(* Title: HOL/Word/Bits.thy
Author: Author: Brian Huffman, PSU and Gerwin Klein, NICTA
*)
section \<open>Syntactic classes for bitwise operations\<close>
theory Bits
imports Main
begin
class bit =
fixes bitNOT :: "'a \<Rightarrow> 'a" ("NOT _" [70] 71)
and bitAND :: "'a \<Rightarrow> 'a \<Rightarrow> 'a" (infixr "AND" 64)
and bitOR :: "'a \<Rightarrow> 'a \<Rightarrow> 'a" (infixr "OR" 59)
and bitXOR :: "'a \<Rightarrow> 'a \<Rightarrow> 'a" (infixr "XOR" 59)
text \<open>
We want the bitwise operations to bind slightly weaker
than \<open>+\<close> and \<open>-\<close>, but \<open>~~\<close> to
bind slightly stronger than \<open>*\<close>.
\<close>
text \<open>Testing and shifting operations.\<close>
class bits = bit +
fixes test_bit :: "'a \<Rightarrow> nat \<Rightarrow> bool" (infixl "!!" 100)
and lsb :: "'a \<Rightarrow> bool"
and set_bit :: "'a \<Rightarrow> nat \<Rightarrow> bool \<Rightarrow> 'a"
and set_bits :: "(nat \<Rightarrow> bool) \<Rightarrow> 'a" (binder "BITS " 10)
and shiftl :: "'a \<Rightarrow> nat \<Rightarrow> 'a" (infixl "<<" 55)
and shiftr :: "'a \<Rightarrow> nat \<Rightarrow> 'a" (infixl ">>" 55)
class bitss = bits +
fixes msb :: "'a \<Rightarrow> bool"
end