Category Theory for Programmers (Exercise solutions)

CategoryTheoryForProgrammersExercises.kt

//
// Category: The Essence of Composition
//

// id function
fun <T> id(a: T) = a

// compose function
fun <A, B, C> compose(a: (A) -> B, b: (B) -> C) = { x: A -> b(a(x)) }

// infix way of doing that
infix fun <A, B, C> ((A) -> B).then(b: (B) -> C) = { x: A -> b(this(x)) }

//
// Types and Functions
//

// memoize function
fun <A, B> ((A) -> B).memoize(): (A) -> B = object : (A) -> B {
    private val map = mutableMapOf<A, B>()
    override fun invoke(p1: A) = map.getOrPut(p1) { this@memoize(p1) }
}
// ::someFunction.memoize()(parameter)