
- in
- eq_ind_r,ty,t1,t2
- | C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
- when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") ->
- let eqT_ind_r =
- C.Const
- (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind_r.con",[])
- in
- eqT_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
- (ProofEngineHelpers.mk_fresh_name context C.Anonymous ty, ty, gty'')
- in
- let fresh_meta = ProofEngineHelpers.new_meta proof in
- let irl =
- ProofEngineHelpers.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])
- ~status:((curi,metasenv',pbo,pty),goal)
- in
- assert (List.length goals = 0) ;
- (proof',[fresh_meta])
-;;
-
-
-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_back_tac ~term:equality ~status:(proof,goal) =
- let module C = Cic in
- let module U = UriManager in
- let curi,metasenv,pbo,pty = proof in
- let metano,context,gty = List.find (function (m,_,_) -> m=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 (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind") ->
- let eq_ind_r =
- C.Const
- (U.uri_of_string "cic:/Coq/Init/Logic/eq_ind.con",[])
- in
- eq_ind_r,ty,t2,t1
- | C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
- when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") ->
- let eqT_ind_r =
- C.Const
- (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind.con",[])
- in
- eqT_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
- (ProofEngineHelpers.mk_fresh_name context C.Anonymous ty, ty, gty'')
- in
- let fresh_meta = ProofEngineHelpers.new_meta proof in
- let irl =
- ProofEngineHelpers.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])
- ~status:((curi,metasenv',pbo,pty),goal)
- in
- assert (List.length goals = 0) ;
- (proof',[fresh_meta])
-
+let rewrite ~term:equality ?(direction=`Left) (proof,goal) =
+ let module C = Cic in
+ let module U = UriManager in
+ let module PET = ProofEngineTypes in
+ let module PT = PrimitiveTactics in
+ let module HLO = HelmLibraryObjects in
+ let if_left a b =
+ match direction with
+ | `Right -> b
+ | `Left -> a
+ in
+ let curi, metasenv, pbo, pty = proof in
+ let metano, context, gty = CicUtil.lookup_meta goal metasenv in
+ let eq_uri = HLO.Logic.eq_URI in
+ let ty_eq,_ =
+ CicTypeChecker.type_of_aux' metasenv context equality
+ CicUniv.empty_ugraph
+ in
+ let eq_ind, ty, t1, t2 =
+ match ty_eq with
+ | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2] when U.eq uri eq_uri ->
+ let eq_ind =
+ C.Const (if_left HLO.Logic.eq_ind_URI HLO.Logic.eq_ind_r_URI,[])
+ in
+ if_left (eq_ind, ty, t2, t1) (eq_ind, ty, t1, t2)
+ | _ -> raise (PET.Fail "Rewrite: argument is not a proof of an equality")
+ in
+ (* now we always do as if direction was `Left *)
+ 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
+ let gty_red = CicSubstitution.subst t2 gty'' 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,gty_red)::metasenv in
+ let fresh_name =
+ FreshNamesGenerator.mk_fresh_name
+ ~subst:[] metasenv context C.Anonymous ~typ:ty
+ in
+ let pred = C.Lambda (fresh_name, ty, gty'') in
+ let exact_proof =
+ C.Appl [eq_ind ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality]
+ in
+ let (proof',goals) =
+ PET.apply_tactic
+ (PT.exact_tac ~term:exact_proof) ((curi,metasenv',pbo,pty),goal)
+ in
+ assert (List.length goals = 0) ;
+ (proof',[fresh_meta])
+
+
+let rewrite_tac ~term =
+ let rewrite_tac ~term status =
+ rewrite ~term ~direction:`Right status
+ in
+ ProofEngineTypes.mk_tactic (rewrite_tac ~term)
+
+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_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_tac ~term =
+ let rewrite_back_tac ~term status =
+ rewrite ~term ~direction:`Left status
+ in
+ ProofEngineTypes.mk_tactic (rewrite_back_tac ~term)
+
+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:((proof, goal) as 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
let module P = PrimitiveTactics in
let module T = Tacticals in
- let _,metasenv,_,_ = proof in
- let _,context,_ = List.find (function (m,_,_) -> m=goal) metasenv in
- let wty = CicTypeChecker.type_of_aux' metasenv context what in
- try
- if (wty = (CicTypeChecker.type_of_aux' metasenv context with_what))
- then T.thens
- ~start:(
- P.cut_tac
- (C.Appl [
- (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"), 0, [])) ; (* quale uguaglianza usare, eq o eqT ? *)
- wty ;
- what ;
- with_what]))
- ~continuations:[
- T.then_
- ~start:(rewrite_simpl_tac ~term:(C.Rel 1))
- ~continuation:(
- ProofEngineStructuralRules.clear
- ~hyp:(List.hd context)) ;
- T.id_tac]
- ~status
- else raise (ProofEngineTypes.Fail "Replace: terms not replaceable")
- with (Failure "hd") -> raise (ProofEngineTypes.Fail "Replace: empty context")
+ let _,metasenv,_,_ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let wty,u = (* TASSI: FIXME *)
+ CicTypeChecker.type_of_aux' metasenv context what CicUniv.empty_ugraph in
+ let wwty,_ = CicTypeChecker.type_of_aux' metasenv context with_what u in
+ try
+ if (wty = wwty) then
+ ProofEngineTypes.apply_tactic
+ (T.thens
+ ~start:(
+ P.cut_tac
+ (C.Appl [
+ (C.MutInd (HelmLibraryObjects.Logic.eq_URI, 0, [])) ;
+ wty ;
+ what ;
+ with_what]))
+ ~continuations:[
+
+ T.then_ ~start:(rewrite_simpl_tac ~term:(C.Rel 1))
+ ~continuation:(
+ ProofEngineStructuralRules.clear
+ ~hyp:(List.hd context)) ;
+ T.id_tac])
+ status
+ else raise (ProofEngineTypes.Fail "Replace: terms not replaceable")
+ 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 ~status:(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 = List.find (function (m,_,_) -> m=goal) metasenv 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 (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
- PrimitiveTactics.apply_tac ~status:(proof,goal)
- ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic/sym_eq.con", []))
-
- | (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
- PrimitiveTactics.apply_tac ~status:(proof,goal)
- ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic_Type/sym_eqT.con", []))
+ (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:((proof, goal) as 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 module U = UriManager in
let module T = Tacticals in
let (_,metasenv,_,_) = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv 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 = (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
- T.thens
- ~start:(PrimitiveTactics.apply_tac
- ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic/trans_eq.con", [])))
- ~continuations:
- [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac]
- ~status
-
- | (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
- 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 (U.uri_of_string "cic:/Coq/Init/Logic_Type/trans_eqT.con", [])))
+ ~term: (C.Const (HelmLibraryObjects.Logic.trans_eq_URI, [])))
~continuations:
- [T.id_tac ; T.id_tac ; PrimitiveTactics.exact_tac ~term]
- ~status
+ [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
+ status
| _ -> raise (ProofEngineTypes.Fail "Transitivity failed")
+ in
+ ProofEngineTypes.mk_tactic (transitivity_tac ~term)
;;
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