(* *********************************************************************)
(*                                                                     *)
(*              The Compcert verified compiler                         *)
(*                                                                     *)
(*          Xavier Leroy, INRIA Paris-Rocquencourt                     *)
(*                                                                     *)
(*  Copyright Institut National de Recherche en Informatique et en     *)
(*  Automatique.  All rights reserved.  This file is distributed       *)
(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
(*                                                                     *)
(* *********************************************************************)
(** Correctness proof for Asm generation: machine-independent framework *)
Require Intv.
(** * Processor registers and register states *)
Hint Extern 2 (_ <> _) => congruence: asmgen.
Hint Resolve preg_of_data: asmgen.
Hint Resolve data_diff: asmgen.
Hint Resolve preg_of_not_SP preg_of_not_PC: asmgen.
Fixpoint preg_notin (r: preg) (rl: list mreg) : Prop :=
match rl with
| nil => True
| r1 :: nil => r <> preg_of r1
| r1 :: rl => r <> preg_of r1 /\ preg_notin r rl
end.
Remark preg_notin_charact:
forall r rl,
preg_notin r rl <-> (forall mr, In mr rl -> r <> preg_of mr).
(** * Agreement between Mach registers and processor registers *)
Record agree (ms: Mach.regset) (sp: val) (rs: Asm.regset) : Prop := mkagree {
agree_sp: rs#SP = sp;
agree_sp_def: sp <> Vundef;
agree_mregs: forall r: mreg, Val.lessdef (ms r) (rs#(preg_of r))
}.
(** Preservation of register agreement under various assignments. *)

Lemma agree_set_undef_mreg:
forall ms sp rs r v rl rs',
agree ms sp rs ->
Val.lessdef v (rs'#(preg_of r)) ->
(forall r', data_preg r' = true -> r' <> preg_of r -> preg_notin r' rl -> rs'#r' = rs#r') ->
agree (Regmap.set r v (Mach.undef_regs rl ms)) sp rs'.