Type Members

1.  type <~<[-A, +B] = As[A, B]

   A convenient type alias for As, this declares that A is a subtype of B, and should be able to be a B is expected.

2.  type ===[A, B] = Is[A, B]

   A convenient type alias for Is, which declares that A is the same type as B.

3.  type >~>[+B, -A] = As[A, B]

   A flipped alias, for those used to their arrows running left to right

4.  sealed abstract class As[-A, +B] extends Serializable

   As substitutability: A better <:<

   As substitutability: A better <:<

   This class exists to aid in the capture proof of subtyping relationships, which can be applied in other context to widen other type

   A As B holds whenever A could be used in any negative context that expects a B. (e.g. if you could pass an A into any function that expects a B as input.)

   This code was ported directly from scalaz to cats using this version from scalaz: https://github.com/scalaz/scalaz/blob/a89b6d63/core/src/main/scala/scalaz/As.scala

   The original contribution to scalaz came from Jason Zaugg

5.  sealed abstract class AsInstances extends AnyRef
6.  abstract class Is[A, B] extends Serializable

   A value of A Is B is proof that the types A and B are the same.

   A value of A Is B is proof that the types A and B are the same. More powerfully, it asserts that they have the same meaning in all type contexts. This can be a more powerful assertion than A =:= B and is more easily used in manipulation of types while avoiding (potentially erroneous) coercions.

   A Is B is also known as Leibniz equality.

7.  type Leibniz[A, B] = Is[A, B]

   This type level equality represented by Is is referred to as "Leibniz equality", and it had the name "Leibniz" in the scalaz https://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz

8.  type Liskov[-A, +B] = As[A, B]

   The property that a value of type A can be used in a context expecting a B if A <~< B is referred to as the "Liskov Substitution Principle", which is named for Barbara Liskov: https://en.wikipedia.org/wiki/Barbara_Liskov