Doc for SetKW

arrow-docs/docs/docs/datatypes/setkw/README.md

@@ -6,4 +6,54 @@ permalink: /docs/datatypes/setkw/
 
 ## SetKW
 
-TODO
+SetKW(Kinded Wrapper) is a higher kinded wrapper around the the Set collection interface. 
+
+It can be created from the Kotlin Set type with a convient `k()` function.
+
+```kotlin:ank
+import arrow.*
+import arrow.core.*
+import arrow.data.*
+
+setOf(1, 2, 5, 3, 2).k()
+```
+
+It can also be initialized with the following:
+
+```kotlin:ank
+SetKW(setOf(1, 2, 5, 3, 2))
+```
+or
+```kotlin:ank
+SetKW.pure(1)
+```
+
+given the following:
+```kotlin:ank
+val oldNumbers = setOf( -11, 1, 3, 5, 7, 9).k()
+val evenNumbers = setOf(-2, 4, 6, 8, 10).k()
+val integers = setOf(-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5).k()
+```
+SetKW derives the following typeclasses:
+
+[`Semigroup`](/docs/typeclasses/semigroupk/):
+```kotlin:ank
+val uniqueNaturalNumbers_1 = oldNumbers.combineK(evenNumbers.combineK(integers))
+uniqueNaturalNumbers_1
+```
+```kotlin:ank
+val uniqueNaturalNumbers_2 = oldNumbers.combineK(evenNumbers).combineK(integers)
+uniqueNaturalNumbers_2
+```
+[`Foldable`](/docs/typeclasses/foldable/):
+```kotlin:ank
+val sum_1 = uniqueNaturalNumbers_1.foldLeft(0){sum, number -> sum + (number * number)}
+val sum_2 = uniqueNaturalNumbers_2.foldLeft(0){sum, number -> sum + (number * number)}
+sum_1 == sum_2
+```
+[`Monoid`](/docs/typeclasses/monoidk/):
+```kotlin:ank
+val sum_3 = SetKW.monoid<Int>().combine(uniqueNaturalNumbers_1, SetKW.empty()).foldLeft(0){sum, number -> sum + (number * number)}
+val sum_4 = SetKW.monoid<Int>().combine(SetKW.empty(), uniqueNaturalNumbers_1).foldLeft(0){sum, number -> sum + (number * number)}
+sum_3 == sum_4
+```