prefer canonically oriented lists of bits and more direct characterizations in definitions
(* Title: HOL/Word/Bit_Comprehension.thy
Author: Brian Huffman, PSU; Jeremy Dawson and Gerwin Klein, NICTA
*)
section \<open>Comprehension syntax for bit expressions\<close>
theory Bit_Comprehension
imports Bits_Int
begin
class bit_comprehension = semiring_bits +
fixes set_bits :: "(nat \<Rightarrow> bool) \<Rightarrow> 'a" (binder "BITS " 10)
instantiation int :: bit_comprehension
begin
definition
"set_bits f =
(if \<exists>n. \<forall>n'\<ge>n. \<not> f n' then
let n = LEAST n. \<forall>n'\<ge>n. \<not> f n'
in horner_sum of_bool 2 (map f [0..<n])
else if \<exists>n. \<forall>n'\<ge>n. f n' then
let n = LEAST n. \<forall>n'\<ge>n. f n'
in signed_take_bit n (horner_sum of_bool 2 (map f [0..<n] @ [True]))
else 0 :: int)"
instance ..
end
lemma int_set_bits_K_False [simp]: "(BITS _. False) = (0 :: int)"
by (simp add: set_bits_int_def)
lemma int_set_bits_K_True [simp]: "(BITS _. True) = (-1 :: int)"
by (auto simp add: set_bits_int_def bl_to_bin_def)
end