let debug_print = fun _ -> ()
-let rec injection_tac ~term =
+(* 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
let module C = Cic in
let module T = Tacticals in
let _,metasenv,_,_ = proof in
let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let term = CicSubstitution.lift liftno term 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 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") ; *) 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)))
- when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
- let rec traverse_list i liftno l1 l2 =
- match l1,l2 with
- [],[] -> T.id_tac
- | hd1::tl1,hd2::tl2 ->
- if
- fst
- (CicReduction.are_convertible ~metasenv
- context hd1 hd2 CicUniv.empty_ugraph)
- then
- traverse_list (i+1) liftno tl1 tl2
- else
- T.then_
- ~start:
- (injection1_tac ~i ~liftno
- ~term:(CicSubstitution.lift liftno term))
- ~continuation:
- (traverse_list (i+1) (liftno+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 0 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 (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality but a discriminable one"))
- | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality"))
- )
- | _ -> 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)
+ | _ -> 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)),
+ (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) ->
+ 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"))
+ 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)
-and injection1_tac ~term ~i ~liftno =
+and injection1_tac ~term ~i ~liftno ~continuation =
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 U = UriManager in
let module P = PrimitiveTactics in
let module T = Tacticals in
+ let term = CicSubstitution.lift liftno 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
+ 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 LibraryObjects.is_eq_URI equri -> (
in
C.Lambda (binder',source,(aux target (k+1)))
| _ ->
-if id = i_constr_id then (
-prerr_endline ("k= " ^ string_of_int k);
-prerr_endline ("paramsno= " ^ string_of_int paramsno);
-prerr_endline ("nr_param_constr " ^ string_of_int (k - 1 - paramsno));
-prerr_endline ("rel= " ^ string_of_int (k - i));
-);
let nr_param_constr = k - 1 - paramsno in
if id = i_constr_id
then C.Rel (k - i)
in
ProofEngineTypes.apply_tactic
(T.thens
- ~start:(P.cut_tac (C.Appl [(C.MutInd (equri,0,[])) ; tty' ; t1' ; t2']))
- ~continuations:[
- T.then_
- ~start:T.id_tac (*(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
-let aaa =
- ProofEngineTypes.apply_tactic
- (ReductionTactics.change_tac
- ~pattern:(ProofEngineTypes.conclusion_pattern
- (Some new_t1'))
- (fun _ m u ->
-let xxx =
- C.Appl [
- C.Lambda
- (C.Name "x",
- tty,
- C.MutCase
- (turi,typeno,outtype,C.Rel 1,patterns)) ;
- t1]
-in
-prerr_endline ("i=" ^ string_of_int i ^ "; liftno=" ^ string_of_int liftno);
-prerr_endline ("XXX: " ^ CicPp.ppterm xxx);
-prerr_endline ("WITH: " ^ CicPp.ppterm new_t1');
-xxx,
- m, u))
- status
-in
-prerr_endline "OK";
-aaa
- ))
- ~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"))
ProofEngineTypes.mk_tactic (injection1_tac ~term ~i)
;;
-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")
+(* 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)
;;
-
-*)
-
-
-
projects / helm.git / blobdiff