[Agda] Closed Predicate f in lib07
Sergei Meshveliani
mechvel at botik.ru
Fri Aug 30 20:38:30 CEST 2013
People,
I define
Closed : ∀ {a p} {A : Set a} → (A → Set p) → (A → A) → Set _
Closed P f = ∀ {x} → P x → P (f x)
to express that a predicate P is closed under f : A -> A,
Closed₂ : ∀ {a p} {A : Set a} → (A → Set p) → Op₂ A → Set _
Closed₂ P _*_ = ∀ {x y} → P x → P y → P (x * y)
to express that a predicate P is closed under _*_ : Op₂ A.
For example, a subsemigroup carrier membership is closed under the
semigroup operation _*_.
Now, the Standard library lib-0.7 has
_Respects_, _Respects₂_, _Preserves_ ...
Has it something to express Closed, Closed₂ ?
Thanks,
------
Sergei
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