module Ast = NotationPt
open NTactics
+open NTacStatus
-let assume name ty =
- exact_tac ("",0,(Ast.Binder (`Lambda,(Ast.Ident (name,None),Some ty),Ast.Implicit `JustOne)))
+type just = [ `Term of NTacStatus.tactic_term | `Auto of NnAuto.auto_params ]
+
+let mk_just =
+ function
+ `Auto (l,params) -> distribute_tac (fun status goal -> NnAuto.auto_lowtac
+ ~params:(l,params) status goal)
+ | `Term t -> apply_tac t
+
+exception NotAProduct
+exception FirstTypeWrong
+exception NotEquivalentTypes
+
+let extract_conclusion_type status goal =
+ let gty = get_goalty status goal in
+ let ctx = ctx_of gty in
+ let status,gty = term_of_cic_term status gty ctx in
+ gty
+;;
+
+let same_type_as_conclusion ty t status goal =
+ let gty = get_goalty status goal in
+ let ctx = ctx_of gty in
+ let status,cicterm = disambiguate status ctx ty `XTNone (*(`XTSome (mk_cic_term ctx t))*) in
+ let (_,_,metasenv,subst,_) = status#obj in
+ let status,ty = term_of_cic_term status cicterm ctx in
+ if NCicReduction.alpha_eq status metasenv subst ctx t ty then
+ true
+ else
+ false
+;;
+
+let are_convertible ty1 ty2 status goal =
+ let gty = get_goalty status goal in
+ let ctx = ctx_of gty in
+ let status,cicterm1 = disambiguate status ctx ty1 `XTNone (*(`XTSome (mk_cic_term ctx t))*) in
+ let status,cicterm2 = disambiguate status ctx ty2 `XTNone (*(`XTSome (mk_cic_term ctx t))*) in
+ NTacStatus.are_convertible status ctx cicterm1 cicterm2
+
+(* LCF-like tactic that checks whether the conclusion of the sequent of the given goal is a product, checks that
+the type of the conclusion's bound variable is the same as t1 and then uses an exact_tac with
+\lambda id: t1. ?. If a t2 is given it checks that t1 ~_{\beta} t2 and uses and exact_tac with \lambda id: t2. ?
+*)
+let lambda_abstract_tac id t1 t2 status goal =
+ match extract_conclusion_type status goal with
+ | NCic.Prod (_,t,_) ->
+ if same_type_as_conclusion t1 t status goal then
+ match t2 with
+ | None ->
+ let (_,_,t1) = t1 in
+ exec (exact_tac ("",0,(Ast.Binder (`Lambda,(Ast.Ident (id,None),Some t1),Ast.Implicit
+ `JustOne)))) status goal
+
+ | Some t2 ->
+ let status,res = are_convertible t1 t2 status goal in
+ if res then
+ let (_,_,t2) = t2 in
+ exec (exact_tac ("",0,(Ast.Binder (`Lambda,(Ast.Ident (id,None),Some t2),Ast.Implicit
+ `JustOne)))) status goal
+ else
+ raise NotEquivalentTypes
+ else
+ raise FirstTypeWrong
+ | _ -> raise NotAProduct
+
+let assume name ty eqty =
+ distribute_tac (fun status goal ->
+ try lambda_abstract_tac name ty eqty status goal
+ with
+ | NotAProduct -> fail (lazy "You can't assume without an universal quantification")
+ | FirstTypeWrong -> fail (lazy "The assumed type is wrong")
+ | NotEquivalentTypes -> fail (lazy "The two given types are not equivalent")
+ )
+;;
+
+let suppose t1 id t2 =
+ distribute_tac (fun status goal ->
+ try lambda_abstract_tac id t1 t2 status goal
+ with
+ | NotAProduct -> fail (lazy "You can't suppose without a logical implication")
+ | FirstTypeWrong -> fail (lazy "The supposed proposition is different from the premise")
+ | NotEquivalentTypes -> fail (lazy "The two given propositions are not equivalent")
+ )
+;;
+
+let assert_tac t1 t2 status goal continuation =
+ let t = extract_conclusion_type status goal in
+ if same_type_as_conclusion t1 t status goal then
+ match t2 with
+ | None -> exec continuation status goal
+ | Some t2 ->
+ let status,res = are_convertible t1 t2 status goal in
+ if res then
+ exec continuation status goal
+ else
+ raise NotEquivalentTypes
+ else
+ raise FirstTypeWrong
+
+let we_need_to_prove t id t1 =
+ distribute_tac (fun status goal ->
+ match id with
+ | None ->
+ (
+ match t1 with
+ | None -> (* We need to prove t *)
+ (
+ try
+ assert_tac t None status goal id_tac
+ with
+ | FirstTypeWrong -> fail (lazy "The given proposition is not the same as the conclusion")
+ )
+ | Some t1 -> (* We need to prove t or equivalently t1 *)
+ (
+ try
+ assert_tac t (Some t1) status goal (change_tac ~where:("",0,(None,[],Some Ast.UserInput)) ~with_what:t1)
+ with
+ | FirstTypeWrong -> fail (lazy "The given proposition is not the same as the conclusion")
+ | NotEquivalentTypes -> fail (lazy "The given propositions are not equivalent")
+ )
+ )
+ | Some id ->
+ (
+ match t1 with
+ | None -> (* We need to prove t (id) *)
+ exec (block_tac [cut_tac t; branch_tac ~force:false; shift_tac; intro_tac id;
+ (*merge_tac*)]) status goal
+ | Some t1 -> (* We need to prove t (id) or equivalently t1 *)
+ exec (block_tac [cut_tac t; branch_tac ~force:false; change_tac ~where:("",0,(None,[],Some Ast.UserInput))
+ ~with_what:t1; shift_tac; intro_tac id; merge_tac]) status goal
+ )
+ )
+;;
+
+let by_just_we_proved just ty id ty' =
+ distribute_tac (fun status goal ->
+ let just = mk_just just in
+ match id with
+ | None ->
+ (match ty' with
+ | None -> (* just we proved P done *)
+ (
+ try
+ assert_tac ty None status goal just
+ with
+ | FirstTypeWrong -> fail (lazy "The given proposition is not the same as the conclusion")
+ | NotEquivalentTypes -> fail (lazy "The given propositions are not equivalent")
+ )
+ | Some ty' -> (* just we proved P that is equivalent to P' done *)
+ (
+ try
+ assert_tac ty' (Some ty) status goal (block_tac [change_tac
+ ~where:("",0,(None,[],Some Ast.UserInput)) ~with_what:ty; just])
+ with
+ | FirstTypeWrong -> fail (lazy "The second proposition is not the same as the conclusion")
+ | NotEquivalentTypes -> fail (lazy "The given propositions are not equivalent")
+ )
+ )
+ | Some id ->
+ (
+ match ty' with
+ | None -> exec (block_tac [cut_tac ty; branch_tac; just; shift_tac; intro_tac
+ id; merge_tac ]) status goal
+ | Some ty' -> exec (block_tac [cut_tac ty; branch_tac; just; shift_tac; intro_tac
+ id; change_tac ~where:("",0,(None,[id,Ast.UserInput],None))
+ ~with_what:ty'; merge_tac]) status goal
+ )
+ )
+;;
+
+let thesisbecomes t1 t2 = we_need_to_prove t1 None t2 ;;
+
+let bydone just =
+ mk_just just
+;;
+
+let existselim just id1 t1 t2 id2 =
+ let (_,_,t1) = t1 in
+ let (_,_,t2) = t2 in
+ let just = mk_just just in
+ block_tac [
+ cut_tac ("",0,(Ast.Appl [Ast.Ident ("ex",None); t1; Ast.Binder (`Lambda,(Ast.Ident
+ (id1,None), Some t1),t2)]));
+ branch_tac ~force:false;
+ just;
+ shift_tac;
+ case1_tac "_";
+ intros_tac ~names_ref:(ref []) [id1;id2];
+ merge_tac
+ ]
+
+let andelim just t1 id1 t2 id2 =
+ let (_,_,t1) = t1 in
+ let (_,_,t2) = t2 in
+ let just = mk_just just in
+ block_tac [
+ cut_tac ("",0,(Ast.Appl [Ast.Ident ("And",None); t1 ; t2]));
+ branch_tac ~force:false;
+ just;
+ shift_tac;
+ case1_tac "_";
+ intros_tac ~names_ref:(ref []) [id1;id2];
+ merge_tac
+ ]
+;;
+
+
+
+let rewritingstep lhs rhs just last_step = fail (lazy "Not implemented");
+ (*
+ let aux ((proof,goal) as status) =
+ let (curi,metasenv,_subst,proofbo,proofty, attrs) = proof in
+ let _,context,gty = CicUtil.lookup_meta goal metasenv in
+ let eq,trans =
+ match LibraryObjects.eq_URI () with
+ None -> raise (ProofEngineTypes.Fail (lazy "You need to register the default equality first. Please use the \"default\" command"))
+ | Some uri ->
+ Cic.MutInd (uri,0,[]), Cic.Const (LibraryObjects.trans_eq_URI ~eq:uri,[])
+ in
+ let ty,_ =
+ CicTypeChecker.type_of_aux' metasenv context rhs CicUniv.oblivion_ugraph in
+ let just' =
+ match just with
+ `Auto (univ, params) ->
+ let params =
+ if not (List.exists (fun (k,_) -> k = "timeout") params) then
+ ("timeout","3")::params
+ else params
+ in
+ let params' =
+ if not (List.exists (fun (k,_) -> k = "paramodulation") params) then
+ ("paramodulation","1")::params
+ else params
+ in
+ if params = params' then
+ Tactics.auto ~dbd ~params:(univ, params) ~automation_cache
+ else
+ Tacticals.first
+ [Tactics.auto ~dbd ~params:(univ, params) ~automation_cache ;
+ Tactics.auto ~dbd ~params:(univ, params') ~automation_cache]
+ | `Term just -> Tactics.apply just
+ | `SolveWith term ->
+ Tactics.demodulate ~automation_cache ~dbd
+ ~params:(Some [term],
+ ["all","1";"steps","1"; "use_context","false"])
+ | `Proof ->
+ Tacticals.id_tac
+ in
+ let plhs,prhs,prepare =
+ match lhs with
+ None ->
+ let plhs,prhs =
+ match gty with
+ Cic.Appl [_;_;plhs;prhs] -> plhs,prhs
+ | _ -> assert false
+ in
+ plhs,prhs,
+ (fun continuation ->
+ ProofEngineTypes.apply_tactic continuation status)
+ | Some (None,lhs) ->
+ let plhs,prhs =
+ match gty with
+ Cic.Appl [_;_;plhs;prhs] -> plhs,prhs
+ | _ -> assert false
+ in
+ (*CSC: manca check plhs convertibile con lhs *)
+ plhs,prhs,
+ (fun continuation ->
+ ProofEngineTypes.apply_tactic continuation status)
+ | Some (Some name,lhs) ->
+ let newmeta = CicMkImplicit.new_meta metasenv [] in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context in
+ let plhs = lhs in
+ let prhs = Cic.Meta(newmeta,irl) in
+ plhs,prhs,
+ (fun continuation ->
+ let metasenv = (newmeta, context, ty)::metasenv in
+ let mk_fresh_name_callback =
+ fun metasenv context _ ~typ ->
+ FreshNamesGenerator.mk_fresh_name ~subst:[] metasenv context
+ (Cic.Name name) ~typ
+ in
+ let proof = curi,metasenv,_subst,proofbo,proofty, attrs in
+ let proof,goals =
+ ProofEngineTypes.apply_tactic
+ (Tacticals.thens
+ ~start:(Tactics.cut ~mk_fresh_name_callback
+ (Cic.Appl [eq ; ty ; lhs ; prhs]))
+ ~continuations:[Tacticals.id_tac ; continuation]) (proof,goal)
+ in
+ let goals =
+ match just,goals with
+ `Proof, [g1;g2;g3] -> [g2;g3;newmeta;g1]
+ | _, [g1;g2] -> [g2;newmeta;g1]
+ | _, l ->
+ prerr_endline (String.concat "," (List.map string_of_int l));
+ prerr_endline (CicMetaSubst.ppmetasenv [] metasenv);
+ assert false
+ in
+ proof,goals)
+ in
+ let continuation =
+ if last_step then
+ (*CSC:manca controllo sul fatto che rhs sia convertibile con prhs*)
+ just'
+ else
+ Tacticals.thens
+ ~start:(Tactics.apply ~term:(Cic.Appl [trans;ty;plhs;rhs;prhs]))
+ ~continuations:[just' ; Tacticals.id_tac]
+ in
+ prepare continuation
+ in
+ ProofEngineTypes.mk_tactic aux
+;;
+ *)
projects / helm.git / blobdiff