Class =:=.=:=

sealed abstract class =:=[From, To] extends From <:< To with Serializable

An instance of A =:= B witnesses that the types A and B are equal. It also acts as a A <:< B, but not a B <:< A (directly) due to restrictions on subclassing.

In case of any confusion over which method goes in what direction, all the "Co" methods (including apply) go from left to right in the type ("with" the type), and all the "Contra" methods go from right to left ("against" the type). E.g., apply turns a From into a To, and substituteContra replaces the Tos in a type with Froms.

implicit class BufOps[A](private val buf: ArrayBuffer[A]) extends AnyVal {
  def inPlaceTranspose[E]()(implicit ev: A =:= ArrayBuffer[E]) = ???
  // Because ArrayBuffer is invariant, we can't make do with just a A <:< ArrayBuffer[E]
  // Getting buffers *out* from buf would work, but adding them back *in* wouldn't.
}

Abstract methods

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override def substituteBoth[F[_, _]](ftf: F[To, From]): F[From, To]

Substitute To for From and From for To in the type F[To, From], given that F is a type constructor of two arguments. Essentially swaps To and From in ftf's type.

Equivalent in power to each of substituteCo and substituteContra.

This method is impossible to implement without throwing or otherwise "cheating" unless From = To, so it ensures that this really represents a type equality.

Concrete methods

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def andThen[C](r: To =:= C): From =:= C

If From = To and To = C, then From = C (equality is transitive)

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override def apply(f: From): To

Coerce a From into a To. This is guaranteed to be the identity function.

This method is often called implicitly as an implicit A =:= B doubles as an implicit view A => B.

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def compose[C](r: C =:= From): C =:= To

If From = To and C = From, then C = To (equality is transitive)

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def flip: To =:= From

If From = To then To = From (equality is symmetric)

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override def liftCo[F[_]]: F[From] =:= F[To]

Lift this evidence over any type constructor F.

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override def liftContra[F[_]]: F[To] =:= F[From]

Lift this evidence over the type constructor F, but flipped.

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override def substituteCo[F[_]](ff: F[From]): F[To]

Substitute the From in the type F[From], where F is any type constructor, for To.

Equivalent in power to each of substituteBoth and substituteContra.

This method is impossible to implement without throwing or otherwise "cheating" unless From = To, so it ensures that this really represents a type equality.

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override def substituteContra[F[_]](ft: F[To]): F[From]

Substitute the To in the type F[To], where F is any type constructor, for From.

Equivalent in power to each of substituteBoth and substituteCo.

This method is impossible to implement without throwing or otherwise "cheating" unless From = To, so it ensures that this really represents a type equality.

Inherited methods

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def andThen[C](r: To <:< C): From <:< C

If From <: To and To <: C, then From <: C (subtyping is transitive)

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override def andThen[C](r: To => C): From => C

Composes two instances of Function1 in a new Function1, with this function applied first.

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def compose[C](r: C <:< From): C <:< To

If From <: To and C <: From, then C <: To (subtyping is transitive)

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override def compose[C](r: C => From): C => To

Composes two instances of Function1 in a new Function1, with this function applied last.

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override def toString(): String

Returns a string representation of the object.

The default representation is platform dependent.