open Preamble

open Div_and_mod

open Jmeq

open Russell

open Bool

open Relations

open Nat

open Hints_declaration

open Core_notation

open Pts

open Logic

open Types

open List

open Util

open Extra_bool

open Coqlib

open Values

open FrontEndVal

open GenMem

open FrontEndMem

open Globalenvs

open String

open Sets

open Listb

open LabelledObjects

open BitVectorTrie

open Graphs

open I8051

open Order

open Registers

open CostLabel

open Hide

open Proper

open PositiveMap

open Deqsets

open ErrorMessages

open PreIdentifiers

open Errors

open Extralib

open Lists

open Identifiers

open Integers

open AST

open Division

open Exp

open Arithmetic

open Setoids

open Monad

open Option

open Extranat

open Vector

open FoldStuff

open BitVector

open Positive

open Z

open BitVectorZ

open Pointers

open ByteValues

open BackEndOps

open Joint

open ERTL

open Set_adt

open Fixpoints

val rl_included :
  (PreIdentifiers.identifier Set_adt.set, I8051.register Set_adt.set)
  Types.prod -> (PreIdentifiers.identifier Set_adt.set, I8051.register
  Set_adt.set) Types.prod -> Bool.bool

val register_lattice : Fixpoints.property_lattice

val rl_bottom : __

val rl_psingleton : Registers.register -> __

val rl_hsingleton : I8051.register -> __

val pairwise :
  ('a1 -> 'a1 -> 'a1) -> ('a2 -> 'a2 -> 'a2) -> ('a1, 'a2) Types.prod ->
  ('a1, 'a2) Types.prod -> ('a1, 'a2) Types.prod

val rl_join : __ -> __ -> __

val rl_diff : __ -> __ -> __

val defined : AST.ident List.list -> Joint.joint_statement -> __

val ret_regs : I8051.register Set_adt.set

val rl_arg : Joint.psd_argument -> __

val used :
  AST.ident List.list -> Joint.joint_statement -> (Registers.register
  Set_adt.set, I8051.register Set_adt.set) Types.prod

val eliminable_step :
  AST.ident List.list -> __ -> Joint.joint_step -> Bool.bool

val eliminable :
  AST.ident List.list -> __ -> Joint.joint_statement -> Bool.bool

val statement_semantics :
  AST.ident List.list -> Joint.joint_statement -> __ -> __

val livebefore :
  AST.ident List.list -> Joint.joint_internal_function -> Fixpoints.valuation
  -> Fixpoints.valuation

val liveafter :
  AST.ident List.list -> Joint.joint_internal_function ->
  PreIdentifiers.identifier -> Fixpoints.valuation -> __

val analyse_liveness :
  Fixpoints.fixpoint_computer -> AST.ident List.list ->
  Joint.joint_internal_function -> Fixpoints.fixpoint

type vertex = (Registers.register, I8051.register) Types.sum

val plives : Registers.register -> __ -> Bool.bool

val hlives : I8051.register -> __ -> Bool.bool

val lives : vertex -> __ -> Bool.bool