(** Similar to effect semantics, event semantics augment memory semantics with suitable effects, in the form
    of a set of memory access traces associated with each internal
    step of the semantics. *)

Record EvSem {C} :=
  { (** [sem] is a memory semantics. *)
    msem :> @MemSem C

    (** The step relation of the new semantics. *)
  ; ev_step: C -> mem -> list mem_event -> C -> mem -> Prop

    (** The next four fields axiomatize [drfstep] and its relation to the
        underlying step relation of [msem]. *)
  ; ev_step_ax1: forall c m T c' m',
       ev_step c m T c' m' ->
            corestep msem c m c' m'
  ; ev_step_ax2: forall c m c' m',
       corestep msem c m c' m' ->
       exists T, ev_step c m T c' m'
  ; ev_step_fun: forall c m T' c' m' T'' c'' m'',
       ev_step c m T' c' m' -> ev_step c m T'' c'' m'' -> T'=T''
(*  ; ev_step_elim: forall g c m T c' m',
       ev_step g c m T c' m' -> ev_elim m T m'*)
  ; ev_step_elim: forall c m T c' m' (STEP: ev_step c m T c' m'),
       ev_elim m T m' (*/\
       (forall mm mm', ev_elim mm T mm' -> exists cc', ev_step c mm T cc' mm')*)
  }.(** Similar to effect semantics, event semantics augment memory semantics with suitable effects, in the form
    of a set of memory access traces associated with each internal
    step of the semantics. *)

Record EvSem {C} :=
  { (** [sem] is a memory semantics. *)
    msem :> @MemSem C

    (** The step relation of the new semantics. *)
  ; ev_step: C -> mem -> list mem_event -> C -> mem -> Prop

    (** The next four fields axiomatize [drfstep] and its relation to the
        underlying step relation of [msem]. *)
  ; ev_step_ax1: forall c m T c' m',
       ev_step c m T c' m' ->
            corestep msem c m c' m'
  ; ev_step_ax2: forall c m c' m',
       corestep msem c m c' m' ->
       exists T, ev_step c m T c' m'
  ; ev_step_fun: forall c m T' c' m' T'' c'' m'',
       ev_step c m T' c' m' -> ev_step c m T'' c'' m'' -> T'=T''
(*  ; ev_step_elim: forall g c m T c' m',
       ev_step g c m T c' m' -> ev_elim m T m'*)
  ; ev_step_elim: forall c m T c' m' (STEP: ev_step c m T c' m'),
       ev_elim m T m' (*/\
       (forall mm mm', ev_elim mm T mm' -> exists cc', ev_step c mm T cc' mm')*)
  }.(** Similar to effect semantics, event semantics augment memory semantics with suitable effects, in the form
    of a set of memory access traces associated with each internal
    step of the semantics. *)

Record EvSem {C} :=
  { (** [sem] is a memory semantics. *)
    msem :> @MemSem C

    (** The step relation of the new semantics. *)
  ; ev_step: C -> mem -> list mem_event -> C -> mem -> Prop

    (** The next four fields axiomatize [drfstep] and its relation to the
        underlying step relation of [msem]. *)
  ; ev_step_ax1: forall c m T c' m',
       ev_step c m T c' m' ->
            corestep msem c m c' m'
  ; ev_step_ax2: forall c m c' m',
       corestep msem c m c' m' ->
       exists T, ev_step c m T c' m'
  ; ev_step_fun: forall c m T' c' m' T'' c'' m'',
       ev_step c m T' c' m' -> ev_step c m T'' c'' m'' -> T'=T''
(*  ; ev_step_elim: forall g c m T c' m',
       ev_step g c m T c' m' -> ev_elim m T m'*)
  ; ev_step_elim: forall c m T c' m' (STEP: ev_step c m T c' m'),
       ev_elim m T m' (*/\
       (forall mm mm', ev_elim mm T mm' -> exists cc', ev_step c mm T cc' mm')*)
  }.(** Similar to effect semantics, event semantics augment memory semantics with suitable effects, in the form
    of a set of memory access traces associated with each internal
    step of the semantics. *)

Record EvSem {C} :=
  { (** [sem] is a memory semantics. *)
    msem :> @MemSem C

    (** The step relation of the new semantics. *)
  ; ev_step: C -> mem -> list mem_event -> C -> mem -> Prop

    (** The next four fields axiomatize [drfstep] and its relation to the
        underlying step relation of [msem]. *)
  ; ev_step_ax1: forall c m T c' m',
       ev_step c m T c' m' ->
            corestep msem c m c' m'
  ; ev_step_ax2: forall c m c' m',
       corestep msem c m c' m' ->
       exists T, ev_step c m T c' m'
  ; ev_step_fun: forall c m T' c' m' T'' c'' m'',
       ev_step c m T' c' m' -> ev_step c m T'' c'' m'' -> T'=T''
(*  ; ev_step_elim: forall g c m T c' m',
       ev_step g c m T c' m' -> ev_elim m T m'*)
  ; ev_step_elim: forall c m T c' m' (STEP: ev_step c m T c' m'),
       ev_elim m T m' (*/\
       (forall mm mm', ev_elim mm T mm' -> exists cc', ev_step c mm T cc' mm')*)
  }.(** Similar to effect semantics, event semantics augment memory semantics with suitable effects, in the form
    of a set of memory access traces associated with each internal
    step of the semantics. *)

Record EvSem {C} :=
  { (** [sem] is a memory semantics. *)
    msem :> @MemSem C

    (** The step relation of the new semantics. *)
  ; ev_step: C -> mem -> list mem_event -> C -> mem -> Prop

    (** The next four fields axiomatize [drfstep] and its relation to the
        underlying step relation of [msem]. *)
  ; ev_step_ax1: forall c m T c' m',
       ev_step c m T c' m' ->
            corestep msem c m c' m'
  ; ev_step_ax2: forall c m c' m',
       corestep msem c m c' m' ->
       exists T, ev_step c m T c' m'
  ; ev_step_fun: forall c m T' c' m' T'' c'' m'',
       ev_step c m T' c' m' -> ev_step c m T'' c'' m'' -> T'=T''
(*  ; ev_step_elim: forall g c m T c' m',
       ev_step g c m T c' m' -> ev_elim m T m'*)
  ; ev_step_elim: forall c m T c' m' (STEP: ev_step c m T c' m'),
       ev_elim m T m' (*/\
       (forall mm mm', ev_elim mm T mm' -> exists cc', ev_step c mm T cc' mm')*)
  }.(** Similar to effect semantics, event semantics augment memory semantics with suitable effects, in the form
    of a set of memory access traces associated with each internal
    step of the semantics. *)

Record EvSem {C} :=
  { (** [sem] is a memory semantics. *)
    msem :> @MemSem C

    (** The step relation of the new semantics. *)
  ; ev_step: C -> mem -> list mem_event -> C -> mem -> Prop

    (** The next four fields axiomatize [drfstep] and its relation to the
        underlying step relation of [msem]. *)
  ; ev_step_ax1: forall c m T c' m',
       ev_step c m T c' m' ->
            corestep msem c m c' m'
  ; ev_step_ax2: forall c m c' m',
       corestep msem c m c' m' ->
       exists T, ev_step c m T c' m'
  ; ev_step_fun: forall c m T' c' m' T'' c'' m'',
       ev_step c m T' c' m' -> ev_step c m T'' c'' m'' -> T'=T''
(*  ; ev_step_elim: forall g c m T c' m',
       ev_step g c m T c' m' -> ev_elim m T m'*)
  ; ev_step_elim: forall c m T c' m' (STEP: ev_step c m T c' m'),
       ev_elim m T m' (*/\
       (forall mm mm', ev_elim mm T mm' -> exists cc', ev_step c mm T cc' mm')*)
  }.(** Similar to effect semantics, event semantics augment memory semantics with suitable effects, in the form
    of a set of memory access traces associated with each internal
    step of the semantics. *)

Record EvSem {C} :=
  { (** [sem] is a memory semantics. *)
    msem :> @MemSem C

    (** The step relation of the new semantics. *)
  ; ev_step: C -> mem -> list mem_event -> C -> mem -> Prop

    (** The next four fields axiomatize [drfstep] and its relation to the
        underlying step relation of [msem]. *)
  ; ev_step_ax1: forall c m T c' m',
       ev_step c m T c' m' ->
            corestep msem c m c' m'
  ; ev_step_ax2: forall c m c' m',
       corestep msem c m c' m' ->
       exists T, ev_step c m T c' m'
  ; ev_step_fun: forall c m T' c' m' T'' c'' m'',
       ev_step c m T' c' m' -> ev_step c m T'' c'' m'' -> T'=T''
(*  ; ev_step_elim: forall g c m T c' m',
       ev_step g c m T c' m' -> ev_elim m T m'*)
  ; ev_step_elim: forall c m T c' m' (STEP: ev_step c m T c' m'),
       ev_elim m T m' (*/\
       (forall mm mm', ev_elim mm T mm' -> exists cc', ev_step c mm T cc' mm')*)
  }.Definition in_free_list (b : block) ofs xs :=
  exists x, List.In x xs /\
       let '(b', lo, hi) := x in
       b = b' /\
       (lo <= ofs < hi)%Z.Fixpoint in_free_list_trace (b : block) ofs es :=
  match es with
  | Free l :: es =>
    in_free_list b ofs l \/ in_free_list_trace b ofs es
  | _ :: es =>
    in_free_list_trace b ofs es
  | nil =>
    False
  end.

Lemma in_free_list_trace_dec b ofs: forall es, {in_free_list_trace b ofs es} + {~in_free_list_trace b ofs es}.