-exception TwoDifferentSubtermsFound of int
-
-(* 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 true_URI =
- match LibraryObjects.true_URI () with
- Some uri -> uri
- | None -> raise (ProofEngineTypes.Fail (lazy "You need to register the default \"true\" definition first. Please use the \"default\" command")) in
- let false_URI =
- match LibraryObjects.false_URI () with
- Some uri -> uri
- | None -> raise (ProofEngineTypes.Fail (lazy "You need to register the default \"false\" definition first. Please use the \"default\" command")) 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(false_URI,0,[]))
- else (C.MutInd(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 (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)
-
-(* DISCRIMINTATE SENZA INJECTION
-
-exception TwoDifferentSubtermsFound of (Cic.term * Cic.term * int)
-
-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,_ = 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])
- when (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"))
- or (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> (
- match tty with
- (C.MutInd (turi,typeno,exp_named_subst))
- | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
-
- let (t1',t2',consno2') = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *)
- try
- let rec traverse t1 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)))
- when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
- t1,t2,0
- | ((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
- [],[] -> t1,t2,0
- | 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 (t1,t2,consno2))
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
- in traverse t1 t2
- with (TwoDifferentSubtermsFound (t1,t2,consno2)) -> (t1,t2,consno2)
- in
-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 fst(CicEnvironment.get_obj turi
- CicUniv.empty_ugraph) with
- C.InductiveDefinition (ind_type_list,_,nr_ind_params) ->
-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
-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
-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 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 (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [])
- else (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/True.ind") 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 (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [] )
- status
- in
- (match goals' with
- [goal'] ->
- let _,metasenv',_,_ = proof' in
- let _,context',gty' =
- CicUtil.lookup_meta goal' metasenv'
- in
- 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:
- (
-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 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
-
-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)
- )
- (proof',goal')
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal")
- )
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
- )
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")