(** ** Whole-program behaviors, big-step style. *)

Inductive bigstep_program_terminates (p: program): trace -> int -> Prop :=
  | bigstep_program_terminates_intro: forall b f m0 m1 t r,
      let ge := globalenv p in
      Genv.init_mem p = Some m0 ->
      Genv.find_symbol ge p.(prog_main) = Some b ->
      Genv.find_funct_ptr ge b = Some f ->
      type_of_fundef f = Tfunction Tnil type_int32s cc_default ->
      eval_funcall ge m0 f nil t m1 (Vint r) ->
      bigstep_program_terminates p t r.(** ** Whole-program behaviors, big-step style. *)

Inductive bigstep_program_terminates (p: program): trace -> int -> Prop :=
  | bigstep_program_terminates_intro: forall b f m0 m1 t r,
      let ge := globalenv p in
      Genv.init_mem p = Some m0 ->
      Genv.find_symbol ge p.(prog_main) = Some b ->
      Genv.find_funct_ptr ge b = Some f ->
      type_of_fundef f = Tfunction Tnil type_int32s cc_default ->
      eval_funcall ge m0 f nil t m1 (Vint r) ->
      bigstep_program_terminates p t r.Inductive bigstep_program_diverges (p: program): traceinf -> Prop :=
  | bigstep_program_diverges_intro: forall b f m0 t,
      let ge := globalenv p in
      Genv.init_mem p = Some m0 ->
      Genv.find_symbol ge p.(prog_main) = Some b ->
      Genv.find_funct_ptr ge b = Some f ->
      type_of_fundef f = Tfunction Tnil type_int32s cc_default ->
      evalinf_funcall ge m0 f nil t ->
      bigstep_program_diverges p t.Inductive bigstep_program_diverges (p: program): traceinf -> Prop :=
  | bigstep_program_diverges_intro: forall b f m0 t,
      let ge := globalenv p in
      Genv.init_mem p = Some m0 ->
      Genv.find_symbol ge p.(prog_main) = Some b ->
      Genv.find_funct_ptr ge b = Some f ->
      type_of_fundef f = Tfunction Tnil type_int32s cc_default ->
      evalinf_funcall ge m0 f nil t ->
      bigstep_program_diverges p t.Inductive bigstep_program_diverges (p: program): traceinf -> Prop :=
  | bigstep_program_diverges_intro: forall b f m0 t,
      let ge := globalenv p in
      Genv.init_mem p = Some m0 ->
      Genv.find_symbol ge p.(prog_main) = Some b ->
      Genv.find_funct_ptr ge b = Some f ->
      type_of_fundef f = Tfunction Tnil type_int32s cc_default ->
      evalinf_funcall ge m0 f nil t ->
      bigstep_program_diverges p t.Definition bigstep_semantics (p: program) :=
  Bigstep_semantics (bigstep_program_terminates p) (bigstep_program_diverges p).

Theorem bigstep_semantics_sound: forall p, bigstep_sound (bigstep_semantics p) (semantics p).