# HG changeset patch
# User Yasutaka Higa <e115763@ie.u-ryukyu.ac.jp>
# Date 1421728512 -32400
# Node ID 26e64661b96951e3948df24645caf1b82fba07a0
# Parent  7c7659d4521d5cccb3ccbb8f9fa16519b38668c3
Add example for Natural Transformation (head)

diff -r 7c7659d4521d -r 26e64661b969 sandbox/FunctorExample.agda
--- a/sandbox/FunctorExample.agda	Tue Jan 20 10:51:33 2015 +0900
+++ b/sandbox/FunctorExample.agda	Tue Jan 20 13:35:12 2015 +0900
@@ -127,4 +127,24 @@
 
 concat-is-natural-transformation : {l : Level} -> NaturalTransformation (\A -> List (List A)) List
                                    {list-fmap ∙ list-fmap} {list-fmap {l}} concat
-concat-is-natural-transformation = record {commute = concat-commute}
\ No newline at end of file
+concat-is-natural-transformation = record {commute = concat-commute}
+
+
+data NonEmptyList {l : Level} (A : Set l)  : Set l where
+  val : A -> NonEmptyList A
+  con : A -> NonEmptyList A -> NonEmptyList A
+
+head : {l : Level} {A : Set l} -> NonEmptyList A -> A
+head (val x)   = x
+head (con x _) = x 
+
+nel-fmap : {l : Level} {A B : Set l} -> (A -> B) -> NonEmptyList A -> NonEmptyList B
+nel-fmap f (val x)   = val (f x)
+nel-fmap f (con x l) = con (f x) (nel-fmap f l)
+
+head-commute : {l : Level} {A B : Set l} -> (f : A -> B) (x : NonEmptyList A) -> head (nel-fmap f x) ≡ id f (head x)
+head-commute f (val x) = refl
+head-commute f (con x v) = refl
+
+head-is-nt : {l : Level} {A : Set l} -> NaturalTransformation {l} NonEmptyList id {nel-fmap} {id} head
+head-is-nt = record { commute = head-commute }
\ No newline at end of file