derivative/groups in kotlin

math.group.derivative.kotlin.kt

//diferentiable mathematical group/ring
//http://breandan.net/public/masters_thesis.pdf#page=58

interface Group<X : Group<X>>
object Top : Fun<Top>()
    
open class Const<T : Fun<T>>(val number : Double) : Fun<T>() { override fun toString() = "$number" }
class Sum<T : Fun<T>>(val left : Fun<T>, val right : Fun<T>) : Fun<T>() { override fun toString() = "($left + $right)" }
class Prod<T : Fun<T>>(val left : Fun<T>, val right : Fun<T>) : Fun<T>() { override fun toString() = "($left * $right)" }
class Var<T : Fun<T>>(val name: String) : Fun<T>() { override val vars: Set<Var<T>> = setOf(this) ; override fun toString() = "$name" }
class Zero<T : Fun<T>> : Const<T>(0.0)
class One<T : Fun<T>> : Const<T>(1.0)
    
sealed class Fun<X : Fun<X>>(open val vars: Set<Var<X>> = emptySet()) : Group<Fun<X>> {
    constructor(vararg fns: Fun<X>) : this(fns.flatMap { it.vars }.toSet())

    operator fun invoke(): Double = when(this) {
        is Top -> 0.0
        is Const -> this.number
        is Var -> 0.0
        is Prod -> left() * right()
        is Sum -> left() + right()
    }
    
    fun d(v : Var<X>) : Fun<X> = when(this) {
        is Top -> One()
        is Const -> Zero()
        is Var -> if (v == this) One() else Zero()
        is Prod -> left.d(v) * right + left * right.d(v)
        is Sum -> left.d(v) + right.d(v)        
    }
    
    operator fun plus(addend : Fun<X>) = Sum(this, addend)
    operator fun times(multiplicand : Fun<X>) = Prod(this, multiplicand)
}
fun main() {
    val x = Var<Top>("x")
    val result = (Const<Top>(2.0) * Sum(x, Const(3.0)))
    val dx = result.d(x)
    println("2x + 3 $result") ; println("d/dx( $dx )", ) ; println("= ${dx()}")
}