* For details, see the HELM World-Wide-Web page,
* 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_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_tac ~direction ~pattern equality =
+ let rewrite_tac ~direction ~pattern:(wanted,hyps_pat,concl_pat) equality status
+ =
+ let module C = Cic in
+ let module U = UriManager in
+ let module PET = ProofEngineTypes in
+ let module PER = ProofEngineReduction in
+ let module PEH = ProofEngineHelpers in
+ let module PT = PrimitiveTactics in
+ assert (wanted = None); (* this should be checked syntactically *)
+ assert (hyps_pat = []); (*CSC: not implemented yet! *)
+ let proof,goal = status in
+ let if_right_to_left a b =
+ match direction with
+ | `RightToLeft -> a
+ | `LeftToRight -> b
+ in
+ let curi, metasenv, pbo, pty = proof in
+ let (metano,context,gty) as conjecture = CicUtil.lookup_meta goal metasenv in
+ let ty_eq,ugraph =
+ CicTypeChecker.type_of_aux' metasenv context equality
+ CicUniv.empty_ugraph in
+ let (ty_eq,metasenv',arguments,fresh_meta) =
+ ProofEngineHelpers.saturate_term
+ (ProofEngineHelpers.new_meta_of_proof proof) metasenv context ty_eq 0 in
+ let equality =
+ if List.length arguments = 0 then
+ equality
+ else
+ C.Appl (equality :: arguments) in
+ let eq_ind, ty, t1, t2 =
+ match ty_eq with
+ | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2]
+ when LibraryObjects.is_eq_URI uri ->
+ let ind_uri =
+ if_right_to_left LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
+ in
+ let eq_ind = C.Const (ind_uri uri,[]) in
+ if_right_to_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 `LeftToRight *)
+ let fresh_name =
+ FreshNamesGenerator.mk_fresh_name
+ ~subst:[] metasenv' context C.Anonymous ~typ:ty in
+ let lifted_t1 = CicSubstitution.lift 1 t1 in
+ let lifted_gty = CicSubstitution.lift 1 gty in
+ let lifted_conjecture =
+ metano,(Some (fresh_name,Cic.Decl ty))::context,lifted_gty in
+ let lifted_pattern =
+ Some (fun _ m u -> lifted_t1, m, u),[],CicSubstitution.lift 1 concl_pat
+ in
+ let subst,metasenv',ugraph,_,selected_terms_with_context =
+ ProofEngineHelpers.select
+ ~metasenv:metasenv' ~ugraph ~conjecture:lifted_conjecture
+ ~pattern:lifted_pattern in
+ let metasenv' = CicMetaSubst.apply_subst_metasenv subst metasenv' in
+ let what,with_what =
+ (* Note: Rel 1 does not live in the context context_of_t *)
+ (* The replace_lifting_csc_0 function will take care of lifting it *)
+ (* to context_of_t *)
+ List.fold_right
+ (fun (context_of_t,t) (l1,l2) -> t::l1, Cic.Rel 1::l2)
+ selected_terms_with_context ([],[]) in
+ let abstr_gty =
+ ProofEngineReduction.replace_lifting_csc 0
+ ~equality:(==) ~what ~with_what:with_what ~where:lifted_gty in
+ let abstr_gty = CicMetaSubst.apply_subst subst abstr_gty in
+ let t1 = CicMetaSubst.apply_subst subst t1 in
+ let t2 = CicMetaSubst.apply_subst subst t2 in
+ let equality = CicMetaSubst.apply_subst subst equality in
+ let gty' = CicSubstitution.subst t2 abstr_gty in
+ let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
+ let metasenv' = (fresh_meta,context,gty')::metasenv' in
+ let pred = C.Lambda (fresh_name, ty, abstr_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) ;
+ let goals =
+ ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
+ ~newmetasenv:metasenv'
+ in
+ (proof',goals)
+ in
+ ProofEngineTypes.mk_tactic (rewrite_tac ~direction ~pattern equality)
+
+
+let rewrite_simpl_tac ~direction ~pattern equality =
+ let rewrite_simpl_tac ~direction ~pattern equality status =
+ ProofEngineTypes.apply_tactic
+ (Tacticals.then_
+ ~start:(rewrite_tac ~direction ~pattern equality)
+ ~continuation:
+ (ReductionTactics.simpl_tac
+ ~pattern:(ProofEngineTypes.conclusion_pattern None)))
+ status
+ in
+ ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality)
;;
-
-let replace_tac ~what ~with_what ~status:((proof, goal) as status) =
+let replace_tac ~pattern ~with_what =
+ let replace_tac ~pattern:(wanted,hyps_pat,concl_pat) ~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
- let equality =
- match CicTypeChecker.type_of_aux' metasenv context wty with
- C.Sort C.Set -> "cic:/Coq/Init/Logic/eq.ind"
- | C.Sort C.Type
- | C.Sort C.Prop -> "cic:/Coq/Init/Logic_Type/eqT.ind"
- | _ -> assert false
- in
- T.thens
- ~start:(
- P.cut_tac
- (C.Appl [
- (C.MutInd ((U.uri_of_string equality), 0, [])) ;
- wty ;
+ let uri,metasenv,pbo,pty = proof in
+ let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
+ assert (hyps_pat = []); (*CSC: not implemented yet *)
+ let context_len = List.length context in
+ let subst,metasenv,u,_,selected_terms_with_context =
+ ProofEngineHelpers.select ~metasenv ~ugraph:CicUniv.empty_ugraph
+ ~conjecture ~pattern in
+ let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
+ let with_what, metasenv, u = with_what context metasenv u in
+ let with_what = CicMetaSubst.apply_subst subst with_what in
+ let pbo = CicMetaSubst.apply_subst subst pbo in
+ let pty = CicMetaSubst.apply_subst subst pty in
+ let status = (uri,metasenv,pbo,pty),goal in
+ let ty_of_with_what,u =
+ CicTypeChecker.type_of_aux'
+ metasenv context with_what CicUniv.empty_ugraph in
+ let whats =
+ match selected_terms_with_context with
+ [] -> raise (ProofEngineTypes.Fail "Replace: no term selected")
+ | l ->
+ List.map
+ (fun (context_of_t,t) ->
+ let t_in_context =
+ try
+ let context_of_t_len = List.length context_of_t in
+ if context_of_t_len = context_len then t
+ else
+ (let t_in_context,subst,metasenv' =
+ CicMetaSubst.delift_rels [] metasenv
+ (context_of_t_len - context_len) t
+ in
+ assert (subst = []);
+ assert (metasenv = metasenv');
+ t_in_context)
+ with
+ CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
+ (*CSC: we could implement something stronger by completely changing
+ the semantics of the tactic *)
+ raise (ProofEngineTypes.Fail
+ "Replace: one of the selected terms is not closed") in
+ let ty_of_t_in_context,u = (* TASSI: FIXME *)
+ CicTypeChecker.type_of_aux' metasenv context t_in_context
+ CicUniv.empty_ugraph in
+ let b,u = CicReduction.are_convertible ~metasenv context
+ ty_of_with_what ty_of_t_in_context u in
+ if b then
+ let concl_pat_for_t = ProofEngineHelpers.pattern_of ~term:ty [t] in
+ let pattern_for_t = None,[],concl_pat_for_t in
+ t_in_context,pattern_for_t
+ else
+ raise
+ (ProofEngineTypes.Fail
+ "Replace: one of the selected terms and the term to be replaced with have not convertible types")
+ ) l in
+ let rec aux n whats status =
+ match whats with
+ [] -> ProofEngineTypes.apply_tactic T.id_tac status
+ | (what,pattern)::tl ->
+ let what = CicSubstitution.lift n what in
+ let with_what = CicSubstitution.lift n with_what in
+ let ty_of_with_what = CicSubstitution.lift n ty_of_with_what in
+ ProofEngineTypes.apply_tactic
+ (T.thens
+ ~start:(
+ P.cut_tac
+ (C.Appl [
+ (C.MutInd (LibraryObjects.eq_URI (), 0, [])) ;
+ ty_of_with_what ;
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")
+ ~continuations:[
+ T.then_
+ ~start:(
+ rewrite_tac ~direction:`LeftToRight ~pattern (C.Rel 1))
+ ~continuation:(
+ T.then_
+ ~start:(
+ ProofEngineTypes.mk_tactic
+ (function ((proof,goal) as status) ->
+ let _,metasenv,_,_ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let hyp =
+ try
+ match List.hd context with
+ Some (Cic.Name name,_) -> name
+ | _ -> assert false
+ with (Failure "hd") -> assert false
+ in
+ ProofEngineTypes.apply_tactic
+ (ProofEngineStructuralRules.clear ~hyp) status))
+ ~continuation:(aux_tac (n + 1) tl));
+ T.id_tac])
+ status
+ and aux_tac n tl = ProofEngineTypes.mk_tactic (aux n tl) in
+ aux 0 whats status
+ in
+ ProofEngineTypes.mk_tactic (replace_tac ~pattern ~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 LibraryObjects.is_eq_URI uri ->
+ ProofEngineTypes.apply_tactic
+ (PrimitiveTactics.apply_tac
+ ~term: (C.Const (LibraryObjects.sym_eq_URI 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 LibraryObjects.is_eq_URI 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 (LibraryObjects.trans_eq_URI 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)
;;