Require Export Maps.
Inductive cmin_effstep (g: Cminor.genv):  (block -> Z -> bool) ->
CMin_core -> mem -> CMin_core -> mem -> Prop :=
| cmin_effstep_skip_seq: forall f s k sp e m,
cmin_effstep g EmptyEffect (CMin_State f Sskip (Kseq s k) sp e) m
(CMin_State f s k sp e) m
| cmin_effstep_skip_block: forall f k sp e m,
cmin_effstep g EmptyEffect (CMin_State f Sskip (Kblock k) sp e) m
(CMin_State f Sskip k sp e) m
| cmin_effstep_skip_call: forall f k sp e m m',
is_call_cont k ->
Mem.free m sp 0 f.(fn_stackspace) = Some m' ->
cmin_effstep g (FreeEffect m 0 (f.(fn_stackspace)) sp) (CMin_State f Sskip k (Vptr sp Int.zero) e) m
(CMin_Returnstate Vundef k) m'
| cmin_effstep_assign: forall f id a k sp e m v,
eval_expr g sp e m a v ->
cmin_effstep g EmptyEffect (CMin_State f (Sassign id a) k sp e) m
(CMin_State f Sskip k sp (PTree.set id v e)) m
| cmin_effstep_store: forall f chunk addr a k sp e m vaddr v m',
eval_expr g sp e m addr vaddr ->
eval_expr g sp e m a v ->
Mem.storev chunk m vaddr v = Some m' ->
cmin_effstep g (StoreEffect vaddr (encode_val chunk v)) (CMin_State f (Sstore chunk addr a) k sp e) m
(CMin_State f Sskip k sp e) m'
| cmin_effstep_call: forall f optid sig a bl k sp e m vf vargs fd,
eval_expr g sp e m a vf ->
eval_exprlist g sp e m bl vargs ->
Genv.find_funct g vf = Some fd ->
funsig fd = sig ->
cmin_effstep g EmptyEffect (CMin_State f (Scall optid sig a bl) k sp e) m
(CMin_Callstate fd vargs (Kcall optid f sp e k)) m
| cmin_effstep_tailcall: forall f sig a bl k sp e m vf vargs fd m',
eval_expr g (Vptr sp Int.zero) e m a vf ->
eval_exprlist g (Vptr sp Int.zero) e m bl vargs ->
Genv.find_funct g vf = Some fd ->
funsig fd = sig ->
Mem.free m sp 0 f.(fn_stackspace) = Some m' ->
cmin_effstep g (FreeEffect m 0 (f.(fn_stackspace)) sp) (CMin_State f (Stailcall sig a bl) k (Vptr sp Int.zero) e) m
(CMin_Callstate fd vargs (call_cont k)) m'
(* WE DO NOT TREAT BUILTINS *)
(*| cmin_effstep_builtin: forall f optid ef bl k sp e m vargs t vres m', eval_exprlist g sp e m bl vargs -> external_call ef g vargs m t vres m' -> cmin_effstep g (BuiltinEffect g (ef_sig ef) vargs m) (CMin_State f (Sbuiltin optid ef bl) k sp e) m (CMin_State f Sskip k sp (set_optvar optid vres e)) m'*)
| cmin_effstep_seq: forall f s1 s2 k sp e m,
cmin_effstep g EmptyEffect (CMin_State f (Sseq s1 s2) k sp e) m
(CMin_State f s1 (Kseq s2 k) sp e) m
| cmin_effstep_ifthenelse: forall f a s1 s2 k sp e m v b,
eval_expr g sp e m a v ->
Val.bool_of_val v b ->
cmin_effstep g EmptyEffect (CMin_State f (Sifthenelse a s1 s2) k sp e) m
(CMin_State f (if b then s1 else s2) k sp e) m
| cmin_effstep_loop: forall f s k sp e m,
cmin_effstep g EmptyEffect (CMin_State f (Sloop s) k sp e) m
(CMin_State f s (Kseq (Sloop s) k) sp e) m
| cmin_effstep_block: forall f s k sp e m,
cmin_effstep g EmptyEffect (CMin_State f (Sblock s) k sp e) m
(CMin_State f s (Kblock k) sp e) m
| cmin_effstep_exit_seq: forall f n s k sp e m,
cmin_effstep g EmptyEffect (CMin_State f (Sexit n) (Kseq s k) sp e) m
(CMin_State f (Sexit n) k sp e) m
| cmin_effstep_exit_block_0: forall f k sp e m,
cmin_effstep g EmptyEffect (CMin_State f (Sexit O) (Kblock k) sp e) m
(CMin_State f Sskip k sp e) m
| cmin_effstep_exit_block_S: forall f n k sp e m,
cmin_effstep g EmptyEffect (CMin_State f (Sexit (S n)) (Kblock k) sp e) m
(CMin_State f (Sexit n) k sp e) m
| cmin_effstep_switch: forall f a cases default k sp e m n,
eval_expr g sp e m a (Vint n) ->
cmin_effstep g EmptyEffect (CMin_State f (Sswitch a cases default) k sp e) m
(CMin_State f (Sexit (Switch.switch_target n default cases)) k sp e) m
| cmin_effstep_return_0: forall f k sp e m m',
Mem.free m sp 0 f.(fn_stackspace) = Some m' ->
cmin_effstep g (FreeEffect m 0 (f.(fn_stackspace)) sp) (CMin_State f (Sreturn None) k (Vptr sp Int.zero) e) m
(CMin_Returnstate Vundef (call_cont k)) m'
| cmin_effstep_return_1: forall f a k sp e m v m',
eval_expr g (Vptr sp Int.zero) e m a v ->
Mem.free m sp 0 f.(fn_stackspace) = Some m' ->
cmin_effstep g (FreeEffect m 0 (f.(fn_stackspace)) sp) (CMin_State f (Sreturn (Some a)) k (Vptr sp Int.zero) e) m
(CMin_Returnstate v (call_cont k)) m'
| cmin_effstep_label: forall f lbl s k sp e m,
cmin_effstep g EmptyEffect (CMin_State f (Slabel lbl s) k sp e) m
(CMin_State f s k sp e) m
| cmin_effstep_goto: forall f lbl k sp e m s' k',
find_label lbl f.(fn_body) (call_cont k) = Some(s', k') ->
cmin_effstep g EmptyEffect (CMin_State f (Sgoto lbl) k sp e) m
(CMin_State f s' k' sp e) m
| cmin_effstep_internal_function: forall f vargs k m m' sp e,
Mem.alloc m 0 f.(fn_stackspace) = (m', sp) ->
set_locals f.(fn_vars) (set_params vargs f.(fn_params)) = e ->
cmin_effstep g EmptyEffect (CMin_Callstate (Internal f) vargs k) m
(CMin_State f f.(fn_body) k (Vptr sp Int.zero) e) m'
(*no external functions in coresteps! | cmin_effstep_external_function: forall ef vargs k m t vres m', external_call ef g vargs m t vres m' -> cmin_effstep g EmptyEffect (CMin_Callstate (External ef) vargs k) m (CMin_Returnstate vres k) m'*)
| cmin_effstep_return: forall v optid f sp e k m,
cmin_effstep g EmptyEffect (CMin_Returnstate v (Kcall optid f sp e k)) m
(CMin_State f Sskip k sp (set_optvar optid v e)) m
| cmin_effstep_sub_val: forall E EE c m c' m',
(forall b ofs, Mem.valid_block m b ->
E b ofs = true -> EE b ofs = true) ->
cmin_effstep g E c m c' m' ->
cmin_effstep g EE c m c' m'.

Lemma cminstep_effax1: forall (M : block -> Z -> bool) g c m c' m',
cmin_effstep g M c m c' m' ->
(corestep cmin_coop_sem g c m c' m' /\
Mem.unchanged_on (fun (b : block) (ofs : Z) => M b ofs = false) m m').