Require compcert.common.Globalenvs.
(*To prove memsem*)
Inductive state : Type :=
State : function ->
statement -> cont -> env -> temp_env -> state
| Callstate : fundef -> list val -> cont -> state
| Returnstate : val -> cont -> state.
Definition CC_core := state.
Definition CC_core_to_CC_state (c:state) (m:mem) : Clight.state :=
match c with
State f st k e te => Clight.State f st k e te m
|  Callstate fd args k => Clight.Callstate fd args k m
| Returnstate v k => Clight.Returnstate v k m
end.
Definition CC_state_to_CC_core (c:Clight.state): state * mem :=
match c with
Clight.State f st k e te m => (State f st k e te, m)
|  Clight.Callstate fd args k m => (Callstate fd args k, m)
| Clight.Returnstate v k m => (Returnstate v k, m)
end.
Definition cl_halted (c: CC_core) : option val :=
match c with
| Returnstate v Kstop => Some v
| _ => None
end.
Definition empty_function : function := mkfunction Tvoid cc_default 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.
Fixpoint params_of_types (i: positive) (l : list type) : list (ident * type) :=
match l with
| nil => nil
| t :: l => (i, t) :: params_of_types (i+1)%positive l
end.
Fixpoint typelist2list (tl: typelist) : list type :=
match tl with
| Tcons t r => t::typelist2list r
| Tnil => nil
end.
Definition params_of_fundef (f: fundef) : list type :=
match f with
| Internal {| fn_params := fn_params |} => map snd fn_params
| External _ t _ _ => typelist2list t
end.
Definition cl_initial_core (ge: genv) (v: val) (args: list val) : option CC_core :=
match v with
Vptr b i =>
if Ptrofs.eq_dec i Ptrofs.zero then
match Genv.find_funct_ptr ge b with
Some f =>
Some (Callstate f args Kstop)
| _ => None end
else None
| _ => None
end.
Definition stuck_signature : signature := mksignature nil None cc_default.
Definition cl_at_external (c: CC_core) : option (external_function * list val) :=
match c with
| Callstate (External ef _ _ _) args _ => Some (ef, args)
| State _ (Sbuiltin _ ef _ args) _ _ _ => Some (EF_external "stuck" stuck_signature, nil)
| _ => None
end.
Definition cl_after_external (vret: option val) (c: CC_core) : option CC_core :=
match c with
| Callstate (External ef _ _ _) _ k =>
Some (Returnstate (match vret with Some v => v | _ => Vundef end) k)
| _ => None
end.
Inductive step: genv -> state -> mem -> state -> mem -> Prop :=
| step_assign:   forall ge f a1 a2 k e le m loc ofs v2 v m',
eval_lvalue ge e le m a1 loc ofs ->
eval_expr ge e le m a2 v2 ->
sem_cast v2 (typeof a2) (typeof a1) m = Some v ->
assign_loc ge (typeof a1) m loc ofs v m' ->
step ge (State f (Sassign a1 a2) k e le) m
(State f Sskip k e le) m'
| step_set:   forall ge f id a k e le m v,
eval_expr ge e le m a v ->
step ge (State f (Sset id a) k e le) m
(State f Sskip k e (PTree.set id v le)) m
| step_call:   forall ge f optid a al k e le m tyargs tyres cconv vf vargs fd,
classify_fun (typeof a) = fun_case_f tyargs tyres cconv ->
eval_expr ge e le m a vf ->
eval_exprlist ge e le m al tyargs vargs ->
Genv.find_funct ge vf = Some fd ->
type_of_fundef fd = Tfunction tyargs tyres cconv ->
step ge (State f (Scall optid a al) k e le) m
(Callstate fd vargs (Kcall optid f e le k)) m
| step_seq:  forall ge f s1 s2 k e le m,
step ge (State f (Ssequence s1 s2) k e le) m
(State f s1 (Kseq s2 k) e le) m
| step_skip_seq: forall ge f s k e le m,
step ge (State f Sskip (Kseq s k) e le) m
(State f s k e le) m
| step_continue_seq: forall ge f s k e le m,
step ge (State f Scontinue (Kseq s k) e le) m
(State f Scontinue k e le) m
| step_break_seq: forall ge f s k e le m,
step ge (State f Sbreak (Kseq s k) e le) m
(State f Sbreak k e le) m
| step_ifthenelse:  forall ge f a s1 s2 k e le m v1 b,
eval_expr ge e le m a v1 ->
bool_val v1 (typeof a) m = Some b ->
step ge (State f (Sifthenelse a s1 s2) k e le) m
(State f (if b then s1 else s2) k e le) m
| step_loop: forall ge f s1 s2 k e le m,
step ge (State f (Sloop s1 s2) k e le) m
(State f s1 (Kloop1 s1 s2 k) e le) m
| step_skip_or_continue_loop1:  forall ge f s1 s2 k e le m x,
x = Sskip \/ x = Scontinue ->
step ge (State f x (Kloop1 s1 s2 k) e le) m
(State f s2 (Kloop2 s1 s2 k) e le) m
| step_break_loop1:  forall ge f s1 s2 k e le m,
step ge (State f Sbreak (Kloop1 s1 s2 k) e le) m
(State f Sskip k e le) m
| step_skip_loop2: forall ge f s1 s2 k e le m,
step ge (State f Sskip (Kloop2 s1 s2 k) e le) m
(State f (Sloop s1 s2) k e le) m
| step_break_loop2: forall ge f s1 s2 k e le m,
step ge (State f Sbreak (Kloop2 s1 s2 k) e le) m
(State f Sskip k e le) m
| step_return_0: forall ge f k e le m m',
Mem.free_list m (blocks_of_env ge e) = Some m' ->
step ge (State f (Sreturn None) k e le) m
(Returnstate Vundef (call_cont k)) m'
| step_return_1: forall ge f a k e le m v v' m',
eval_expr ge e le m a v ->
sem_cast v (typeof a) f.(fn_return) m = Some v' ->
Mem.free_list m (blocks_of_env ge e) = Some m' ->
step ge (State f (Sreturn (Some a)) k e le) m
(Returnstate v' (call_cont k)) m'
| step_skip_call: forall ge f k e le m m',
is_call_cont k ->
Mem.free_list m (blocks_of_env ge e) = Some m' ->
step ge (State f Sskip k e le) m
(Returnstate Vundef k) m'
| step_switch: forall ge f a sl k e le m v n,
eval_expr ge e le m a v ->
sem_switch_arg v (typeof a) = Some n ->
step ge (State f (Sswitch a sl) k e le) m
(State f (seq_of_labeled_statement (select_switch n sl)) (Kswitch k) e le) m
| step_skip_break_switch: forall ge f x k e le m,
x = Sskip \/ x = Sbreak ->
step ge (State f x (Kswitch k) e le) m
(State f Sskip k e le) m
| step_continue_switch: forall ge f k e le m,
step ge (State f Scontinue (Kswitch k) e le) m
(State f Scontinue k e le) m
| step_label: forall ge f lbl s k e le m,
step ge (State f (Slabel lbl s) k e le) m
(State f s k e le) m
| step_goto: forall ge f lbl k e le m s' k',
find_label lbl f.(fn_body) (call_cont k) = Some (s', k') ->
step ge (State f (Sgoto lbl) k e le) m
(State f s' k' e le) m
| step_internal_function: forall ge f vargs k m e le m1,
function_entry2 ge f vargs m e le m1 ->
step ge (Callstate (Internal f) vargs k) m
(State f f.(fn_body) k e le) m1
| step_returnstate: forall ge v optid f e le k m,
step ge (Returnstate v (Kcall optid f e le k)) m
(State f Sskip k e (set_opttemp optid v le)) m.

Lemma cl_step_equiv: forall ge (q: CC_core) (m: mem) q' m',
cl_at_external q = None ->
step ge q m q' m' <-> Clight.step ge (Clight.function_entry2 ge)
(CC_core_to_CC_state q m) Events.E0 (CC_core_to_CC_state q' m').