Require Export Maps.
Inductive RTL_effstep (ge:genv):  (block -> Z -> bool) ->
RTL_core -> mem -> RTL_core -> mem -> Prop :=
| rtl_effstep_exec_Inop:
forall s f sp pc rs m pc',
(fn_code f)!pc = Some(Inop pc') ->
RTL_effstep ge EmptyEffect (RTL_State s f sp pc rs) m
(RTL_State s f sp pc' rs) m
| rtl_effstep_exec_Iop:
forall s f sp pc rs m op args res pc' v,
(fn_code f)!pc = Some(Iop op args res pc') ->
eval_operation ge sp op rs##args m = Some v ->
RTL_effstep ge EmptyEffect (RTL_State s f sp pc rs) m
(RTL_State s f sp pc' (rs#res <- v)) m
| rtl_effstep_exec_Iload:
forall s f sp pc rs m chunk addr args dst pc' a v,
(fn_code f)!pc = Some(Iload chunk addr args dst pc') ->
eval_addressing ge sp addr rs##args = Some a ->
Mem.loadv chunk m a = Some v ->
RTL_effstep ge EmptyEffect (RTL_State s f sp pc rs) m
(RTL_State s f sp pc' (rs#dst <- v)) m
| rtl_effstep_exec_Istore:
forall s f sp pc rs m chunk addr args src pc' a m',
(fn_code f)!pc = Some(Istore chunk addr args src pc') ->
eval_addressing ge sp addr rs##args = Some a ->
Mem.storev chunk m a rs#src = Some m' ->
RTL_effstep ge (StoreEffect a (encode_val chunk (rs#src)))
(RTL_State s f sp pc rs) m
(RTL_State s f sp pc' rs) m'
| rtl_effstep_exec_Icall:
forall s f sp pc rs m sig ros args res pc' fd,
(fn_code f)!pc = Some(Icall sig ros args res pc') ->
find_function ge ros rs = Some fd ->
funsig fd = sig ->
RTL_effstep ge EmptyEffect
(RTL_State s f sp pc rs) m
(RTL_Callstate (Stackframe res f sp pc' rs :: s) fd rs##args) m
| rtl_effstep_exec_Itailcall:
forall s f stk pc rs m sig ros args fd m',
(fn_code f)!pc = Some(Itailcall sig ros args) ->
find_function ge ros rs = Some fd ->
funsig fd = sig ->
Mem.free m stk 0 f.(fn_stacksize) = Some m' ->
RTL_effstep ge (FreeEffect m 0 (f.(fn_stacksize)) stk)
(RTL_State s f (Vptr stk Int.zero) pc rs) m
(RTL_Callstate s fd rs##args) m'
(* WE DO NOT TREAT BUILTINS | rtl_effstep_exec_Ibuiltin: forall s f sp pc rs m ef args res pc' t v m', (fn_code f)!pc = Some(Ibuiltin ef args res pc') -> external_call ef ge rs##args m t v m' -> RTL_effstep ge (BuiltinEffect ge (ef_sig ef) (rs##args) m) (RTL_State s f sp pc rs) m (RTL_State s f sp pc' (rs#res <- v)) m' *)
| rtl_effstep_exec_Icond:
forall s f sp pc rs m cond args ifso ifnot b pc',
(fn_code f)!pc = Some(Icond cond args ifso ifnot) ->
eval_condition cond rs##args m = Some b ->
pc' = (if b then ifso else ifnot) ->
RTL_effstep ge EmptyEffect
(RTL_State s f sp pc rs) m
(RTL_State s f sp pc' rs) m
| rtl_effstep_exec_Ijumptable:
forall s f sp pc rs m arg tbl n pc',
(fn_code f)!pc = Some(Ijumptable arg tbl) ->
rs#arg = Vint n ->
list_nth_z tbl (Int.unsigned n) = Some pc' ->
RTL_effstep ge EmptyEffect
(RTL_State s f sp pc rs) m
(RTL_State s f sp pc' rs) m
| rtl_effstep_exec_Ireturn:
forall s f stk pc rs m or m',
(fn_code f)!pc = Some(Ireturn or) ->
Mem.free m stk 0 f.(fn_stacksize) = Some m' ->
RTL_effstep ge (FreeEffect m 0 (f.(fn_stacksize)) stk)
(RTL_State s f (Vptr stk Int.zero) pc rs) m
(RTL_Returnstate s (regmap_optget or Vundef rs)) m'
| rtl_effstep_exec_function_internal:
forall s f args m m' stk,
Mem.alloc m 0 f.(fn_stacksize) = (m', stk) ->
RTL_effstep ge EmptyEffect
(RTL_Callstate s (Internal f) args) m
(RTL_State s
f
(Vptr stk Int.zero)
f.(fn_entrypoint)
(init_regs args f.(fn_params)))
m'
(*no external calls | rtl_effstep_exec_function_external: forall s ef args res t m m', external_call ef ge args m t res m' -> RTL_effstep ge (Callstate s (External ef) args) m t (Returnstate s res m')*)
| rtl_effstep_exec_return:
forall res f sp pc rs s vres m,
RTL_effstep ge EmptyEffect
(RTL_Returnstate (Stackframe res f sp pc rs :: s) vres) m
(RTL_State s f sp pc (rs#res <- vres)) m
| rtl_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) ->
RTL_effstep ge E c m c' m' ->
RTL_effstep ge EE c m c' m'.

(* Specifications: *)
Lemma rtl_eff_exec_Iload':
forall ge s f sp pc rs m chunk addr args dst pc' rs' a v,
(fn_code f)!pc = Some(Iload chunk addr args dst pc') ->
Op.eval_addressing ge sp addr rs##args = Some a ->
Mem.loadv chunk m a = Some v ->
rs' = (rs#dst <- v) ->
RTL_effstep ge EmptyEffect
(RTL_State s f sp pc rs) m
(RTL_State  s f sp pc' rs') m.
Lemma rtl_eff_exec_Iop':
forall g s f sp pc rs m op args res pc' rs' v,
(fn_code f)!pc = Some(Iop op args res pc') ->
Op.eval_operation g sp op rs##args m = Some v ->
rs' = (Registers.Regmap.set res v rs) ->
RTL_effstep g EmptyEffect (RTL_State s f sp pc rs) m
(RTL_State s f sp pc' rs') m.
Lemma rtl_effax1: forall (M : block -> Z -> bool) g c m c' m',
RTL_effstep g M c m c' m' ->
(corestep rtl_coop_sem g c m c' m' /\
Mem.unchanged_on (fun (b : block) (ofs : Z) => M b ofs = false) m m').
Lemma rtl_effax2: forall  g c m c' m',
corestep rtl_coop_sem g c m c' m' ->
exists M, RTL_effstep g M c m c' m'.