(* *********************************************************************)
(*                                                                     *)
(*              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.     *)
(*                                                                     *)
(* *********************************************************************)
(** Pseudo-registers and register states.  This library defines the type of pseudo-registers (also known as "temporaries" in compiler literature) used in the RTL intermediate language.  We also define finite sets and finite maps over pseudo-registers. *)
Require FSetAVL.
Definition reg: Type := positive.
Module Reg.
Definition eq := peq.
Definition typenv := PMap.t typ.
End Reg.
(** Mappings from registers to some type. *)
Module Regmap := PMap.
Set Implicit Arguments.
Definition regmap_optget
(A: Type) (or: option reg) (dfl: A) (rs: Regmap.t A) : A :=
match or with
| None => dfl
| Some r => Regmap.get r rs
end.
Definition regmap_optset
(A: Type) (or: option reg) (v: A) (rs: Regmap.t A) : Regmap.t A :=
match or with
| None => rs
| Some r => Regmap.set r v rs
end.
Definition regmap_setres
(A: Type) (res: builtin_res reg) (v: A) (rs: Regmap.t A) : Regmap.t A :=
match res with
| BR r => Regmap.set r v rs
| _ => rs
end.
Notation "a # b" := (Regmap.get b a) (at level 1) : rtl.
Notation "a ## b" := (List.map (fun r => Regmap.get r a) b) (at level 1) : rtl.
Notation "a # b <- c" := (Regmap.set b c a) (at level 1, b at next level) : rtl.
Open Scope rtl.
(** Pointwise "less defined than" relation between register maps. *)
Definition regs_lessdef (rs1 rs2: Regmap.t val) : Prop :=
forall r, Val.lessdef (rs1#r) (rs2#r).

(* Specifications: *)
Lemma regs_lessdef_regs:
forall rs1 rs2, regs_lessdef rs1 rs2 ->
forall rl, Val.lessdef_list rs1##rl rs2##rl.
Lemma set_reg_lessdef:
forall r v1 v2 rs1 rs2,
Val.lessdef v1 v2 -> regs_lessdef rs1 rs2 -> regs_lessdef (rs1#r <- v1) (rs2#r <- v2).
Lemma set_res_lessdef:
forall res v1 v2 rs1 rs2,
Val.lessdef v1 v2 -> regs_lessdef rs1 rs2 ->
regs_lessdef (regmap_setres res v1 rs1) (regmap_setres res v2 rs2).