Laziness and partial application

catsPartial.scala

import cats.data.Kleisli
import cats.Eval

type Partial[A, B] = Kleisli[Eval, A, B]

object Partial{
  def apply[A, S, B](f: (S, A) => B)(s: Eval[S]): Partial[A,B] = left(f)(s)
  def right[A, S, B](f: (A, S) => B)(s: Eval[S]): Partial[A, B] = Kleisli(a => s.map(f(a, _)))
  def left[A, S, B](f: (S, A) => B)(s: Eval[S]): Partial[A, B] = Kleisli(a => s.map(f(_, a)))
}

partial.scala

//lazy partial application
class Partial[S, -A, +B](f: (S, A) => B, s: => S) extends (A => B){
  def apply[AA >: A](a: AA) = f(s, a)
  def map[C](g: B => C) = new Partial({ (s, a) => g(f(s, a)) }, s)
  def flatMap[C](g: B => Partial[S, A, C]) = new Partial({ (s, a) => g(f(s, a)).apply(a) }, s)
}

object Partial{
  def apply[S, A, B](f: (S, A) => B)(s: => S) = new Partial(f, s)
  def left[S, A, B](f: (S, A) => B)(s: => S) = apply(s)(f)
  def right[S, A, B](f: (A, S) => B)(s: => S) = apply{ (s, a) => f(a, s) }(s)
}