* http://cs.unibo.it/helm/.
*)
-open HelmLibraryObjects
+let debug_print = fun _ -> ()
-let rec injection_tac ~term ~status:((proof, goal) as status) =
+let rec injection_tac ~term =
+ let injection_tac ~term 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 termty = (CicTypeChecker.type_of_aux' metasenv context term) in
+ let _,metasenv,_,_ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let termty,_ = (* TASSI: FIXME *)
+ CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ ProofEngineTypes.apply_tactic
(match termty with
(C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
- when (U.eq equri Logic.eq_URI)
- or (U.eq equri Logic_Type.eqt_URI) -> (
+ when LibraryObjects.is_eq_URI equri -> (
match tty with
(C.MutInd (turi,typeno,exp_named_subst))
| (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) -> (
match t1,t2 with
((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
(C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
- when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
+ when (uri1 = uri2) && (typeno1 = typeno2) &&
+ (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
(* raise (ProofEngineTypes.Fail "Injection: nothing to do") ; *) T.id_tac
| ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
(C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
T.then_
~start:(injection1_tac ~i ~term)
~continuation:(traverse_list (i+1) tl1 tl2)
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???") ; T.id_tac
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???")) ; T.id_tac
in traverse_list 1 applist1 applist2
| ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
(C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
(* raise (ProofEngineTypes.Fail "Injection: not a projectable equality but a discriminable one") ; *) T.id_tac
| _ -> (* raise (ProofEngineTypes.Fail "Injection: not a projectable equality") ; *) T.id_tac
)
- | _ -> raise (ProofEngineTypes.Fail "Injection: not a projectable equality")
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality"))
)
- | _ -> raise (ProofEngineTypes.Fail "Injection: not an equation")
- ) ~status
-
-
-and injection1_tac ~term ~i ~status:((proof, goal) as status) =
-(* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma differiscono (o potrebbero differire?) nell'i-esimo parametro del costruttore *)
- let module C = Cic in
- let module S = CicSubstitution in
- let module U = UriManager in
- let module P = PrimitiveTactics in
- let module T = Tacticals in
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equation"))
+ ) status
+ in
+ ProofEngineTypes.mk_tactic (injection_tac ~term)
+
+and injection1_tac ~term ~i =
+ let injection1_tac ~term ~i status =
+ let (proof, goal) = status in
+ (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma differiscono (o potrebbero differire?) nell'i-esimo parametro del costruttore *)
+ let module C = Cic in
+ let module S = CicSubstitution 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 termty = (CicTypeChecker.type_of_aux' metasenv context term) in
- match termty with (* an equality *)
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let termty,_ = (* TASSI: FIXME *)
+ CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ match termty with (* an equality *)
(C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
- when (U.eq equri Logic.eq_URI) or
- (U.eq equri Logic_Type.eqt_URI) -> (
- match tty with (* some inductive type *)
- (C.MutInd (turi,typeno,exp_named_subst))
- | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
-prerr_endline ("XXXX term " ^ CicPp.ppterm term) ;
-prerr_endline ("XXXX termty " ^ CicPp.ppterm termty) ;
-prerr_endline ("XXXX t1 " ^ CicPp.ppterm t1) ;
-prerr_endline ("XXXX t2 " ^ CicPp.ppterm t2) ;
-prerr_endline ("XXXX tty " ^ CicPp.ppterm tty) ;
- let t1',t2',consno = (* sono i due sottotermini che differiscono *)
- match t1,t2 with
- ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
- (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
- when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) -> (* controllo ridondante *)
- (List.nth applist1 (i-1)),(List.nth applist2 (i-1)),consno2
- | _ -> raise (ProofEngineTypes.Fail "Injection: qui non dovrei capitarci mai")
- in
- let tty' = (CicTypeChecker.type_of_aux' metasenv context t1') in
-prerr_endline ("XXXX tty' " ^ CicPp.ppterm tty') ;
-prerr_endline ("XXXX t1' " ^ CicPp.ppterm t1') ;
-prerr_endline ("XXXX t2' " ^ CicPp.ppterm t2') ;
-prerr_endline ("XXXX consno " ^ string_of_int consno) ;
- let pattern =
- match (CicEnvironment.get_obj turi) with
- C.InductiveDefinition (ind_type_list,_,nr_ind_params_dx) ->
- let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
- let i_constr_id,_ = List.nth constructor_list (consno - 1) in
- List.map
- (function (id,cty) ->
- let reduced_cty = CicReduction.whd context cty in
- let rec aux t k =
- match t with
- C.Prod (_,_,target) when (k <= nr_ind_params_dx) ->
- aux target (k+1)
- | C.Prod (binder,source,target) when (k > nr_ind_params_dx) ->
- let binder' =
- match binder with
- C.Name b -> C.Name b
- | C.Anonymous -> C.Name "y"
- in
- C.Lambda (binder',source,(aux target (k+1)))
- | _ ->
- let nr_param_constr = k - 1 - nr_ind_params_dx in
- if (id = i_constr_id)
- then C.Rel (nr_param_constr - i + 1)
- else S.lift (nr_param_constr + 1) t1' (* + 1 per liftare anche il lambda agguinto esternamente al case *)
- in aux reduced_cty 1
- )
- constructor_list
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible")
- in
-prerr_endline ("XXXX cominciamo!") ;
- T.thens
- ~start:(P.cut_tac (C.Appl [(C.MutInd (equri,0,[])) ; tty' ; t1' ; t2']))
- ~continuations:[
- T.then_
- ~start:(injection_tac ~term:(C.Rel 1))
- ~continuation:T.id_tac (* !!! qui devo anche fare clear di term tranne al primo passaggio *)
- ;
- T.then_
- ~start:
- (fun ~status:((proof,goal) as status) ->
- let _,metasenv,_,_ = proof in
- let _,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in
-prerr_endline ("XXXX goal " ^ string_of_int goal) ;
-prerr_endline ("XXXX gty " ^ CicPp.ppterm gty) ;
-prerr_endline ("XXXX old t1' " ^ CicPp.ppterm t1') ;
-prerr_endline ("XXXX change " ^ CicPp.ppterm (C.Appl [ C.Lambda (C.Name "x", tty, C.MutCase (turi, typeno, (C.Lambda ((C.Name "x"),(S.lift 1 tty),(S.lift 2 tty'))), (C.Rel 1), pattern)); t1])) ;
- let new_t1' =
- match gty with
- (C.Appl (C.MutInd (_,_,_)::arglist)) ->
- List.nth arglist 1
- | _ -> raise (ProofEngineTypes.Fail "Injection: goal after cut is not correct")
- in
-prerr_endline ("XXXX new t1' " ^ CicPp.ppterm new_t1') ;
- P.change_tac
- ~what:new_t1'
- ~with_what:
- (C.Appl [
- C.Lambda (
- C.Name "x", tty,
- C.MutCase (
- turi, typeno,
- (C.Lambda (
- (C.Name "x"),
- (S.lift 1 tty),
- (S.lift 2 tty'))),
- (C.Rel 1), pattern
- )
- );
- t1]
- )
- ~status
- )
- ~continuation:
- (T.then_
- ~start:(EqualityTactics.rewrite_simpl_tac ~term)
- ~continuation:EqualityTactics.reflexivity_tac
- )
- ]
- ~status
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
- )
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")
-;;
-
-
-
-exception TwoDifferentSubtermsFound of int
-
-(* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
-diversi *)
-
-let discriminate'_tac ~term ~status:((proof, goal) as status) =
- 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 termty = (CicTypeChecker.type_of_aux' metasenv context term) in
- match termty with
- (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
- when (U.eq equri Logic.eq_URI) or (U.eq equri Logic_Type.eqt_URI) -> (
- match tty with
+ when LibraryObjects.is_eq_URI equri -> (
+ match tty with (* some inductive type *)
(C.MutInd (turi,typeno,exp_named_subst))
| (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
-
- let consno2 = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *)
- try
- let rec traverse t1 t2 =
-prerr_endline ("XXXX t1 " ^ CicPp.ppterm t1) ;
-prerr_endline ("XXXX t2 " ^ CicPp.ppterm t2) ;
- match t1,t2 with
- ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
- (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
- when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
- 0
- | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
- (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
- when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
- let rec traverse_list l1 l2 =
- match l1,l2 with
- [],[] -> 0
- | hd1::tl1,hd2::tl2 -> traverse hd1 hd2; traverse_list tl1 tl2
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???")
- in traverse_list applist1 applist2
-
- | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
- (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
- | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
- (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
- | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
- (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
- | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
- (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
- when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
- raise (TwoDifferentSubtermsFound consno2)
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
- in traverse t1 t2
- with (TwoDifferentSubtermsFound consno2) -> consno2
+ let t1',t2',consno = (* sono i due sottotermini che differiscono *)
+ match t1,t2 with
+ ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
+ (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
+ when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) -> (* controllo ridondante *)
+ (List.nth applist1 (i-1)),(List.nth applist2 (i-1)),consno2
+ | _ -> assert false
+ in
+ let tty',_ =
+ CicTypeChecker.type_of_aux' metasenv context t1'
+ CicUniv.empty_ugraph in
+ let pattern =
+ match fst(CicEnvironment.get_obj
+ CicUniv.empty_ugraph turi ) with
+ C.InductiveDefinition (ind_type_list,_,nr_ind_params_dx,_) ->
+ let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
+ let i_constr_id,_ = List.nth constructor_list (consno - 1) in
+ List.map
+ (function (id,cty) ->
+ let reduced_cty = CicReduction.whd context cty in
+ let rec aux t k =
+ match t with
+ C.Prod (_,_,target) when (k <= nr_ind_params_dx) ->
+ aux target (k+1)
+ | C.Prod (binder,source,target) when (k > nr_ind_params_dx) ->
+ let binder' =
+ match binder with
+ C.Name b -> C.Name b
+ | C.Anonymous -> C.Name "y"
+ in
+ C.Lambda (binder',source,(aux target (k+1)))
+ | _ ->
+ let nr_param_constr = k - 1 - nr_ind_params_dx in
+ if (id = i_constr_id)
+ then C.Rel (nr_param_constr - i + 1)
+ else S.lift (nr_param_constr + 1) t1' (* + 1 per liftare anche il lambda agguinto esternamente al case *)
+ in aux reduced_cty 1
+ )
+ constructor_list
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible"))
in
-prerr_endline ("XXXX consno2 " ^ (string_of_int consno2)) ;
- if consno2 = 0
- then raise (ProofEngineTypes.Fail "Discriminate: Discriminating terms are structurally equal")
- else
-
- let pattern =
- (* a list of "True" except for the element in position consno2 which is "False" *)
- match (CicEnvironment.get_obj turi) with
- C.InductiveDefinition (ind_type_list,_,nr_ind_params) ->
-prerr_endline ("XXXX nth " ^ (string_of_int (List.length ind_type_list)) ^ " " ^ (string_of_int typeno)) ;
- let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
-prerr_endline ("XXXX nth " ^ (string_of_int (List.length constructor_list)) ^ " " ^ (string_of_int consno2)) ;
- let false_constr_id,_ = List.nth constructor_list (consno2 - 1) in
-prerr_endline ("XXXX nth funzionano ") ;
- List.map
- (function (id,cty) ->
- let red_ty = CicReduction.whd context cty in (* dubbio: e' corretto ridurre in questo context ??? *)
- let rec aux t k =
- match t with
- C.Prod (_,_,target) when (k <= nr_ind_params) ->
- aux target (k+1)
- | C.Prod (binder,source,target) when (k > nr_ind_params) ->
- C.Lambda (binder,source,(aux target (k+1)))
- | _ ->
- if (id = false_constr_id)
- then (C.MutInd(Logic.false_URI,0,[]))
- else (C.MutInd(Logic.true_URI,0,[]))
- in aux red_ty 1
- )
- constructor_list
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible")
- in
-
- let (proof',goals') =
- EliminationTactics.elim_type_tac
- ~term:(C.MutInd(Logic.false_URI,0,[]))
- ~status
- in
- (match goals' with
- [goal'] ->
- let _,metasenv',_,_ = proof' in
- let _,context',gty' = List.find (function (m,_,_) -> m=goal') metasenv' in
-prerr_endline ("XXXX gty " ^ CicPp.ppterm gty') ;
-prerr_endline ("XXXX tty " ^ CicPp.ppterm tty) ;
-prerr_endline ("XXXX t1 " ^ CicPp.ppterm t1) ;
-prerr_endline ("XXXX t2 " ^ CicPp.ppterm t2) ;
-ignore (List.map (fun t -> prerr_endline ("XXXX t " ^ CicPp.ppterm t)) pattern) ;
-prerr_endline ("XXXX case " ^ CicPp.ppterm (C.Appl [
- C.Lambda (
- C.Name "x", tty,
- C.MutCase (
- turi, typeno,
- (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))),
- (C.Rel 1), pattern
- )
- ); t2])) ;
- T.then_
- ~start:
- (P.change_tac
- ~what:gty'
- ~with_what:
- (C.Appl [
- C.Lambda (
- C.Name "x", tty,
- C.MutCase (
- turi, typeno,
- (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))),
- (C.Rel 1), pattern
- )
- );
- t2]
- )
- )
- ~continuation:
- (
-prerr_endline ("XXXX rewrite<-: " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1 ; t2])));
-prerr_endline ("XXXX rewrite<-: " ^ CicPp.ppterm (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1 ; t2])) ;
-prerr_endline ("XXXX equri: " ^ U.string_of_uri equri) ;
-prerr_endline ("XXXX tty : " ^ CicPp.ppterm tty) ;
-prerr_endline ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1)) ;
-prerr_endline ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2)) ;
-if (CicTypeChecker.type_of_aux' metasenv' context' t1) <> tty then prerr_endline ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1)) ;
-if (CicTypeChecker.type_of_aux' metasenv' context' t2) <> tty then prerr_endline ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2)) ;
-if (CicTypeChecker.type_of_aux' metasenv' context' t1) <> (CicTypeChecker.type_of_aux' metasenv' context' t2)
- then prerr_endline ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1)) ; prerr_endline ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2)) ;
-prerr_endline ("XXXX rewrite<- " ^ CicPp.ppterm term ^ " : " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' term));
- T.then_
- ~start:(EqualityTactics.rewrite_back_simpl_tac ~term)
- ~continuation:(IntroductionTactics.constructor_tac ~n:1)
- )
- ~status:(proof',goal')
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal")
- )
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
+ ProofEngineTypes.apply_tactic
+ (T.thens
+ ~start:(P.cut_tac (C.Appl [(C.MutInd (equri,0,[])) ; tty' ; t1' ; t2']))
+ ~continuations:[
+ T.then_
+ ~start:(injection_tac ~term:(C.Rel 1))
+ ~continuation:T.id_tac (* !!! qui devo anche fare clear di term tranne al primo passaggio *)
+ ;
+ T.then_
+ ~start:(ProofEngineTypes.mk_tactic
+ (fun status ->
+ let (proof, goal) = status in
+ let _,metasenv,_,_ = proof in
+ let _,context,gty = CicUtil.lookup_meta goal metasenv in
+ let new_t1' =
+ match gty with
+ (C.Appl (C.MutInd (_,_,_)::arglist)) ->
+ List.nth arglist 1
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: goal after cut is not correct"))
+ in
+ ProofEngineTypes.apply_tactic
+ (ReductionTactics.change_tac
+ ~pattern:(ProofEngineTypes.conclusion_pattern
+ (Some new_t1'))
+ (fun _ m u ->
+ C.Appl [ C.Lambda (C.Name "x", tty,
+ C.MutCase (turi, typeno,
+ (C.Lambda ((C.Name "x"),
+ (S.lift 1 tty),
+ (S.lift 2 tty'))),
+ (C.Rel 1), pattern
+ )
+ );
+ t1], m, u))
+ status
+ ))
+ ~continuation:
+ (T.then_
+ ~start:
+ (EqualityTactics.rewrite_simpl_tac
+ ~direction:`LeftToRight
+ ~pattern:(ProofEngineTypes.conclusion_pattern None)
+ term)
+ ~continuation:EqualityTactics.reflexivity_tac
+ )
+ ])
+ status
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: not a discriminable equality"))
)
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: not an equality"))
+ in
+ ProofEngineTypes.mk_tactic (injection1_tac ~term ~i)
;;
+exception TwoDifferentSubtermsFound of int
-let discriminate_tac ~term ~status =
- Tacticals.then_
- ~start:(* (injection_tac ~term) *) Tacticals.id_tac
- ~continuation:(discriminate'_tac ~term) (* NOOO!!! non term ma una (qualunque) delle nuove hyp introdotte da inject *)
- ~status
-;;
-
+(* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
+diversi *)
+let discriminate'_tac ~term =
+ let module C = Cic in
+ let module U = UriManager in
+ let module P = PrimitiveTactics in
+ let module T = Tacticals in
+ let fail msg = raise (ProofEngineTypes.Fail (lazy ("Discriminate: " ^ msg))) in
+ let find_discriminating_consno t1 t2 =
+ let rec aux t1 t2 =
+ match t1, t2 with
+ | C.MutConstruct _, C.MutConstruct _ when t1 = t2 -> None
+ | C.Appl ((C.MutConstruct _ as constr1) :: args1),
+ C.Appl ((C.MutConstruct _ as constr2) :: args2)
+ when constr1 = constr2 ->
+ let rec aux_list l1 l2 =
+ match l1, l2 with
+ | [], [] -> None
+ | hd1 :: tl1, hd2 :: tl2 ->
+ (match aux hd1 hd2 with
+ | None -> aux_list tl1 tl2
+ | Some _ as res -> res)
+ | _ -> (* same constructor applied to a different number of args *)
+ assert false
+ in
+ aux_list args1 args2
+ | ((C.MutConstruct (_,_,consno1,subst1)),
+ (C.MutConstruct (_,_,consno2,subst2)))
+ | ((C.MutConstruct (_,_,consno1,subst1)),
+ (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
+ | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
+ (C.MutConstruct (_,_,consno2,subst2)))
+ | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
+ (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
+ when (consno1 <> consno2) || (subst1 <> subst2) ->
+ Some consno2
+ | _ -> fail "not a discriminable equality"
+ in
+ aux t1 t2
+ in
+ let mk_pattern turi typeno consno context left_args =
+ (* a list of "True" except for the element in position consno which
+ * is "False" *)
+ match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with
+ | C.InductiveDefinition (ind_type_list,_,nr_ind_params,_) ->
+ let _,_,_,constructor_list = List.nth ind_type_list typeno in
+ let false_constr_id,_ = List.nth constructor_list (consno - 1) in
+ List.map
+ (fun (id,cty) ->
+ (* dubbio: e' corretto ridurre in questo context ??? *)
+ let red_ty = CicReduction.whd context cty in
+ let rec aux t k =
+ match t with
+ | C.Prod (_,_,target) when (k <= nr_ind_params) ->
+ CicSubstitution.subst (List.nth left_args (k-1))
+ (aux target (k+1))
+ | C.Prod (binder,source,target) when (k > nr_ind_params) ->
+ C.Lambda (binder, source, (aux target (k+1)))
+ | _ ->
+ if (id = false_constr_id)
+ then (C.MutInd(LibraryObjects.false_URI (),0,[]))
+ else (C.MutInd(LibraryObjects.true_URI (),0,[]))
+ in
+ (CicSubstitution.lift 1 (aux red_ty 1)))
+ constructor_list
+ | _ -> (* object is not an inductive definition *)
+ assert false
+ in
+ let discriminate'_tac ~term status =
+ let (proof, goal) = status in
+ let _,metasenv,_,_ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let termty,_ =
+ CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph
+ in
+ match termty with
+ | (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
+ when LibraryObjects.is_eq_URI equri ->
+ let turi,typeno,exp_named_subst,left_args =
+ match tty with
+ | (C.MutInd (turi,typeno,exp_named_subst)) ->
+ turi,typeno,exp_named_subst,[]
+ | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::left_args)) ->
+ turi,typeno,exp_named_subst,left_args
+ | _ -> fail "not a discriminable equality"
+ in
+ let consno =
+ match find_discriminating_consno t1 t2 with
+ | Some consno -> consno
+ | None -> fail "discriminating terms are structurally equal"
+ in
+ let pattern = mk_pattern turi typeno consno context left_args in
+ let (proof',goals') =
+ ProofEngineTypes.apply_tactic
+ (EliminationTactics.elim_type_tac
+ (C.MutInd (LibraryObjects.false_URI (), 0, [])))
+ status
+ in
+ (match goals' with
+ | [goal'] ->
+ let _,metasenv',_,_ = proof' in
+ let _,context',gty' = CicUtil.lookup_meta goal' metasenv' in
+ ProofEngineTypes.apply_tactic
+ (T.then_
+ ~start:
+ (ReductionTactics.change_tac
+ ~pattern:(ProofEngineTypes.conclusion_pattern (Some gty'))
+ (fun _ m u ->
+ C.Appl [
+ C.Lambda ( C.Name "x", tty,
+ C.MutCase (turi, typeno,
+ (C.Lambda ((C.Name "x"),
+ (CicSubstitution.lift 1 tty),
+ (C.Sort C.Prop))),
+ (C.Rel 1), pattern));
+ t2 ], m, u))
+ ~continuation:
+ (T.then_
+ ~start:
+ (EqualityTactics.rewrite_simpl_tac
+ ~direction:`RightToLeft
+ ~pattern:(ProofEngineTypes.conclusion_pattern None)
+ term)
+ ~continuation:
+ (IntroductionTactics.constructor_tac ~n:1)))
+ (proof',goal')
+ | [] -> fail "ElimType False left no goals"
+ | _ -> fail "ElimType False left more than one goal")
+ | _ -> fail "not an equality"
+ in
+ ProofEngineTypes.mk_tactic (discriminate'_tac ~term)
+
+let discriminate_tac ~term =
+ let discriminate_tac ~term status =
+ ProofEngineTypes.apply_tactic
+ (Tacticals.then_
+ ~start:(* (injection_tac ~term) *) Tacticals.id_tac
+ ~continuation:(discriminate'_tac ~term)) (* NOOO!!! non term ma una (qualunque) delle nuove hyp introdotte da inject *)
+ status
+ in
+ ProofEngineTypes.mk_tactic (discriminate_tac ~term)
let decide_equality_tac =
(* il goal e' un termine della forma t1=t2\/~t1=t2; la tattica decide se l'uguaglianza
e' vera o no e lo risolve *)
Tacticals.id_tac
-;;
-
-
-let compare_tac ~term ~status:((proof, goal) as status) = Tacticals.id_tac ~status
-(*
+let compare_tac ~term = Tacticals.id_tac
+ (*
(* term is in the form t1=t2; the tactic leaves two goals: in the first you have to *)
(* demonstrate the goal with the additional hyp that t1=t2, in the second the hyp is ~t1=t2 *)
let module C = Cic in
let module P = PrimitiveTactics in
let module T = Tacticals in
let _,metasenv,_,_ = proof in
- let _,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in
+ let _,context,gty = CicUtil.lookup_meta goal metasenv in
let termty = (CicTypeChecker.type_of_aux' metasenv context term) in
match termty with
(C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
~continuations:[
T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ;
decide_equality_tac]
- ~status
+ status
| (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
let term' = (* (t1=t2) \/ ~(t1=t2) *)
C.Appl [
~continuations:[
T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ;
decide_equality_tac]
- ~status
+ status
| _ -> raise (ProofEngineTypes.Fail "Compare: Not an equality")
*)
;;
exception TwoDifferentSubtermsFound of (Cic.term * Cic.term * int)
-let discriminate_tac ~term ~status:((proof, goal) as status) =
+let discriminate_tac ~term status =
let module C = Cic in
let module U = UriManager in
let module P = PrimitiveTactics in
let module T = Tacticals in
+ let (proof, goal) = status in
let _,metasenv,_,_ = proof in
- let _,context,_ = List.find (function (m,_,_) -> m=goal) metasenv in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
let termty = (CicTypeChecker.type_of_aux' metasenv context term) in
match termty with
(C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
let (t1',t2',consno2') = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *)
try
let rec traverse t1 t2 =
-prerr_endline ("XXXX t1 " ^ CicPp.ppterm t1) ;
-prerr_endline ("XXXX t2 " ^ CicPp.ppterm t2) ;
+debug_print (lazy ("XXXX t1 " ^ CicPp.ppterm t1)) ;
+debug_print (lazy ("XXXX t2 " ^ CicPp.ppterm t2)) ;
match t1,t2 with
((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
(C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
in traverse t1 t2
with (TwoDifferentSubtermsFound (t1,t2,consno2)) -> (t1,t2,consno2)
in
-prerr_endline ("XXXX consno2' " ^ (string_of_int consno2')) ;
+debug_print (lazy ("XXXX consno2' " ^ (string_of_int consno2'))) ;
if consno2' = 0
then raise (ProofEngineTypes.Fail "Discriminate: Discriminating terms are structurally equal")
else
let pattern =
(* a list of "True" except for the element in position consno2' which is "False" *)
- match (CicEnvironment.get_obj turi) with
+ match fst(CicEnvironment.get_obj turi
+ CicUniv.empty_ugraph) with
C.InductiveDefinition (ind_type_list,_,nr_ind_params) ->
-prerr_endline ("XXXX nth " ^ (string_of_int (List.length ind_type_list)) ^ " " ^ (string_of_int typeno)) ;
+debug_print (lazy ("XXXX nth " ^ (string_of_int (List.length ind_type_list)) ^ " " ^ (string_of_int typeno))) ;
let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
-prerr_endline ("XXXX nth " ^ (string_of_int (List.length constructor_list)) ^ " " ^ (string_of_int consno2')) ;
+debug_print (lazy ("XXXX nth " ^ (string_of_int (List.length constructor_list)) ^ " " ^ (string_of_int consno2'))) ;
let false_constr_id,_ = List.nth constructor_list (consno2' - 1) in
-prerr_endline ("XXXX nth funzionano ") ;
+debug_print (lazy "XXXX nth funzionano ") ;
List.map
(function (id,cty) ->
let red_ty = CicReduction.whd context cty in (* dubbio: e' corretto ridurre in questo context ??? *)
let (proof',goals') =
EliminationTactics.elim_type_tac
~term:(C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [] )
- ~status
+ status
in
(match goals' with
[goal'] ->
let _,metasenv',_,_ = proof' in
- let _,context',gty' = List.find (function (m,_,_) -> m=goal') metasenv' in
-prerr_endline ("XXXX gty " ^ CicPp.ppterm gty') ;
-prerr_endline ("XXXX tty " ^ CicPp.ppterm tty) ;
-prerr_endline ("XXXX t1' " ^ CicPp.ppterm t1') ;
-prerr_endline ("XXXX t2' " ^ CicPp.ppterm t2') ;
-ignore (List.map (fun t -> prerr_endline ("XXXX t " ^ CicPp.ppterm t)) pattern) ;
-prerr_endline ("XXXX case " ^ CicPp.ppterm (C.Appl [
- C.Lambda (
- C.Name "x", tty,
- C.MutCase (
- turi, typeno,
- (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))),
- (C.Rel 1), pattern
- )
- ); t2'])) ;
+ let _,context',gty' =
+ CicUtil.lookup_meta goal' metasenv'
+ in
T.then_
~start:
(P.change_tac
)
~continuation:
(
-prerr_endline ("XXXX rewrite<-: " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2'])));
-prerr_endline ("XXXX rewrite<-: " ^ CicPp.ppterm (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2'])) ;
-prerr_endline ("XXXX equri: " ^ U.string_of_uri equri) ;
-prerr_endline ("XXXX tty : " ^ CicPp.ppterm tty) ;
-prerr_endline ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1')) ;
-prerr_endline ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ;
-if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> tty then prerr_endline ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1')) ;
-if (CicTypeChecker.type_of_aux' metasenv' context' t2') <> tty then prerr_endline ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ;
+debug_print (lazy ("XXXX rewrite<-: " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2']))));
+debug_print (lazy ("XXXX rewrite<-: " ^ CicPp.ppterm (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2']))) ;
+debug_print (lazy ("XXXX equri: " ^ U.string_of_uri equri)) ;
+debug_print (lazy ("XXXX tty : " ^ CicPp.ppterm tty)) ;
+debug_print (lazy ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1'))) ;
+debug_print (lazy ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2'))) ;
+if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> tty then debug_print (lazy ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1'))) ;
+if (CicTypeChecker.type_of_aux' metasenv' context' t2') <> tty then debug_print (lazy ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2'))) ;
if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> (CicTypeChecker.type_of_aux' metasenv' context' t2')
- then prerr_endline ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1')) ; prerr_endline ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ;
+ then debug_print (lazy ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux'
+ metasenv' context' t1'))) ; debug_print (lazy ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2'))) ;
let termty' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t1 ~with_what:t1' ~where:termty in
let termty'' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t2 ~with_what:t2' ~where:termty' in
-prerr_endline ("XXXX rewrite<- " ^ CicPp.ppterm term ^ " : " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' term));
+debug_print (lazy ("XXXX rewrite<- " ^ CicPp.ppterm term ^ " : " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' term)));
T.then_
~start:(EqualityTactics.rewrite_back_simpl_tac ~term:term)
~continuation:(IntroductionTactics.constructor_tac ~n:1)
)
- ~status:(proof',goal')
+ (proof',goal')
| _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal")
)
| _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
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