Minor reformatting of https://gist.github.com/Baccata/8fea4427923d1fa0c180

TypeEqualityChecks.scala

package org.shape

object TypeEqualityChecks {

  trait Bool {
    type not <: Bool
  }
  trait True extends Bool {
    type not = False
  }
  trait False extends Bool {
    type not = True
  }

  //Defining
  def unexpected: Nothing = sys.error("Unexpected invocation")
  trait =:!=[A, B]

  implicit def neq[A, B]: A =:!= B = new =:!=[A, B] {}
  implicit def neqAmbig1[A]: A =:!= A = unexpected
  implicit def neqAmbig2[A]: A =:!= A = unexpected

  //Typeclass that SHOULD witness that two types are equal by "returning" a Bool type.
  trait TypeEquality[A, B] {
    type Out <: Bool
    def out: Boolean
  }

  //Implicit definitions
  object TypeEquality {
    implicit def eq[A, B](implicit eq: A =:= B) = new TypeEquality[A, B] { type Out = True; def out = true }
    implicit def neq[A, B](implicit eq: A =:!= B) = new TypeEquality[A, B] { type Out = False; def out = false }
  }

}

object TypeEqualityChecksApp extends App {

  import TypeEqualityChecks._

  val sii = implicitly[TypeEquality[Int, Int]]
  val sis = implicitly[TypeEquality[Int, String]]

  //This runs flawlessly
  println(sii.out)
  println(sis.out)

  //val checkTypes = implicitly[False =:= s.Out] // DOES NOT COMPILE
  //val checkTypes2 = implicitly[True =:= s.Out] // DOES NOT COMPILE

}