Add empty list and append natural transformations

1 files changed, 23 insertions, 0 deletions

diff --git a/NaturalTransformation/Instance/EmptyList.agda b/NaturalTransformation/Instance/EmptyList.agda
new file mode 100644
index 0000000..2164d6c
--- /dev/null
+++ b/NaturalTransformation/Instance/EmptyList.agda
@@ -0,0 +1,23 @@
+{-# OPTIONS --without-K --safe #-}
+
+module NaturalTransformation.Instance.EmptyList where
+
+import Function.Construct.Constant as Const
+
+open import Categories.NaturalTransformation using (NaturalTransformation; ntHelper)
+open import Categories.Functor using (Functor)
+open import Categories.Category.Instance.SingletonSet using (SingletonSetoid)
+open import Categories.Functor.Construction.Constant using (const)
+open import Data.List.Relation.Binary.Pointwise using (refl)
+open import Data.List using ([])
+open import Level using (0ℓ)
+open import Functor.Instance.List {0ℓ} {0ℓ} using (List)
+open import Relation.Binary using (Setoid)
+
+module List = Functor List
+
+⊤⇒[] : NaturalTransformation (const SingletonSetoid) List
+⊤⇒[] = ntHelper record
+    { η = λ X → Const.function SingletonSetoid (List.₀ X) []
+    ; commute = λ {_} {B} f → let module B = Setoid B in refl B.refl
+    }