(*to enable reuse of the lemmas eval_unop_valid and eval_binop_valid*)
(*Obtained from Cminor.state by deleting the memory components.*)
Inductive CSharpMin_core: Type :=
| CSharpMin_State:                      (**r Execution within a function *)
forall (f: function)              (**r currently executing function  *)
(s: stmt)                  (**r statement under consideration *)
(k: cont)                  (**r its continuation -- what to do next *)
(e: Csharpminor.env)                   (**r current local environment *)
(le: Csharpminor.temp_env),             (**r current temporary environment *)
CSharpMin_core
| CSharpMin_Callstate:                  (**r Invocation of a function *)
forall (f: fundef)                (**r function to invoke *)
(args: list val)           (**r arguments provided by caller *)
(k: cont),                  (**r what to do next  *)
CSharpMin_core
| CSharpMin_Returnstate:                (**r Return from a function *)
forall (v: val)                   (**r Return value *)
(k: cont),                  (**r what to do next *)
CSharpMin_core.
Definition ToState (q:CSharpMin_core) (m:mem): Csharpminor.state :=
match q with
CSharpMin_State f s k sp e => State f s k sp e m
| CSharpMin_Callstate f args k => Callstate f args k m
| CSharpMin_Returnstate v k => Returnstate v k m
end.
Definition FromState (c: Csharpminor.state) : CSharpMin_core * mem :=
match c with
State f s k sp e m => (CSharpMin_State f s k sp e, m)
| Callstate f args k m => (CSharpMin_Callstate f args k, m)
| Returnstate v k m => (CSharpMin_Returnstate v k, m)
end.
Definition CSharpMin_at_external (c: CSharpMin_core) : option (external_function * signature * list val) :=
match c with
| CSharpMin_State _ _ _ _ _ => None
| CSharpMin_Callstate fd args k => match fd with
Internal f => None
| External ef => Some (ef, ef_sig ef, args)
end
| CSharpMin_Returnstate v k => None
end.
Definition CSharpMin_after_external (vret: option val) (c: CSharpMin_core) : option CSharpMin_core :=
match c with
CSharpMin_Callstate fd args k =>
match fd with
Internal f => None
| External ef => match vret with
None => Some (CSharpMin_Returnstate Vundef k)
| Some v => Some (CSharpMin_Returnstate v k)
end
end
| _ => None
end.
Inductive CSharpMin_corestep (ge : genv) : CSharpMin_core -> mem -> CSharpMin_core ->  mem -> Prop :=
csharpmin_corestep_skip_seq: forall f s k e le m,
CSharpMin_corestep ge (CSharpMin_State f Sskip (Kseq s k) e le) m
(CSharpMin_State f s k e le) m
| csharpmin_corestep_skip_block: forall f k e le m,
CSharpMin_corestep ge (CSharpMin_State f Sskip (Kblock k) e le) m
(CSharpMin_State f Sskip k e le) m
| csharpmin_corestep_skip_call: forall f k e le m m',
is_call_cont k ->
Mem.free_list m (blocks_of_env e) = Some m' ->
CSharpMin_corestep ge (CSharpMin_State f Sskip k e le) m
(CSharpMin_Returnstate Vundef k) m'
| csharpmin_corestep_set: forall f id a k e le m v,
eval_expr ge e le m a v ->
CSharpMin_corestep ge (CSharpMin_State f (Sset id a) k e le) m
(CSharpMin_State f Sskip k e (PTree.set id v le)) m
| csharpmin_corestep_store: forall f chunk addr a k e le m vaddr v m',
eval_expr ge e le m addr vaddr ->
eval_expr ge e le m a v ->
Mem.storev chunk m vaddr v = Some m' ->
CSharpMin_corestep ge (CSharpMin_State f (Sstore chunk addr a) k e le) m
(CSharpMin_State f Sskip k e le) m'
| csharpmin_corestep_call: forall f optid sig a bl k e le m vf vargs fd,
eval_expr ge e le m a vf ->
eval_exprlist ge e le m bl vargs ->
Genv.find_funct ge vf = Some fd ->
funsig fd = sig ->
CSharpMin_corestep ge (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_corestep_builtin: forall f optid ef bl k e le m vargs t vres m', eval_exprlist ge e le m bl vargs -> external_call ef ge vargs m t vres m' -> CSharpMin_corestep ge (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_corestep_seq: forall f s1 s2 k e le m,
CSharpMin_corestep ge (CSharpMin_State f (Sseq s1 s2) k e le) m
(CSharpMin_State f s1 (Kseq s2 k) e le) m
| csharpmin_corestep_ifthenelse: forall f a s1 s2 k e le m v b,
eval_expr ge e le m a v ->
Val.bool_of_val v b ->
CSharpMin_corestep ge (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_corestep_loop: forall f s k e le m,
CSharpMin_corestep ge (CSharpMin_State f (Sloop s) k e le) m
(CSharpMin_State f s (Kseq (Sloop s) k) e le) m
| csharpmin_corestep_block: forall f s k e le m,
CSharpMin_corestep ge (CSharpMin_State f (Sblock s) k e le) m
(CSharpMin_State f s (Kblock k) e le) m
| csharpmin_corestep_exit_seq: forall f n s k e le m,
CSharpMin_corestep ge (CSharpMin_State f (Sexit n) (Kseq s k) e le) m
(CSharpMin_State f (Sexit n) k e le) m
| csharpmin_corestep_exit_block_0: forall f k e le m,
CSharpMin_corestep ge (CSharpMin_State f (Sexit O) (Kblock k) e le) m
(CSharpMin_State f Sskip k e le) m
| step_exit_block_S: forall f n k e le m,
CSharpMin_corestep ge (CSharpMin_State f (Sexit (S n)) (Kblock k) e le) m
(CSharpMin_State f (Sexit n) k e le) m
| csharpmin_corestep_switch: forall f a cases k e le m n,
eval_expr ge e le m a (Vint n) ->
CSharpMin_corestep ge (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_corestep_return_0: forall f k e le m m',
Mem.free_list m (blocks_of_env e) = Some m' ->
CSharpMin_corestep ge (CSharpMin_State f (Sreturn None) k e le) m
(CSharpMin_Returnstate Vundef (call_cont k)) m'
| csharpmin_corestep_return_1: forall f a k e le m v m',
eval_expr ge e le m a v ->
Mem.free_list m (blocks_of_env e) = Some m' ->
CSharpMin_corestep ge (CSharpMin_State f (Sreturn (Some a)) k e le) m
(CSharpMin_Returnstate v (call_cont k)) m'
| csharpmin_corestep_label: forall f lbl s k e le m,
CSharpMin_corestep ge (CSharpMin_State f (Slabel lbl s) k e le) m
(CSharpMin_State f s k e le) m
| csharpmin_corestep_goto: forall f lbl k e le m s' k',
find_label lbl f.(fn_body) (call_cont k) = Some(s', k') ->
CSharpMin_corestep ge (CSharpMin_State f (Sgoto lbl) k e le) m
(CSharpMin_State f s' k' e le) m
| csharpmin_corestep_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_corestep ge (CSharpMin_Callstate (Internal f) vargs k) m
(CSharpMin_State f f.(fn_body) k e le) m1
(* | csharpmin_corestep_external_function: forall ef vargs k m t vres m', external_call ef ge vargs m t vres m' -> step (Callstate (External ef) vargs k) m t (Returnstate vres k m') *)
| csharpmin_corestep_return: forall v optid f e le k m,
CSharpMin_corestep ge (CSharpMin_Returnstate v (Kcall optid f e le k)) m
(CSharpMin_State f Sskip k e (Cminor.set_optvar optid v le)) m.

Lemma CSharpMin_corestep_not_at_external:
forall ge m q m' q', CSharpMin_corestep ge q m q' m' ->
CSharpMin_at_external q = None.