(* $Id$ *)
+module C = Cic
+module U = UriManager
+module P = PrimitiveTactics
+module T = Tacticals
+module CR = CicReduction
+module PST = ProofEngineStructuralRules
+module PET = ProofEngineTypes
+module CTC = CicTypeChecker
+module CU = CicUniv
+module S = CicSubstitution
+
let debug = false
let debug_print =
if debug then (fun x -> prerr_endline (Lazy.force x)) else (fun _ -> ())
;;
+(* funzione generale di rilocazione dei riferimenti locali *)
+
+let relocate_term map t =
+ let rec map_xnss k xnss =
+ let imap (uri, t) = uri, map_term k t in
+ List.map imap xnss
+ and map_mss k mss =
+ let imap = function
+ | None -> None
+ | Some t -> Some (map_term k t)
+ in
+ List.map imap mss
+ and map_fs len k fs =
+ let imap (name, i, ty, bo) = name, i, map_term k ty, map_term (k + len) bo in
+ List.map imap fs
+ and map_cfs len k cfs =
+ let imap (name, ty, bo) = name, map_term k ty, map_term (k + len) bo in
+ List.map imap cfs
+ and map_term k = function
+ | C.Rel m -> if m < k then C.Rel m else C.Rel (map (m - k))
+ | C.Sort _ as t -> t
+ | C.Implicit _ as t -> t
+ | C.Var (uri, xnss) -> C.Var (uri, map_xnss k xnss)
+ | C.Const (uri, xnss) -> C.Const (uri, map_xnss k xnss)
+ | C.MutInd (uri, tyno, xnss) -> C.MutInd (uri, tyno, map_xnss k xnss)
+ | C.MutConstruct (uri, tyno, consno, xnss) ->
+ C.MutConstruct (uri, tyno, consno, map_xnss k xnss)
+ | C.Meta (i, mss) -> C.Meta(i, map_mss k mss)
+ | C.Cast (te, ty) -> C.Cast (map_term k te, map_term k ty)
+ | C.Appl ts -> C.Appl (List.map (map_term k) ts)
+ | C.MutCase (sp, i, outty, t, pl) ->
+ C.MutCase (sp, i, map_term k outty, map_term k t, List.map (map_term k) pl)
+ | C.Prod (n, s, t) -> C.Prod (n, map_term k s, map_term (succ k) t)
+ | C.Lambda (n, s, t) -> C.Lambda (n, map_term k s, map_term (succ k) t)
+ | C.LetIn (n, s, t) -> C.LetIn (n, map_term k s, map_term (succ k) t)
+ | C.Fix (i, fs) -> C.Fix (i, map_fs (List.length fs) k fs)
+ | C.CoFix (i, cfs) -> C.CoFix (i, map_cfs (List.length cfs) k cfs)
+ in
+ map_term 0 t
+
(* 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
+ | None -> raise (PET.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
+ | None -> raise (PET.Fail (lazy "You need to register the default \"false\" definition first. Please use the \"default\" command")) in
+ let fail msg = raise (PET.Fail (lazy ("Discriminate: " ^ msg))) in
let find_discriminating_consno t1 t2 =
let rec aux t1 t2 =
match t1, t2 with
List.map
(fun (id,cty) ->
(* dubbio: e' corretto ridurre in questo context ??? *)
- let red_ty = CicReduction.whd context cty in
+ let red_ty = CR.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))
+ S.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)))
then (C.MutInd(false_URI,0,[]))
else (C.MutInd(true_URI,0,[]))
in
- (CicSubstitution.lift 1 (aux red_ty 1)))
+ (S.lift 1 (aux red_ty 1)))
constructor_list in
let outtype =
let seed = ref 0 in
C.Appl
(C.MutInd (turi, typeno, []) ::
(List.map
- (CicSubstitution.lift (argsno + 1))
+ (S.lift (argsno + 1))
(List.rev rev_left_args)) @
mk_rels argsno)
else
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)
+ mk_lambdas (he::rev_left_args)(n-1,tl,S.subst he ta)
| n,_,_ ->
assert false (* we should probably reduce in some context *)
in
let _,metasenv,_subst,_,_, _ = proof in
let _,context,_ = CicUtil.lookup_meta goal metasenv in
let termty,_ =
- CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph
+ CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
in
match termty with
| C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
let branches,outtype =
mk_branches_and_outtype turi typeno consno context args
in
- ProofEngineTypes.apply_tactic
+ PET.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)
+ ~pattern:(PET.conclusion_pattern None)
(fun _ m u ->
C.Appl [
C.Lambda ( C.Name "x", tty,
~start:
(EqualityTactics.rewrite_simpl_tac
~direction:`RightToLeft
- ~pattern:(ProofEngineTypes.conclusion_pattern None)
+ ~pattern:(PET.conclusion_pattern None)
term [])
~continuation:
(IntroductionTactics.constructor_tac ~n:1)))) status
| _ -> fail "not an equality"
in
- ProofEngineTypes.mk_tactic (discriminate'_tac ~term)
-;;
+ PET.mk_tactic (discriminate'_tac ~term)
let exn_nonproj =
- ProofEngineTypes.Fail (lazy "Injection: not a projectable equality");;
+ PET.Fail (lazy "Injection: not a projectable equality")
let exn_noneq =
- ProofEngineTypes.Fail (lazy "Injection: not an equality");;
+ PET.Fail (lazy "Injection: not an equality")
let exn_nothingtodo =
- ProofEngineTypes.Fail (lazy "Nothing to do");;
+ PET.Fail (lazy "Nothing to do")
let exn_discrnonind =
- ProofEngineTypes.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible");;
+ PET.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible")
let exn_injwronggoal =
- ProofEngineTypes.Fail (lazy "Injection: goal after cut is not correct");;
+ PET.Fail (lazy "Injection: goal after cut is not correct")
let exn_noneqind =
- ProofEngineTypes.Fail (lazy "Injection: not an equality over elements of an inductive type");;
+ PET.Fail (lazy "Injection: not an equality over elements of an inductive type")
let pp ctx t =
let names = List.map (function Some (n,_) -> Some n | None -> None) ctx in
CicPp.pp t names
-;;
-let rec injection_tac ~first_time ~term ~liftno ~continuation =
- let module C = Cic in
- let module CR = CicReduction in
- let module U = UriManager in
- let module P = PrimitiveTactics in
- let module T = Tacticals in
- let module PST = ProofEngineStructuralRules in
- let module PET = ProofEngineTypes in
- let are_convertible hd1 hd2 metasenv context =
- fst (CR.are_convertible ~metasenv context hd1 hd2 CicUniv.empty_ugraph)
- in
- let injection_tac ~term status =
- let (proof, goal) = status in
- let _,metasenv,_subst, _,_, _ = proof in
- let _,context,_ = CicUtil.lookup_meta goal metasenv in
- let term = CicSubstitution.lift liftno term in
- let termty,_ =
- CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph
- in
- debug_print (lazy ("\ninjection su: " ^ pp context termty));
- let tac =
- match termty with
- | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
- when LibraryObjects.is_eq_URI equri -> begin
- match (CicReduction.whd ~delta:true context tty) with
- | C.MutInd (turi,typeno,ens)
- | C.Appl (C.MutInd (turi,typeno,ens)::_) -> begin
- match t1,t2 with
- | C.MutConstruct (uri1,typeno1,consno1,ens1),
- C.MutConstruct (uri2,typeno2,consno2,ens2)
- when (uri1 = uri2) && (typeno1 = typeno2) &&
- (consno1 = consno2) && (ens1 = ens2) ->
- if first_time then raise exn_nothingtodo
- else continuation ~liftno
- | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::applist1),
- C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::applist2)
- when (uri1 = uri2) && (typeno1 = typeno2) &&
- (consno1 = consno2) && (ens1 = ens2) ->
- let rec traverse_list i l1 l2 =
- match l1,l2 with
- | [],[] when first_time -> continuation
- | [],[] -> begin
- match term with
- | C.Rel n -> begin
- match List.nth context (n-1) with
- | Some (C.Name id,_) ->
- fun ~liftno ->
- T.then_ ~start:(PST.clear ~hyps:[id])
- ~continuation:(continuation ~liftno)
- | _ -> assert false
- end
- | _ -> assert false
- end
- | hd1::tl1,hd2::tl2 ->
- if are_convertible hd1 hd2 metasenv context 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,ens1),
- C.MutConstruct (uri2,typeno2,consno2,ens2)
- | C.MutConstruct (uri1,typeno1,consno1,ens1),
- C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::_)
- | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::_),
- C.MutConstruct (uri2,typeno2,consno2,ens2)
- | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::_),
- C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::_)
- when (consno1 <> consno2) || (ens1 <> ens2) ->
- discriminate_tac ~term
- | _ when not first_time -> continuation ~liftno
- | _ (* when first_time *) ->
- match term with
- | Cic.Rel i ->
- let name =
- match List.nth context (i-1) with
- | Some (Cic.Name s, Cic.Def _) -> s
- | Some (Cic.Name s, Cic.Decl _) -> s
- | _ -> assert false
- in
- Tacticals.then_
- ~start:(ReductionTactics.simpl_tac
- ~pattern:(None,[name,Cic.Implicit (Some `Hole)],None))
- ~continuation:(injection_tac ~first_time:false ~term ~liftno
- ~continuation)
- | _ -> raise exn_nonproj
- end
- | _ when not first_time -> continuation ~liftno
- | _ (* when first_time *) -> raise exn_nonproj
- end
- | _ -> raise exn_nonproj
- in
- PET.apply_tactic tac status
- in
- PET.mk_tactic (injection_tac ~term)
-
-and injection1_tac ~term ~i ~liftno ~continuation =
- let module C = Cic in
- let module CTC = CicTypeChecker in
- let module CU = CicUniv in
- let module S = CicSubstitution in
- let module U = UriManager in
- let module P = PrimitiveTactics in
- let module PET = ProofEngineTypes in
- let module T = Tacticals in
+let rec injection_tac ~term ~i ~liftno ~continuation =
let give_name seed = function
| C.Name _ as name -> name
| C.Anonymous -> C.Name (incr seed; "y" ^ string_of_int !seed)
in
let rec mk_rels = function | 0 -> [] | n -> C.Rel n :: (mk_rels (n - 1)) in
- let injection1_tac ~term ~i status =
+ let injection_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 term = CicSubstitution.lift liftno term in
+ let term = S.lift liftno term in
let _,metasenv,_subst,_,_, _ = proof in
let _,context,_ = CicUtil.lookup_meta goal metasenv in
let termty,_ =
- CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph
+ CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
in
debug_print (lazy ("\ninjection1 su : " ^ pp context termty));
match termty with (* an equality *)
let seed = ref 0 in
List.map
(function (id,cty) ->
- let reduced_cty = CicReduction.whd context cty in
+ let reduced_cty = CR.whd context cty in
let rec aux k = function
| C.Prod (_,_,tgt) when k <= paramsno ->
let left = List.nth left_params (k-1) in
- aux (k+1) (CicSubstitution.subst left tgt)
+ aux (k+1) (S.subst left tgt)
| C.Prod (binder,source,target) when k > paramsno ->
let binder' = give_name seed binder in
C.Lambda (binder',source,(aux (k+1) target))
else S.lift nr_param_constr t1'
(* + 1 per liftare anche il lambda aggiunto
* esternamente al case *)
- in CicSubstitution.lift 1 (aux 1 reduced_cty))
+ in S.lift 1 (aux 1 reduced_cty))
constructor_list
in
(* this code should be taken from cases_tac *)
let outtype =
let seed = ref 0 in
let rec to_lambdas te head =
- match CicReduction.whd context te with
+ match CR.whd context te with
| C.Prod (binder,so,ta) ->
let binder' = give_name seed binder in
C.Lambda (binder',so,to_lambdas ta head)
| _ -> head
in
let rec skip_prods params te =
- match params, CicReduction.whd context te with
+ match params, CR.whd context te with
| [], _ -> te
| left::tl, C.Prod (_,_,ta) ->
- skip_prods tl (CicSubstitution.subst left ta)
+ skip_prods tl (S.subst left ta)
| _, _ -> assert false
in
let abstracted_tty =
let tty =
- List.fold_left (fun x y -> CicSubstitution.subst y x) tty left_params
+ List.fold_left (fun x y -> S.subst y x) tty left_params
in
(* non lift, ma subst coi left! *)
match S.lift 1 tty with
(* check if cutted and changed are well typed and if t1' ~ changed *)
let go_on =
try
- let _,g = CicTypeChecker.type_of_aux' metasenv context cutted
+ let _,g = CTC.type_of_aux' metasenv context cutted
CicUniv.empty_ugraph
in
- let _,g = CicTypeChecker.type_of_aux' metasenv context changed g in
- fst (CicReduction.are_convertible ~metasenv context t1' changed g)
+ let _,g = CTC.type_of_aux' metasenv context changed g in
+ fst (CR.are_convertible ~metasenv context t1' changed g)
with
- | CicTypeChecker.TypeCheckerFailure _ -> false
+ | CTC.TypeCheckerFailure _ -> false
in
if not go_on then
- PET.apply_tactic Tacticals.id_tac status
+ PET.apply_tactic T.id_tac status
else
(debug_print (lazy ("CUT: " ^ pp context cutted));
PET.apply_tactic
(T.thens ~start: (P.cut_tac cutted)
~continuations:
- [injection_tac ~first_time:false ~liftno:0 ~term:(C.Rel 1)
+ [injection1_tac ~first_time:false ~liftno:0 ~term:(C.Rel 1)
~continuation:
(fun ~liftno:x -> continuation ~liftno:(liftno+1+x))
(* here I need to lift all the continuations by 1;
status)
| _ -> raise exn_noneq
in
- PET.mk_tactic (injection1_tac ~term ~i)
-;;
+ PET.mk_tactic (injection_tac ~term ~i)
+
+and injection1_tac ~first_time ~term ~liftno ~continuation =
+ let are_convertible hd1 hd2 metasenv context =
+ fst (CR.are_convertible ~metasenv context hd1 hd2 CicUniv.empty_ugraph)
+ in
+ let injection1_tac ~term status =
+ let (proof, goal) = status in
+ let _,metasenv,_subst, _,_, _ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let term = S.lift liftno term in
+ let termty,_ =
+ CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
+ in
+ debug_print (lazy ("\ninjection su: " ^ pp context termty));
+ let tac =
+ match termty with
+ | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
+ when LibraryObjects.is_eq_URI equri -> begin
+ match (CR.whd ~delta:true context tty) with
+ | C.MutInd (turi,typeno,ens)
+ | C.Appl (C.MutInd (turi,typeno,ens)::_) -> begin
+ match t1,t2 with
+ | C.MutConstruct (uri1,typeno1,consno1,ens1),
+ C.MutConstruct (uri2,typeno2,consno2,ens2)
+ when (uri1 = uri2) && (typeno1 = typeno2) &&
+ (consno1 = consno2) && (ens1 = ens2) ->
+ if first_time then raise exn_nothingtodo
+ else continuation ~liftno
+ | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::applist1),
+ C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::applist2)
+ when (uri1 = uri2) && (typeno1 = typeno2) &&
+ (consno1 = consno2) && (ens1 = ens2) ->
+ let rec traverse_list i l1 l2 =
+ match l1,l2 with
+ | [],[] when first_time -> continuation
+ | [],[] -> begin
+ match term with
+ | C.Rel n -> begin
+ match List.nth context (n-1) with
+ | Some (C.Name id,_) ->
+ fun ~liftno ->
+ T.then_ ~start:(PST.clear ~hyps:[id])
+ ~continuation:(continuation ~liftno)
+ | _ -> assert false
+ end
+ | _ -> assert false
+ end
+ | hd1::tl1,hd2::tl2 ->
+ if are_convertible hd1 hd2 metasenv context then
+ traverse_list (i+1) tl1 tl2
+ else
+ injection_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,ens1),
+ C.MutConstruct (uri2,typeno2,consno2,ens2)
+ | C.MutConstruct (uri1,typeno1,consno1,ens1),
+ C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::_)
+ | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::_),
+ C.MutConstruct (uri2,typeno2,consno2,ens2)
+ | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::_),
+ C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::_)
+ when (consno1 <> consno2) || (ens1 <> ens2) ->
+ discriminate_tac ~term
+ | _ when not first_time -> continuation ~liftno
+ | _ (* when first_time *) ->
+ match term with
+ | Cic.Rel i ->
+ let name =
+ match List.nth context (i-1) with
+ | Some (Cic.Name s, Cic.Def _) -> s
+ | Some (Cic.Name s, Cic.Decl _) -> s
+ | _ -> assert false
+ in
+ T.then_
+ ~start:(ReductionTactics.simpl_tac
+ ~pattern:(None,[name,Cic.Implicit (Some `Hole)],None))
+ ~continuation:(injection1_tac ~first_time:false ~term ~liftno
+ ~continuation)
+ | _ -> raise exn_nonproj
+ end
+ | _ when not first_time -> continuation ~liftno
+ | _ (* when first_time *) -> raise exn_nonproj
+ end
+ | _ -> raise exn_nonproj
+ in
+ PET.apply_tactic tac status
+ in
+ PET.mk_tactic (injection1_tac ~term)
(* 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)
-;;
+ injection1_tac
+ ~first_time:true ~liftno:0 ~continuation:(fun ~liftno -> T.id_tac)
projects / helm.git / commitdiff