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