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lib/monads: style cleanup in Empty_Fail 

Mostly contraction and some refactoring.

Signed-off-by: Gerwin Klein <gerwin.klein@proofcraft.systems>
This commit is contained in:
Gerwin Klein 2023-01-30 09:38:12 +11:00
parent e51723ce5a
commit b93335745e
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GPG Key ID: 20A847CE6AB7F5F3
1 changed files with 13 additions and 16 deletions
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29
lib/Monads/Empty_Fail.thy
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@ -55,23 +55,26 @@ lemma empty_fail_select_f [simp]:
lemma empty_fail_bind [simp]:
"\<lbrakk> empty_fail a; \<And>x. empty_fail (b x) \<rbrakk> \<Longrightarrow> empty_fail (a >>= b)"
apply (simp add: bind_def empty_fail_def split_def)
apply clarsimp
apply (case_tac "fst (a s) = {}")
apply blast
apply (clarsimp simp: ex_in_conv [symmetric])
done
by (fastforce simp: bind_def empty_fail_def split_def)
lemma empty_fail_return [simp, wp]:
"empty_fail (return x)"
by (simp add: empty_fail_def return_def)
lemma empty_fail_error_bits[simp]:
"empty_fail (returnOk v)"
"empty_fail (throwError v)"
"empty_fail (liftE f) = empty_fail f"
by (fastforce simp: returnOk_def throwError_def liftE_def empty_fail_def bind_def return_def)+
lemma empty_fail_lift:
"\<lbrakk> \<And>x. empty_fail (f x) \<rbrakk> \<Longrightarrow> empty_fail (lift f x)"
unfolding lift_def
by (auto split: sum.split)
lemma empty_fail_bindE:
"\<lbrakk> empty_fail f; \<And>rv. empty_fail (g rv) \<rbrakk> \<Longrightarrow> empty_fail (f >>=E g)"
apply (simp add: bindE_def)
apply (erule empty_fail_bind)
apply (simp add: lift_def throwError_def split: sum.split)
done
by (simp add: bindE_def empty_fail_lift)
lemma empty_fail_If:
"\<lbrakk> P \<Longrightarrow> empty_fail f; \<not> P \<Longrightarrow> empty_fail g \<rbrakk> \<Longrightarrow> empty_fail (if P then f else g)"
@ -111,12 +114,6 @@ lemma empty_fail_gets_map[simp]:
"empty_fail (gets_map f p)"
unfolding gets_map_def by simp
lemma empty_fail_error_bits[simp]:
"empty_fail (returnOk v)"
"empty_fail (throwError v)"
"empty_fail (liftE f) = empty_fail f"
by (fastforce simp: returnOk_def throwError_def liftE_def empty_fail_def bind_def return_def)+
lemma empty_fail_whenEs:
"empty_fail f \<Longrightarrow> empty_fail (whenE P f)"
"empty_fail f \<Longrightarrow> empty_fail (unlessE P f)"