Algebra

This package is part of the Axle domain specific language.

The axle.algebra package contains typeclasses for algebraic structures including Monoid, Functor, and Monad.

Monoid

  3 |+| 4                                         //> res3: Int = 7

  Monoid.checkAxiom1(3)                           //> res7: Boolean = true
  Monoid.checkAxiom2(3)                           //> res8: Boolean = true
  Monoid.checkAxiom3(2, 4, 5)                     //> res9: Boolean = true

Functor

  Functor.checkAxiom1(List(1, 2, 3))              //> res5: Boolean = true

  Functor.checkAxiom2(List(1, 2, 3), (x: Int) => x + 3, (y: Int) => y * 5)
                                                  //> res6: Boolean = true

Monad

  Monad.checkAxiom1(3, (x: Int) => List(x + 1))   //> res11: Boolean = true
  Monad.checkAxiom2(List(1, 2, 3))                //> res12: Boolean = true

  Monad.checkAxiom3(
    List(1, 2, 3),
    (x: Int) => List(x + 4),
    (x: Int) => List(x + 10))                     //> res13: Boolean = true