Inductive csharpmin_effstep (g: Csharpminor.genv):  (block -> Z -> bool) ->
CSharpMin_core -> mem -> CSharpMin_core -> mem -> Prop :=
| csharpmin_effstep_skip_seq: forall f s k e le m,
csharpmin_effstep g EmptyEffect (CSharpMin_State f Sskip (Kseq s k) e le) m
(CSharpMin_State f s k e le) m
| csharpmin_effstep_skip_block: forall f k e le m,
csharpmin_effstep g EmptyEffect (CSharpMin_State f Sskip (Kblock k) e le) m
(CSharpMin_State f Sskip k e le) m
| csharpmin_effstep_skip_call: forall f k e le m m',
is_call_cont k ->
Mem.free_list m (blocks_of_env e) = Some m' ->
csharpmin_effstep g (FreelistEffect m (blocks_of_env e)) (CSharpMin_State f Sskip k e le) m
(CSharpMin_Returnstate Vundef k) m'
| csharpmin_effstep_set: forall f id a k e le m v,
eval_expr g e le m a v ->
csharpmin_effstep g EmptyEffect (CSharpMin_State f (Sset id a) k e le) m
(CSharpMin_State f Sskip k e (PTree.set id v le)) m
| csharpmin_effstep_store: forall f chunk addr a k e le m vaddr v m',
eval_expr g e le m addr vaddr ->
eval_expr g e le m a v ->
Mem.storev chunk m vaddr v = Some m' ->
csharpmin_effstep g (StoreEffect vaddr (encode_val chunk v))
(CSharpMin_State f (Sstore chunk addr a) k e le) m
(CSharpMin_State f Sskip k e le) m'
| csharpmin_effstep_call: forall f optid sig a bl k e le m vf vargs fd,
eval_expr g e le m a vf ->
eval_exprlist g e le m bl vargs ->
Genv.find_funct g vf = Some fd ->
funsig fd = sig ->
csharpmin_effstep g EmptyEffect (CSharpMin_State f (Scall optid sig a bl) k e le) m
(CSharpMin_Callstate fd vargs (Kcall optid f e le k)) m
(* WE DO NOT TREAT BUILTINS *)
(*  | csharpmin_effstep_builtin: forall f optid ef bl k e le m vargs t vres m', eval_exprlist g e le m bl vargs -> external_call ef g vargs m t vres m' -> csharpmin_effstep g (BuiltinEffect g (ef_sig ef) vargs m) (CSharpMin_State f (Sbuiltin optid ef bl) k e le) m (CSharpMin_State f Sskip k e (Cminor.set_optvar optid vres le)) m'*)
| csharpmin_effstep_seq: forall f s1 s2 k e le m,
csharpmin_effstep g EmptyEffect (CSharpMin_State f (Sseq s1 s2) k e le) m
(CSharpMin_State f s1 (Kseq s2 k) e le) m
| csharpmin_effstep_ifthenelse: forall f a s1 s2 k e le m v b,
eval_expr g e le m a v ->
Val.bool_of_val v b ->
csharpmin_effstep g EmptyEffect (CSharpMin_State f (Sifthenelse a s1 s2) k e le) m
(CSharpMin_State f (if b then s1 else s2) k e le) m
| csharpmin_effstep_loop: forall f s k e le m,
csharpmin_effstep g EmptyEffect (CSharpMin_State f (Sloop s) k e le) m
(CSharpMin_State f s (Kseq (Sloop s) k) e le) m
| csharpmin_effstep_block: forall f s k e le m,
csharpmin_effstep g EmptyEffect (CSharpMin_State f (Sblock s) k e le) m
(CSharpMin_State f s (Kblock k) e le) m
| csharpmin_effstep_exit_seq: forall f n s k e le m,
csharpmin_effstep g EmptyEffect (CSharpMin_State f (Sexit n) (Kseq s k) e le) m
(CSharpMin_State f (Sexit n) k e le) m
| csharpmin_effstep_exit_block_0: forall f k e le m,
csharpmin_effstep g EmptyEffect (CSharpMin_State f (Sexit O) (Kblock k) e le) m
(CSharpMin_State f Sskip k e le) m
| csharpmin_effstep_exit_block_S: forall f n k e le m,
csharpmin_effstep g EmptyEffect
(CSharpMin_State f (Sexit (S n)) (Kblock k) e le) m
(CSharpMin_State f (Sexit n) k e le) m
| csharpmin_effstep_switch: forall f a cases k e le m n,
eval_expr g e le m a (Vint n) ->
csharpmin_effstep g EmptyEffect (CSharpMin_State f (Sswitch a cases) k e le) m
(CSharpMin_State f (seq_of_lbl_stmt (select_switch n cases)) k e le) m
| csharpmin_effstep_return_0: forall f k e le m m',
Mem.free_list m (blocks_of_env e) = Some m' ->
csharpmin_effstep g (FreelistEffect m (blocks_of_env e)) (CSharpMin_State f (Sreturn None) k e le) m
(CSharpMin_Returnstate Vundef (call_cont k)) m'
| csharpmin_effstep_return_1: forall f a k e le m v m',
eval_expr g e le m a v ->
Mem.free_list m (blocks_of_env e) = Some m' ->
csharpmin_effstep g (FreelistEffect m (blocks_of_env e)) (CSharpMin_State f (Sreturn (Some a)) k e le) m
(CSharpMin_Returnstate v (call_cont k)) m'
| csharpmin_effstep_label: forall f lbl s k e le m,
csharpmin_effstep g EmptyEffect (CSharpMin_State f (Slabel lbl s) k e le) m
(CSharpMin_State f s k e le) m
| csharpmin_effstep_goto: forall f lbl k e le m s' k',
find_label lbl f.(fn_body) (call_cont k) = Some(s', k') ->
csharpmin_effstep g EmptyEffect (CSharpMin_State f (Sgoto lbl) k e le) m
(CSharpMin_State f s' k' e le) m
| csharpmin_effstep_internal_function: forall f vargs k m m1 e le,
list_norepet (map fst f.(fn_vars)) ->
list_norepet f.(fn_params) ->
list_disjoint f.(fn_params) f.(fn_temps) ->
alloc_variables empty_env m (fn_vars f) e m1 ->
bind_parameters f.(fn_params) vargs (create_undef_temps f.(fn_temps)) = Some le ->
csharpmin_effstep g EmptyEffect
(CSharpMin_Callstate (Internal f) vargs k) m
(CSharpMin_State f f.(fn_body) k e le) m1
(* no external call | csharpmin_effstep_external_function: forall ef vargs k m t vres m', external_call ef g vargs m t vres m' -> csharpmin_effstep g EmptyEffect (CSharpMin_Callstate (External ef) vargs k) m (CSharpMin_Returnstate vres k) m' *)
| csharpmin_effstep_return: forall v optid f e le k m,
csharpmin_effstep g EmptyEffect (CSharpMin_Returnstate v (Kcall optid f e le k)) m
(CSharpMin_State f Sskip k e (Cminor.set_optvar optid v le)) m
| csharpmin_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) ->
csharpmin_effstep g E c m c' m' ->
csharpmin_effstep g EE c m c' m'.

Lemma csharpminstep_effax1: forall (M : block -> Z -> bool) g c m c' m'
(H: csharpmin_effstep g M c m c' m'),
corestep csharpmin_coop_sem g c m c' m' /\
Mem.unchanged_on (fun (b : block) (ofs : Z) => M b ofs = false) m m'.