let debug_print = fun _ -> ()
-let rec injection_tac ~term ~liftno ~continuation =
+let rec injection_tac ~first_time ~term ~liftno ~continuation =
let injection_tac ~term status =
let (proof, goal) = status in
let module C = Cic in
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 LibraryObjects.is_eq_URI equri -> (
+ (match termty with
+ (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
+ when LibraryObjects.is_eq_URI equri ->
+ begin
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) ->
- (* raise (ProofEngineTypes.Fail "Injection: nothing to do") ; *) continuation ~liftno
- | ((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 i l1 l2 =
- match l1,l2 with
- [],[] -> continuation
- | hd1::tl1,hd2::tl2 ->
- if
- fst
- (CicReduction.are_convertible ~metasenv
- context hd1 hd2 CicUniv.empty_ugraph)
- then
- traverse_list (i+1) tl1 tl2
- else
- injection1_tac ~i ~term
- ~continuation:(traverse_list (i+1) tl1 tl2)
- | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???"))
- in traverse_list 1 applist1 applist2 ~liftno
- | ((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 (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality but a discriminable one"))
- | _ -> continuation ~liftno (*raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality"))*)
- )
- | _ -> continuation ~liftno (*raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality"))*)
- )
- | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equation"))
- ) status
+ | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
+ begin
+ 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)
+ ->
+ if first_time then
+ raise
+ (ProofEngineTypes.Fail (lazy "Injection: nothing to do"))
+ else
+ continuation ~liftno
+ | 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 i l1 l2 =
+ match l1,l2 with
+ [],[] ->
+ if first_time then
+ continuation
+ else
+ (match term with
+ C.Rel n ->
+ (match List.nth context (n-1) with
+ Some (C.Name id,_) ->
+ fun ~liftno ->
+ T.then_
+ ~start:
+ (ProofEngineStructuralRules.clear
+ ~hyps:[id])
+ ~continuation:(continuation ~liftno)
+ | _ -> assert false)
+ | _ -> assert false)
+ | hd1::tl1,hd2::tl2 ->
+ if
+ fst
+ (CicReduction.are_convertible ~metasenv
+ context hd1 hd2 CicUniv.empty_ugraph)
+ then
+ traverse_list (i+1) tl1 tl2
+ else
+ injection1_tac ~i ~term
+ ~continuation:(traverse_list (i+1) tl1 tl2)
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???"))
+ in
+ traverse_list 1 applist1 applist2 ~liftno
+ | ((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 (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality but a discriminable one"))
+ | _ ->
+ if first_time then
+ raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality"))
+ else
+ continuation ~liftno
+ end
+ | _ ->
+ if first_time then
+ raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality"))
+ else
+ continuation ~liftno
+ end
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equation"))
+ ) status
in
ProofEngineTypes.mk_tactic (injection_tac ~term)
in
ProofEngineTypes.apply_tactic
(T.thens
- ~start:(P.cut_tac (C.Appl [(C.MutInd (equri,0,[])) ; tty' ; t1' ; t2']))
- ~continuations:[
- T.then_
- ~start:(injection_tac ~liftno:0 ~term:(C.Rel 1)
- ~continuation:(fun ~liftno:x -> continuation ~liftno:(liftno + 1 + x)))
- ~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,outtype,C.Rel 1,patterns)) ;
- t1],
- m, u))
- status
- ))
- ~continuation:
- (T.then_
- ~start:
- (EqualityTactics.rewrite_simpl_tac
- ~direction:`LeftToRight
- ~pattern:(ProofEngineTypes.conclusion_pattern None)
- term)
- ~continuation:EqualityTactics.reflexivity_tac
- )
+ ~start:
+ (P.cut_tac
+ (C.Appl [C.MutInd (equri,0,[]) ; tty' ; t1' ; t2']))
+ ~continuations:
+ [ injection_tac ~first_time:false ~liftno:0
+ ~term:(C.Rel 1)
+ (* here I need to lift all the continuations by 1;
+ since I am setting back liftno to 0, I actually
+ need to lift all the continuations by liftno + 1 *)
+ ~continuation:
+ (fun ~liftno:x ->
+ continuation ~liftno:(liftno + 1 + x)) ;
+ 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,outtype,C.Rel 1,patterns)) ;
+ 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 "Injection: not an equality over elements of an inductive type"))
;;
let injection_tac =
- injection_tac ~liftno:0 ~continuation:(fun ~liftno -> Tacticals.id_tac)
+ injection_tac ~first_time:true ~liftno:0 ~continuation:(fun ~liftno -> Tacticals.id_tac)
;;
exception TwoDifferentSubtermsFound of int