Require Export Maps.
Inductive cminsel_effstep (g:genv):  (block -> Z -> bool) ->
CMinSel_core -> mem -> CMinSel_core -> mem -> Prop :=
| cminsel_effstep_skip_seq: forall f s k sp e m,
cminsel_effstep g EmptyEffect (CMinSel_State f Sskip (Kseq s k) sp e) m
(CMinSel_State f s k sp e) m
| cminsel_effstep_skip_block: forall f k sp e m,
cminsel_effstep g EmptyEffect (CMinSel_State f Sskip (Kblock k) sp e) m
(CMinSel_State f Sskip k sp e) m
| cminsel_effstep_skip_call: forall f k sp e m m',
is_call_cont k ->
Mem.free m sp 0 f.(fn_stackspace) = Some m' ->
cminsel_effstep g (FreeEffect m 0 (f.(fn_stackspace)) sp)
(CMinSel_State f Sskip k (Vptr sp Int.zero) e) m
(CMinSel_Returnstate Vundef k) m'
| cminsel_effstep_assign: forall f id a k sp e m v,
CminorSel.eval_expr g sp e m nil a v ->
cminsel_effstep g EmptyEffect (CMinSel_State f (Sassign id a) k sp e) m
(CMinSel_State f Sskip k sp (PTree.set id v e)) m
| cminsel_effstep_store: forall f chunk addr al b k sp e m vl v vaddr m',
CminorSel.eval_exprlist g sp e m nil al vl ->
CminorSel.eval_expr g sp e m nil b v ->
Op.eval_addressing g sp addr vl = Some vaddr ->
Mem.storev chunk m vaddr v = Some m' ->
cminsel_effstep g (StoreEffect vaddr (encode_val chunk v))
(CMinSel_State f (Sstore chunk addr al b) k sp e) m
(CMinSel_State f Sskip k sp e) m'
| cminsel_effstep_call:forall f optid sig a bl k sp e m vf vargs fd,
CminorSel.eval_expr_or_symbol g sp e m nil a vf ->
CminorSel.eval_exprlist g sp e m nil bl vargs ->
Genv.find_funct g vf = Some fd ->
funsig fd = sig ->
cminsel_effstep g EmptyEffect
(CMinSel_State f (Scall optid sig a bl) k sp e) m
(CMinSel_Callstate fd vargs (Kcall optid f sp e k)) m
| cminsel_effstep_tailcall: forall f sig a bl k sp e m vf vargs fd m',
CminorSel.eval_expr_or_symbol g (Vptr sp Int.zero) e m nil a vf ->
CminorSel.eval_exprlist g (Vptr sp Int.zero) e m nil bl vargs ->
Genv.find_funct g vf = Some fd ->
funsig fd = sig ->
Mem.free m sp 0 f.(fn_stackspace) = Some m' ->
cminsel_effstep g (FreeEffect m 0 (f.(fn_stackspace)) sp)
(CMinSel_State f (Stailcall sig a bl) k (Vptr sp Int.zero) e) m
(CMinSel_Callstate fd vargs (call_cont k)) m'
(* WE DO NOT TREAT BUILTINS | cminsel_effstep_builtin: forall f optid ef al k sp e m vl t v m', CminorSel.eval_exprlist g sp e m nil al vl -> external_call ef g vl m t v m' -> cminsel_effstep g (BuiltinEffect g (ef_sig ef) vl m) (CMinSel_State f (Sbuiltin optid ef al) k sp e) m (CMinSel_State f Sskip k sp (Cminor.set_optvar optid v e)) m' *)
| cminsel_effstep_seq: forall f s1 s2 k sp e m,
cminsel_effstep g EmptyEffect (CMinSel_State f (Sseq s1 s2) k sp e) m
(CMinSel_State f s1 (Kseq s2 k) sp e) m
| cminsel_effstep_ifthenelse:  forall f c s1 s2 k sp e m b,
CminorSel.eval_condexpr g sp e m nil c b ->
cminsel_effstep g EmptyEffect
(CMinSel_State f (Sifthenelse c s1 s2) k sp e) m
(CMinSel_State f (if b then s1 else s2) k sp e) m
| cminsel_effstep_loop: forall f s k sp e m,
cminsel_effstep g EmptyEffect
(CMinSel_State f (Sloop s) k sp e) m
(CMinSel_State f s (Kseq (Sloop s) k) sp e) m
| cminsel_effstep_block: forall f s k sp e m,
cminsel_effstep g EmptyEffect (CMinSel_State f (Sblock s) k sp e) m
(CMinSel_State f s (Kblock k) sp e) m
| cminsel_effstep_exit_seq: forall f n s k sp e m,
cminsel_effstep g EmptyEffect (CMinSel_State f (Sexit n) (Kseq s k) sp e) m
(CMinSel_State f (Sexit n) k sp e) m
| cminsel_effstep_exit_block_0: forall f k sp e m,
cminsel_effstep g EmptyEffect (CMinSel_State f (Sexit O) (Kblock k) sp e) m
(CMinSel_State f Sskip k sp e) m
| cminsel_effstep_exit_block_S: forall f n k sp e m,
cminsel_effstep g EmptyEffect (CMinSel_State f (Sexit (S n)) (Kblock k) sp e) m
(CMinSel_State f (Sexit n) k sp e) m
| cminsel_effstep_switch: forall f a cases default k sp e m n,
CminorSel.eval_expr g sp e m nil a (Vint n) ->
cminsel_effstep g EmptyEffect
(CMinSel_State f (Sswitch a cases default) k sp e) m
(CMinSel_State f (Sexit (Switch.switch_target n default cases)) k sp e) m
| cminsel_effstep_return_0: forall f k sp e m m',
Mem.free m sp 0 f.(fn_stackspace) = Some m' ->
cminsel_effstep g (FreeEffect m 0 (f.(fn_stackspace)) sp) (CMinSel_State f (Sreturn None) k (Vptr sp Int.zero) e) m
(CMinSel_Returnstate Vundef (call_cont k)) m'
| cminsel_effstep_return_1: forall f a k sp e m v m',
CminorSel.eval_expr g (Vptr sp Int.zero) e m nil a v ->
Mem.free m sp 0 f.(fn_stackspace) = Some m' ->
cminsel_effstep g (FreeEffect m 0 (f.(fn_stackspace)) sp)
(CMinSel_State f (Sreturn (Some a)) k (Vptr sp Int.zero) e) m
(CMinSel_Returnstate v (call_cont k)) m'
| cminsel_effstep_label: forall f lbl s k sp e m,
cminsel_effstep g EmptyEffect
(CMinSel_State f (Slabel lbl s) k sp e) m
(CMinSel_State f s k sp e) m
| cminsel_effstep_goto: forall f lbl k sp e m s' k',
find_label lbl f.(fn_body) (call_cont k) = Some(s', k') ->
cminsel_effstep g EmptyEffect
(CMinSel_State f (Sgoto lbl) k sp e) m
(CMinSel_State f s' k' sp e) m
| cminsel_effstep_internal_function: forall f vargs k m m' sp e,
Mem.alloc m 0 f.(fn_stackspace) = (m', sp) ->
Cminor.set_locals f.(fn_vars) (Cminor.set_params vargs f.(fn_params)) = e ->
cminsel_effstep g EmptyEffect
(CMinSel_Callstate (Internal f) vargs k) m
(CMinSel_State f f.(fn_body) k (Vptr sp Int.zero) e) m'
(*no external functions in coresteps! | cminsel_effstep_external_function: forall ef vargs k m t vres m', external_call ef g vargs m t vres m' -> cminsel_effstep g EmptyEffect (CMinSel_Callstate (External ef) vargs k) m (CMinSel_Returnstate vres k) m'*)
| cminsel_effstep_return: forall v optid f sp e k m,
cminsel_effstep g EmptyEffect
(CMinSel_Returnstate v (Kcall optid f sp e k)) m
(CMinSel_State f Sskip k sp (Cminor.set_optvar optid v e)) m
| cminsel_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) ->
cminsel_effstep g E c m c' m' ->
cminsel_effstep g EE c m c' m'.

(* Specifications: *)
Lemma cminselstep_effax1: forall (M : block -> Z -> bool) g c m c' m',
cminsel_effstep g M c m c' m' ->
(corestep cminsel_coop_sem g c m c' m' /\
Mem.unchanged_on (fun (b : block) (ofs : Z) => M b ofs = false) m m').
Lemma cminselstep_effax2: forall  g c m c' m',
corestep cminsel_coop_sem g c m c' m' ->
exists M, cminsel_effstep g M c m c' m'.