X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=components%2Ftactics%2FdiscriminationTactics.ml;h=9c5d002ca2720a3f3aecb0531f1cba705301d146;hb=f9512e878bd27f8cb5261bb18b0da0d42c8184d0;hp=69739a4b0ccd1f70a128c085b39914b720c3fcf4;hpb=d723cac1efffbc8ef3ffcbaa96a2c390e2b8780e;p=helm.git diff --git a/components/tactics/discriminationTactics.ml b/components/tactics/discriminationTactics.ml index 69739a4b0..9c5d002ca 100644 --- a/components/tactics/discriminationTactics.ml +++ b/components/tactics/discriminationTactics.ml @@ -27,6 +27,173 @@ let debug_print = fun _ -> () +(* 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 rec injection_tac ~first_time ~term ~liftno ~continuation = let injection_tac ~term status = let (proof, goal) = status in @@ -99,7 +266,7 @@ let rec injection_tac ~first_time ~term ~liftno ~continuation = 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???")) + | _ -> assert false (* i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini *) in traverse_list 1 applist1 applist2 ~liftno | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)), @@ -111,7 +278,8 @@ let rec injection_tac ~first_time ~term ~liftno ~continuation = | ((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")) + discriminate_tac ~term + (*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")) @@ -302,182 +470,9 @@ and injection1_tac ~term ~i ~liftno ~continuation = ProofEngineTypes.mk_tactic (injection1_tac ~term ~i) ;; -let injection_tac = - injection_tac ~first_time:true ~liftno:0 ~continuation:(fun ~liftno -> Tacticals.id_tac) +(* destruct performs either injection or discriminate *) +(* equivalent to Coq's "analyze equality" *) +let destruct_tac = + injection_tac + ~first_time:true ~liftno:0 ~continuation:(fun ~liftno -> Tacticals.id_tac) ;; - -(* 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)