End ThreadPoolWF.
End ThreadPoolWF.
(** Assumptions on the threadwise semantics of the machine *)
(** ** Lemmas about threadwise semantics*)
Module CoreLanguage.
Section CoreLanguage.
Context {Sem : Semantics}.
Class SemAxioms :=
{ (** If the [Cur] permission is below [Writable] on some location then
a thread step cannot change the contents at this location *)
corestep_unchanged_on:
forall  c m c' m' b ofs
(Hstep: corestep (msem semSem) c m c' m')
(Hvalid: Mem.valid_block m b)
(Hstable: ~ Mem.perm m b ofs Cur Writable),
Maps.ZMap.get ofs (Maps.PMap.get b (Mem.mem_contents m)) =
Maps.ZMap.get ofs (Maps.PMap.get b (Mem.mem_contents m'));
(** Memories between thread steps are related by [decay] of permissions*)
corestep_decay:
forall c c' m m',
corestep semSem c m c' m' ->
decay m m';
(** [Mem.nextblock] is monotonic with respect to thread steps*)
corestep_nextblock:
forall c m c' m',
corestep semSem c m c' m' ->
(Mem.nextblock m <= Mem.nextblock m')%positive;
(** A core cannot be both at external and halted *)
at_external_halted_excl:
forall q m, at_external semSem q m = None \/ forall i, ~ halted semSem q i;
(** If the [Cur] permission is below [Writable] on some location then [initial_core] cannot change the contents at this location *)
initial_core_unchanged_on:
forall  i v args c m m' b ofs
(Hstep: initial_core semSem i m c m' v args)
(Hvalid: Mem.valid_block m b)
(Hstable: ~ Mem.perm m b ofs Cur Writable),
Maps.ZMap.get ofs (Maps.PMap.get b (Mem.mem_contents m)) =
Maps.ZMap.get ofs (Maps.PMap.get b (Mem.mem_contents m'));
(** Memories after [initial_core] are related by [decay] of permissions*)
initial_core_decay:
forall i v args c m m',
initial_core semSem i m c m' v args ->
strong_decay m m';
(** [Mem.nextblock] is monotonic with respect to [initial_core]*)
initial_core_nextblock:
forall i v args c m m',
initial_core semSem i m c m' v args ->
(Mem.nextblock m <= Mem.nextblock m')%positive;
}.
Class SemDet :=
{ (** The thread semantics are deterministic*)
corestep_det: corestep_fun semSem;
(** [initial_core] is deterministic *)
initial_core_det:
forall i m v args c c' m' m'',
initial_core semSem i m c m' v args ->
initial_core semSem i m c' m'' v args ->
c = c' /\ m' = m''
}.
Context {SemAx : SemAxioms} {SemD : SemDet}.

(* Specifications: *)
Lemma corestep_validblock:
forall c m c' m',
corestep semSem c m c' m' ->
forall b, Mem.valid_block m b ->
Mem.valid_block m' b.
Lemma initial_core_validblock:
forall i c m m' v args,
initial_core semSem i m c m' v args ->
forall b, Mem.valid_block m b ->
Mem.valid_block m' b.