-
-(* 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_branches_and_outtype turi typeno consno context 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,_,paramsno,_) ->
- let _,_,rty,constructor_list = List.nth ind_type_list typeno in
- let false_constr_id,_ = List.nth constructor_list (consno - 1) in
- let branches =
- 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 <= paramsno) ->
- CicSubstitution.subst (List.nth args (k-1))
- (aux target (k+1))
- | C.Prod (binder,source,target) when (k > paramsno) ->
- 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 in
- let outtype =
- let seed = ref 0 in
- let rec mk_lambdas rev_left_args =
- function
- 0, args, C.Prod (_,so,ta) ->
- C.Lambda
- (C.Name (incr seed; "x" ^ string_of_int !seed),
- so,
- mk_lambdas rev_left_args (0,args,ta))
- | 0, args, C.Sort _ ->
- let rec mk_rels =
- function
- 0 -> []
- | n -> C.Rel n :: mk_rels (n - 1) in
- let argsno = List.length args in
- C.Lambda
- (C.Name "x",
- (if argsno + List.length rev_left_args > 0 then
- C.Appl
- (C.MutInd (turi, typeno, []) ::
- (List.map
- (CicSubstitution.lift (argsno + 1))
- (List.rev rev_left_args)) @
- mk_rels argsno)
- else
- C.MutInd (turi,typeno,[])),
- C.Sort C.Prop)
- | 0, _, _ -> assert false (* seriously screwed up *)
- | n, he::tl, C.Prod (_,_,ta) ->
- mk_lambdas (he::rev_left_args)(n-1,tl,CicSubstitution.subst he ta)
- | n,_,_ ->
- assert false (* we should probably reduce in some context *)
- in
- mk_lambdas [] (paramsno, args, rty)
- in
- branches, outtype
- | _ -> 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,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)::args)) ->
- turi,typeno,exp_named_subst,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 branches,outtype =
- mk_branches_and_outtype turi typeno consno context args
- in
- ProofEngineTypes.apply_tactic
- (T.then_
- ~start:(EliminationTactics.elim_type_tac (C.MutInd (false_URI, 0, [])))
- ~continuation:
- (T.then_
- ~start:
- (ReductionTactics.change_tac
- ~pattern:(ProofEngineTypes.conclusion_pattern None)
- (fun _ m u ->
- C.Appl [
- C.Lambda ( C.Name "x", tty,
- C.MutCase (turi, typeno, outtype, (C.Rel 1), branches));
- 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)))) status
- | _ -> 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)