From e30376ce891d0710757c65e85a24e7d2550a37ed Mon Sep 17 00:00:00 2001 From: Sylvain Boulmé Date: Thu, 27 May 2021 13:49:35 +0200 Subject: cleaning BTL_SEtheory --- scheduling/BTL.v | 73 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 73 insertions(+) (limited to 'scheduling/BTL.v') diff --git a/scheduling/BTL.v b/scheduling/BTL.v index 6f699cd0..bf19f4ac 100644 --- a/scheduling/BTL.v +++ b/scheduling/BTL.v @@ -540,6 +540,79 @@ Proof. Qed. *) +(* * Reasoning modulo extensionality of [regset] into BTL semantics *) +Inductive equiv_stackframe: stackframe -> stackframe -> Prop := + | equiv_stackframe_intro res f sp pc rs1 rs2 + (EQUIV: forall r : positive, rs1 !! r = rs2 !! r): + equiv_stackframe (Stackframe res f sp pc rs1) (Stackframe res f sp pc rs2) + . + +Inductive equiv_state: state -> state -> Prop := + | State_equiv stack f sp pc rs1 m rs2 + (EQUIV: forall r, rs1#r = rs2#r): + equiv_state (State stack f sp pc rs1 m) (State stack f sp pc rs2 m) + | Call_equiv stk stk' f args m + (STACKS: list_forall2 equiv_stackframe stk stk'): + equiv_state (Callstate stk f args m) (Callstate stk' f args m) + | Return_equiv stk stk' v m + (STACKS: list_forall2 equiv_stackframe stk stk'): + equiv_state (Returnstate stk v m) (Returnstate stk' v m) + . + +Local Hint Constructors equiv_stackframe equiv_state: core. + +Lemma equiv_stackframe_refl stf: equiv_stackframe stf stf. +Proof. + destruct stf; eauto. +Qed. + +Lemma equiv_stack_refl stk: list_forall2 equiv_stackframe stk stk. +Proof. + Local Hint Resolve equiv_stackframe_refl: core. + induction stk; simpl; constructor; auto. +Qed. + +Lemma equiv_state_refl s: equiv_state s s. +Proof. + Local Hint Resolve equiv_stack_refl: core. + induction s; simpl; constructor; auto. +Qed. + +Lemma equiv_stackframe_trans stf1 stf2 stf3: + equiv_stackframe stf1 stf2 -> equiv_stackframe stf2 stf3 -> equiv_stackframe stf1 stf3. +Proof. + destruct 1; intros EQ; inv EQ; try econstructor; eauto. + intros; eapply eq_trans; eauto. +Qed. + +Lemma equiv_stack_trans stk1 stk2: + list_forall2 equiv_stackframe stk1 stk2 -> + forall stk3, list_forall2 equiv_stackframe stk2 stk3 -> + list_forall2 equiv_stackframe stk1 stk3. +Proof. + Local Hint Resolve equiv_stackframe_trans: core. + induction 1; intros stk3 EQ; inv EQ; econstructor; eauto. +Qed. + +Lemma equiv_state_trans s1 s2 s3: equiv_state s1 s2 -> equiv_state s2 s3 -> equiv_state s1 s3. +Proof. + Local Hint Resolve equiv_stack_trans: core. + destruct 1; intros EQ; inv EQ; econstructor; eauto. + intros; eapply eq_trans; eauto. +Qed. + +Lemma regmap_setres_eq (rs rs': regset) res vres: + (forall r, rs # r = rs' # r) -> + forall r, (regmap_setres res vres rs) # r = (regmap_setres res vres rs') # r. +Proof. + intros RSEQ r. destruct res; simpl; try congruence. + destruct (peq x r). + - subst. repeat (rewrite Regmap.gss). reflexivity. + - repeat (rewrite Regmap.gso); auto. +Qed. + + + (** TODO: est-ce qu'il faudrait déplacer ceci dans une librairie du genre "BTLlib" ? *) (** Matching BTL and RTL code -- cgit