An instance of A <:< B witnesses that A is a subtype of B.
An instance of A <:< B witnesses that A is a subtype of B.
Requiring an implicit argument of the type A <:< B encodes
the generalized constraint A <: B.
To constrain any abstract type T that's in scope in a method's
argument list (not just the method's own type parameters) simply
add an implicit argument of type T <:< U, where U is the required
upper bound; or for lower-bounds, use: L <:< T, where L is the
required lower bound.
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.
In part contributed by Jason Zaugg.
- Type Params
- From
a type which is proved a subtype of
To- To
a type which is proved a supertype of
From
- See also
=:= for expressing equality constraints
- Example
sealed trait Option[+A] { // def flatten[B, A <: Option[B]]: Option[B] = ... // won't work, since the A in flatten shadows the class-scoped A. def flatten[B](implicit ev: A <:< Option[B]): Option[B] = if(isEmpty) None else ev(get) // Because (A <:< Option[B]) <: (A => Option[B]), ev can be called to turn the // A from get into an Option[B], and because ev is implicit, that call can be // left out and inserted automatically. }- Companion
- object
Value members
Abstract methods
Substitute To for From and From for To in the type F[To, From], given that F is contravariant in the first argument and covariant in the second.
Substitute To for From and From for To in the type F[To, From], given that F is contravariant in the first argument and covariant in the second.
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 subtyping relationship.
- Returns
ftf, but with a (potentially) different type
Concrete methods
If From <: To and To <: C, then From <: C (subtyping is transitive)
If From <: To and To <: C, then From <: C (subtyping is transitive)
Coerce a From into a 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.
- Value Params
- f
some value of type
From
- Returns
f, but with a (potentially) different type- Definition Classes
If From <: To and C <: From, then C <: To (subtyping is transitive)
If From <: To and C <: From, then C <: To (subtyping is transitive)
Lift this evidence over a covariant type constructor F.
Lift this evidence over a covariant type constructor F.
Lift this evidence over a contravariant type constructor F.
Lift this evidence over a contravariant type constructor F.
Substitute the From in the type F[From], where F is a covariant type constructor, for To.
Substitute the From in the type F[From], where F is a covariant 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 subtyping relationship.
- Returns
ff, but with a (potentially) different type
Substitute the To in the type F[To], where F is a contravariant type constructor, for From.
Substitute the To in the type F[To], where F is a contravariant 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 subtyping relationship.
- Returns
ft, but with a (potentially) different type