runarorama

import scalaz._, Scalaz._

// Adjunction between `F` and `G` means there is an
// isomorphism between `A => G[B]` and `F[A] => B`.
trait Adjunction[F[_],G[_]] {
  def leftAdjunct[A, B](a: A)(f: F[A] => B): G[B]
  def rightAdjunct[A, B](a: F[A])(f: A => G[B]): B
}

// Adjunction between free and forgetful functor.

Lysxia

{-# LANGUAGE DeriveFunctor, DeriveFoldable, DeriveTraversable, TypeFamilies, TemplateHaskell #-}

import Data.Functor.Foldable
import Data.Functor.Foldable.TH
import Data.Functor.Compose

-- Example type
data Exp
  = IntValue Int
  | Sum Exp Exp