56 lines
1.5 KiB
Plaintext
56 lines
1.5 KiB
Plaintext
(*
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* Copyright 2014, NICTA
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*
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* This software may be distributed and modified according to the terms of
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* the BSD 2-Clause license. Note that NO WARRANTY is provided.
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* See "LICENSE_BSD2.txt" for details.
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*
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* @TAG(NICTA_BSD)
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*)
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theory EmptyFailLib
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imports
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"Monad_WP/NonDetMonad"
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HaskellLib_H
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begin
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(* Collect generic empty_fail lemmas here. naming convention is emtpy_fail_NAME.
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Unless there is a good reason, they should all be [intro!, simp] *)
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lemma empty_fail_when [simp, intro!]:
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"(P \<Longrightarrow> empty_fail x) \<Longrightarrow> empty_fail (when P x)"
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unfolding when_def by simp
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lemma empty_fail_bindD1:
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"empty_fail (a >>= b) \<Longrightarrow> empty_fail a"
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unfolding empty_fail_def bind_def
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apply (clarsimp simp: split_def image_image)
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apply (drule_tac x = s in spec)
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apply simp
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done
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lemma empty_fail_liftM [simp, intro!]:
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"empty_fail (liftM f m) = empty_fail m"
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unfolding liftM_def
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apply (rule iffI)
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apply (erule empty_fail_bindD1)
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apply (erule empty_fail_bind)
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apply simp
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done
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lemma empty_fail_assert [simp, intro!]:
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"empty_fail (assert P)"
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unfolding empty_fail_def assert_def
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by (simp add: return_def fail_def)
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lemma empty_fail_unless [intro!, simp]:
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"empty_fail f \<Longrightarrow> empty_fail (unless P f)"
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by (simp add: unless_def)
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lemma empty_fail_stateAssert [intro!, simp]:
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"empty_fail (stateAssert P l)"
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by (simp add: stateAssert_def empty_fail_def get_def assert_def
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return_def fail_def bind_def)
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end
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