* For details, see the HELM World-Wide-Web page,
* http://cs.unibo.it/helm/.
*)
-
-let rewrite_tac ~term:equality =
- let rewrite_tac ~term:equality (proof,goal) =
+
+let rec 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 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 ~subst:[] metasenv context C.Anonymous ~typ:ty,
- ty, 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,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)
+ 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 *)
+ let proof,goal = status in
+ let curi, metasenv, pbo, pty = proof in
+ let (metano,context,gty) as conjecture = CicUtil.lookup_meta goal metasenv in
+ match hyps_pat with
+ he::(_::_ as tl) ->
+ PET.apply_tactic
+ (Tacticals.then_
+ (rewrite_tac ~direction
+ ~pattern:(None,[he],Cic.Implicit None) equality)
+ (rewrite_tac ~direction ~pattern:(None,tl,concl_pat) equality)
+ ) status
+ | [_] as hyps_pat when concl_pat <> Cic.Implicit None ->
+ PET.apply_tactic
+ (Tacticals.then_
+ (rewrite_tac ~direction
+ ~pattern:(None,hyps_pat,Cic.Implicit None) equality)
+ (rewrite_tac ~direction ~pattern:(None,[],concl_pat) equality)
+ ) status
+ | _ ->
+ let arg,dir2,tac,concl_pat,gty =
+ match hyps_pat with
+ [] -> None,true,(fun ~term _ -> PT.exact_tac term),concl_pat,gty
+ | [name,pat] ->
+ let rec find_hyp n =
+ function
+ [] -> assert false
+ | Some (Cic.Name s,Cic.Decl ty)::_ when name = s ->
+ Cic.Rel n, CicSubstitution.lift n ty
+ | Some (Cic.Name s,Cic.Def _)::_ -> assert false (*CSC: not implemented yet! But does this make any sense?*)
+ | _::tl -> find_hyp (n+1) tl
in
- assert (List.length goals = 0) ;
- (proof',[fresh_meta])
+ let arg,gty = find_hyp 1 context in
+ let last_hyp_name_of_status (proof,goal) =
+ let curi, metasenv, pbo, pty = proof in
+ let metano,context,gty = CicUtil.lookup_meta goal metasenv in
+ match context with
+ (Some (Cic.Name s,_))::_ -> s
+ | _ -> assert false
+ in
+ let dummy = "dummy" in
+ Some arg,false,
+ (fun ~term typ ->
+ Tacticals.seq
+ ~tactics:
+ [ProofEngineStructuralRules.rename name dummy;
+ PT.letin_tac
+ ~mk_fresh_name_callback:(fun _ _ _ ~typ -> Cic.Name name) term;
+ ProofEngineStructuralRules.clearbody name;
+ ReductionTactics.change_tac
+ ~pattern:
+ (None,[name,Cic.Implicit (Some `Hole)],Cic.Implicit None)
+ (ProofEngineTypes.const_lazy_term typ);
+ ProofEngineStructuralRules.clear dummy
+ ]),
+ pat,gty
+ | _::_ -> assert false
+ in
+ let if_right_to_left do_not_change a b =
+ match direction with
+ | `RightToLeft -> if do_not_change then a else b
+ | `LeftToRight -> if do_not_change then b else a
+ 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
+ (* t1x is t2 if we are rewriting in an hypothesis *)
+ let eq_ind, ty, t1, t2, t1x =
+ 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 dir2
+ LibraryObjects.eq_ind_URI LibraryObjects.eq_ind_r_URI
+ in
+ let eq_ind = C.Const (ind_uri uri,[]) in
+ if dir2 then
+ if_right_to_left true (eq_ind,ty,t2,t1,t2) (eq_ind,ty,t1,t2,t1)
+ else
+ if_right_to_left true (eq_ind,ty,t1,t2,t2) (eq_ind,ty,t2,t1,t1)
+ | _ -> raise (PET.Fail (lazy "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 t1x 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 t1 = CicMetaSubst.apply_subst subst t1 in
+ let t2 = CicMetaSubst.apply_subst subst t2 in
+ let equality = CicMetaSubst.apply_subst subst equality 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 pred = C.Lambda (fresh_name, ty, abstr_gty) in
+ (* The argument is either a meta if we are rewriting in the conclusion
+ or the hypothesis if we are rewriting in an hypothesis *)
+ let metasenv',arg,newtyp =
+ match arg with
+ None ->
+ 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
+ metasenv', C.Meta (fresh_meta,irl), Cic.Rel (-1) (* dummy term, never used *)
+ | Some arg ->
+ let gty' = CicSubstitution.subst t1 abstr_gty in
+ metasenv,arg,gty'
+ in
+ let exact_proof =
+ C.Appl [eq_ind ; ty ; t2 ; pred ; arg ; t1 ;equality]
+ in
+ let (proof',goals) =
+ PET.apply_tactic
+ (tac ~term:exact_proof newtyp) ((curi,metasenv',pbo,pty),goal)
+ in
+ let goals =
+ goals@(ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
+ ~newmetasenv:metasenv')
+ in
+ (proof',goals)
in
- ProofEngineTypes.mk_tactic (rewrite_tac ~term:equality)
-;;
-
-
-let rewrite_simpl_tac ~term =
- let rewrite_simpl_tac ~term status =
+ 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 ~term)
+ ~start:(rewrite_tac ~direction ~pattern equality)
~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 =
- 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 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 ~subst:[] metasenv context C.Anonymous ~typ:ty,
- ty, 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,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 =
- 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))
+ (ReductionTactics.simpl_tac
+ ~pattern:(ProofEngineTypes.conclusion_pattern None)))
status
in
- ProofEngineTypes.mk_tactic (rewrite_back_simpl_tac ~term)
+ ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~direction ~pattern equality)
;;
-let replace_tac ~what ~with_what =
- let replace_tac ~what ~with_what 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,_ = CicUtil.lookup_meta 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
- ProofEngineTypes.apply_tactic
+ 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 (lazy "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
+ (lazy "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
+ (lazy "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 (HelmLibraryObjects.Logic.eq_URI, 0, [])) ;
- wty ;
+ ~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 ~what ~with_what)
+ ProofEngineTypes.mk_tactic (replace_tac ~pattern ~with_what)
;;
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) ->
+ when LibraryObjects.is_eq_URI uri ->
ProofEngineTypes.apply_tactic
(PrimitiveTactics.apply_tac
- ~term: (C.Const (HelmLibraryObjects.Logic.sym_eq_URI, [])))
+ ~term: (C.Const (LibraryObjects.sym_eq_URI uri, [])))
(proof,goal)
- | _ -> raise (ProofEngineTypes.Fail "Symmetry failed")
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Symmetry failed"))
in
ProofEngineTypes.mk_tactic symmetry_tac
;;
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) ->
+ when LibraryObjects.is_eq_URI uri ->
ProofEngineTypes.apply_tactic
(T.thens
~start:(PrimitiveTactics.apply_tac
- ~term: (C.Const (HelmLibraryObjects.Logic.trans_eq_URI, [])))
+ ~term: (C.Const (LibraryObjects.trans_eq_URI uri, [])))
~continuations:
[PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
status
- | _ -> raise (ProofEngineTypes.Fail "Transitivity failed")
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Transitivity failed"))
in
ProofEngineTypes.mk_tactic (transitivity_tac ~term)
;;
projects / helm.git / blobdiff