Module RTLpathSE_simplify

Require Import Coqlib Floats Values Memory.
Require Import Integers.
Require Import Op Registers.
Require Import RTLpathSE_theory.
Require Import RTLpathSE_simu_specs.

Target op simplifications using "fake" values

Definition target_op_simplify (op: operation) (lr: list reg) (hst: hsistate_local): option hsval :=
  None.

Definition target_cbranch_expanse (prev: hsistate_local) (cond: condition) (args: list reg) : option (condition * list_hsval) :=
  None.


Lemma target_op_simplify_correct op lr hst fsv ge sp rs0 m0 st args m: forall
   (H: target_op_simplify op lr hst = Some fsv)
   (REF: hsilocal_refines ge sp rs0 m0 hst st)
   (OK0: hsok_local ge sp rs0 m0 hst)
   (OK1: seval_list_sval ge sp (list_sval_inj (map (si_sreg st) lr)) rs0 m0 = Some args)
   (OK2: seval_smem ge sp (si_smem st) rs0 m0 = Some m),
   seval_sval ge sp (hsval_proj fsv) rs0 m0 = eval_operation ge sp op args m.
Proof.
  unfold target_op_simplify; simpl.
  intros H (LREF & SREF & SREG & SMEM) ? ? ?.
  congruence.
Qed.

Lemma target_cbranch_expanse_correct hst c l ge sp rs0 m0 st c' l': forall
  (TARGET: target_cbranch_expanse hst c l = Some (c', l'))
  (LREF : hsilocal_refines ge sp rs0 m0 hst st)
  (OK: hsok_local ge sp rs0 m0 hst),
  seval_condition ge sp c' (hsval_list_proj l') (si_smem st) rs0 m0 =
  seval_condition ge sp c (list_sval_inj (map (si_sreg st) l)) (si_smem st) rs0 m0.
Proof.
  unfold target_cbranch_expanse, seval_condition; simpl.
  intros H (LREF & SREF & SREG & SMEM) ?.
  congruence.
Qed.
Global Opaque target_op_simplify.
Global Opaque target_cbranch_expanse.