Fixpoint precontinue_cont (k: cont) : cont :=
  match k with
  | Kseq s :: k' => precontinue_cont k'
  | Kloop1 _ _ :: _ => k
  | Kswitch :: k' => precontinue_cont k'
  | _ => nil (* stuck *)
  end.Fixpoint break_cont (k: cont) : cont :=
  match k with
  | Kseq s :: k' => break_cont k'
  | Kloop1 _ _ :: k' => k'
  | Kloop2 _ _ :: _ => nil  (* stuck *)
  | Kswitch :: k' => k'
  | _ =>  nil (* stuck *)
  end.Inductive corestate :=
 | State: forall (ve: env) (te: temp_env) (k: cont), corestate
 | ExtCall: forall (ef: external_function) (sig: signature) (args: list val)
                   (lid: option ident) (ve: env) (te: temp_env) (k: cont),
                corestate.Inductive corestate :=
 | State: forall (ve: env) (te: temp_env) (k: cont), corestate
 | ExtCall: forall (ef: external_function) (sig: signature) (args: list val)
                   (lid: option ident) (ve: env) (te: temp_env) (k: cont),
                corestate.Inductive corestate :=
 | State: forall (ve: env) (te: temp_env) (k: cont), corestate
 | ExtCall: forall (ef: external_function) (sig: signature) (args: list val)
                   (lid: option ident) (ve: env) (te: temp_env) (k: cont),
                corestate.Fixpoint strip_skip (k: cont) : cont :=
 match k with Kseq Sskip :: k' => strip_skip k' | _ => k end.Definition cl_at_external (c: corestate) : option (external_function * signature *list val) :=
  match c with
  | State _ _ k => None
  | ExtCall ef sig args lid ve te k => Some (ef, sig, args)
 end.Definition cl_after_external (vret: option val) (c: corestate) : option corestate :=
  match vret, c with
  | Some v, ExtCall ef sig args (Some id) ve te k => Some (State ve (PTree.set id v te) k)
  | None, ExtCall ef sig args None ve te k => Some (State ve te k)
  | _, _ => None
  end.(** Find the statement and manufacture the continuation
  corresponding to a label *)

Fixpoint find_label (lbl: label) (s: statement) (k: cont)
                    {struct s}: option cont :=
  match s with
  | Ssequence s1 s2 =>
      match find_label lbl s1 (Kseq s2 :: k) with
      | Some sk => Some sk
      | None => find_label lbl s2 k
      end
  | Sifthenelse a s1 s2 =>
      match find_label lbl s1 k with
      | Some sk => Some sk
      | None => find_label lbl s2 k
      end
  | Sloop s1 a3 =>
      match find_label lbl s1 (Kseq Scontinue :: Kloop1 s1 a3 :: k) with
      | Some sk => Some sk
      | None => find_label lbl a3 (Kloop2 s1 a3 :: k)
      end
  | Sswitch e sl =>
      find_label_ls lbl sl (Kswitch :: k)
  | Slabel lbl' s' =>
      if ident_eq lbl lbl' then Some(Kseq s' :: k) else find_label lbl s' k
  | _ => None
  end

with find_label_ls (lbl: label) (sl: labeled_statements) (k: cont)
                    {struct sl}: option cont :=
  match sl with
  | LSdefault s => find_label lbl s k
  | LScase _ s sl' =>
      match find_label lbl s (Kseq (seq_of_labeled_statement sl') :: k) with
      | Some sk => Some sk
      | None => find_label_ls lbl sl' k
      end
  end.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.(** Transition relation *)

Inductive cl_step (ge: Clight.genv): forall (q: corestate) (m: mem) (q': corestate) (m': mem), Prop :=

  | step_assign: forall ve te k m a1 a2 loc ofs v2 v m',
     type_is_volatile (typeof a1) = false ->
      Clight.eval_lvalue ge ve te m a1 loc ofs ->
      Clight.eval_expr ge ve te m a2 v2 ->
      Cop.sem_cast v2 (typeof a2) (typeof a1) = Some v ->
      Clight.assign_loc (typeof a1) m loc ofs v m' ->
      cl_step ge (State ve te (Kseq (Sassign a1 a2):: k)) m (State ve te k) m'

  | step_set:   forall ve te k m id a v,
      Clight.eval_expr ge ve te m a v ->
      cl_step ge (State ve te (Kseq (Sset id a) :: k)) m (State ve (PTree.set id v te) k) m

  | step_call_internal:   forall ve te k m optid a al tyargs tyres vf vargs f m1 ve' le',
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (Internal f) ->
      type_of_function f = Tfunction tyargs tyres ->
      list_norepet (var_names f.(fn_params) ++ var_names f.(fn_temps)) ->
      forall (NRV: list_norepet (var_names f.(fn_vars))),
      Clight.alloc_variables empty_env m (f.(fn_vars)) ve' m1 ->
      bind_parameter_temps f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some
le' ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m
                   (State ve' le' (Kseq f.(fn_body) :: Kseq (Sreturn None) :: Kcall optid f ve te :: k)) m1

  | step_call_external:   forall ve te k m optid a al tyargs tyres vf vargs ef,
      Cop.classify_fun (typeof a) = Cop.fun_case_f tyargs tyres ->
      Clight.eval_expr ge ve te m a vf ->
      Clight.eval_exprlist ge ve te m al tyargs vargs ->
      Genv.find_funct ge vf = Some (External ef tyargs tyres) ->
      cl_step ge (State ve te (Kseq (Scall optid a al) :: k)) m (ExtCall ef (signature_of_type tyargs tyres) vargs optid ve te k) m

  | step_seq: forall ve te k m s1 s2 st' m',
          cl_step ge (State ve te (Kseq s1 :: Kseq s2 :: k)) m st' m' ->
          cl_step ge (State ve te (Kseq (Ssequence s1 s2) :: k)) m st' m'

  | step_skip: forall ve te k m st' m',
          cl_step ge (State ve te k) m st' m' ->
          cl_step ge (State ve te (Kseq Sskip :: k)) m st' m'

  | step_continue: forall ve te k m st' m',
           cl_step ge (State ve te (continue_cont k)) m st' m' ->
           cl_step ge (State ve te (Kseq Scontinue :: k)) m st' m'

  | step_break: forall ve te k m st' m',
                   cl_step ge (State ve te (break_cont k)) m st' m' ->
                   cl_step ge (State ve te (Kseq Sbreak :: k)) m st' m'

  | step_ifthenelse:  forall ve te k m a s1 s2 v1 b,
      Clight.eval_expr ge ve te m a v1 ->
      Cop.bool_val v1 (typeof a) = Some b ->
      cl_step ge (State ve te (Kseq (Sifthenelse a s1 s2) :: k)) m (State ve te  (Kseq (if b then s1 else s2) :: k)) m

  | step_for: forall ve te k m s1 s2,
      cl_step ge (State ve te (Kseq (Sloop s1 s2) :: k)) m
              (State ve te (Kseq s1 :: Kseq Scontinue :: Kloop1 s1 s2 :: k)) m

  | step_loop2: forall ve te k m a3 s,
      cl_step ge (State ve te (Kloop2 s a3 :: k)) m
             (State ve te (Kseq s :: Kseq Scontinue :: Kloop1 s a3 :: k)) m

  | step_return: forall f ve te optexp optid k m v' m' ve' te' te'' k',
      call_cont k = Kcall optid f ve' te' :: k' ->
      Mem.free_list m (Clight.blocks_of_env ve) = Some m' ->
      match optexp with None => True
                                  | Some a => exists v, Clight.eval_expr ge ve te m a v /\ Cop.sem_cast v (typeof a) f.(fn_return) = Some v'
                            end ->
      match optid with None => f.(fn_return) = Tvoid /\ te''=te'
                                | Some id => optexp <> None /\ te'' = PTree.set id v' te'
      end ->
      cl_step ge (State ve te (Kseq (Sreturn optexp) :: k)) m (State ve' te'' k') m'

  | step_switch: forall ve te k m a sl n,
      Clight.eval_expr ge ve te m a (Vint n) ->
      cl_step ge (State ve te (Kseq (Sswitch a sl) :: k)) m
              (State ve te (Kseq (seq_of_labeled_statement (select_switch n sl)) :: Kswitch :: k)) m

  | step_label: forall ve te k m lbl s st' m',
       cl_step ge (State ve te (Kseq s :: k)) m st' m' ->
       cl_step ge (State ve te (Kseq (Slabel lbl s) :: k)) m st' m'

  | step_goto: forall f ve te k m lbl k'
                     (* make sure to take a step here, so that every loop ticks the clock *)
      (CUR: current_function k = Some f),
      find_label lbl f.(fn_body) (Kseq (Sreturn None) :: (call_cont k)) = Some k' ->
      cl_step ge (State ve te (Kseq (Sgoto lbl) :: k)) m (State ve te k') m.Definition vret2v (vret: list val) : val :=
  match vret with v::nil => v | _ => Vundef end.Definition exit_syscall_number : ident := 1%positive.Definition cl_halted (c: corestate) : option val := None.Definition empty_function : function := mkfunction Tvoid nil nil nil Sskip.Fixpoint temp_bindings (i: positive) (vl: list val) :=
 match vl with
 | nil => PTree.empty val
 | v::vl' => PTree.set i v (temp_bindings (i+1)%positive vl')
 end.Definition Tint32s := Tint I32 Signed noattr.Definition true_expr : Clight.expr := Clight.Econst_int Int.one Tint32s.Fixpoint typed_params (i: positive) (n: nat) : list (ident * type) :=
 match n with
 | O => nil
 | S n' => (i, Tint32s) :: typed_params (i+1)%positive n'
 end.Definition cl_initial_core (ge: genv) (v: val) (args: list val) : option corestate :=
  let tl := typed_params 2%positive (length args)
   in Some (State empty_env (temp_bindings 1%positive (v::args))
                  (Kseq (Scall None
                                  (Etempvar 1%positive (Tfunction (type_of_params tl) Tvoid))
                                  (map (fun x => Etempvar (fst x) (snd x)) tl)) ::
                     Kseq (Sloop Sskip Sskip) :: nil)).

(* Specifications: *)
Lemma cl_corestep_not_at_external: forall ge m q m' q', cl_step ge q m q' m' -> cl_at_external q = None.
Lemma cl_corestep_not_halted : forall ge m q m' q', cl_step ge q m q' m' -> cl_halted q = None.
Lemma cl_after_at_external_excl : forall retv q q', cl_after_external retv q = Some q' -> cl_at_external q' = None.