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Joined 2026-09-21 Message
Incoming links: Trait
Mixin 2026-10-24
Reusable behavior composed into a host class in object-oriented programming, often through a trait. Scala allows one superclass and several mixed-in traits. Required abstract members let a mixin depend on host capabilities without fixing one concrete superclass; member conflicts and
super calls are resolved using the language's linearization rules.val square: Fun[Int, Int] = new Fun[Int, Int] {
override def apply(x: Int): Int = x * x
}Parametric polymorphism occurs because the generic trait is specialized by choosing its argument and result types. Subtype polymorphism occurs because the anonymous implementing software class is used through a
Fun[Int, Int] reference; calls to its apply operation use the object interface contract and dynamic dispatch. Multiplication itself is not the second polymorphism needed for this explanation.For values whose mathematical squares fit in a signed 32-bit integer, the result is the ordinary square. Outside that range, the supplied integer return type cannot represent every mathematical square, and the multiplication follows Scala integer-overflow behavior. An implementation requiring exact mathematical results for all integer inputs would need a wider result type or an explicit overflow exception.
Fun[Base, Derived] can safely supply a Fun[Base, Base] contract; Fun[Base, Base] cannot in general supply a Fun[Base, Derived] contract. The input obligation is unchanged, while a derived result satisfies every base-result promise. This is the covariant output rule of function subtyping.With the invariant printed trait, implement the safe view explicitly:
def widenResult(f: Fun[Base, Derived]): Fun[Base, Base] =
new Fun[Base, Base] {
def apply(x: Base): Base = f(x)
}Using the illustrative classes from part i, an unsafe substitution would let a client assume a derived-only operation on a result that is merely a base software object:
val broadResult = new Fun[Base, Base] {
def apply(x: Base): Base = new Base
}
def derivedResultClient(f: Fun[Base, Derived]): Int =
f(new Base).special()
// derivedResultClient(broadResult) must be rejected.The direct, variance-aware object interface that would express both safe directions is
trait Fun[-S, +T] { def apply(x: S): T }. Its object method consumes the contravariant parameter and produces the covariant parameter. This is an explicitly proposed variant of the printed invariant declaration, not an assumption that its annotations were already present.A function accepting every
Base can safely be used where only Derived inputs will be supplied. The reverse direction is unsafe. A Derived argument is already a valid Base argument; restricting the possible callers introduces no new obligation for the function. This is the contravariant input rule of function subtyping.The printed trait has generic type invariance, so Scala does not directly permit either parameter-changing assignment. The safe behavior can be exposed using an explicit adapter without changing that trait:
def restrictInput(f: Fun[Base, Base]): Fun[Derived, Base] =
new Fun[Derived, Base] {
def apply(x: Derived): Base = f(x)
}For the unsafe direction, take illustrative classes in which a derived software object has an extra operation:
class Base
class Derived extends Base { def special(): Int = 1 }
val narrow = new Fun[Derived, Base] {
def apply(x: Derived): Base = { x.special(); x }
}
def broadClient(f: Fun[Base, Base]): Base = f(new Base)
// broadClient(narrow) must be rejected.If that substitution were accepted, the client could pass an ordinary base software object to code that calls
special, which that software object does not support. The rejected call is intentional counterexample code, not a promised compilable application. Variance annotations are needed to make sound direct conversions part of the generic trait's declared subtyping relation.[ref]Scala 2.13 variance annotations specification. Variance Annotations: missing annotation is invariant; method-input positions reverse variance
Use the trait and node definition above. The reference to a “stack” in this part is a wording error: the declared class and operations implement a FIFO queue.
class ListQueue extends Queue[Int] {
private var first: QueueNode = null
private var last: QueueNode = null
private var size = 0
def enqueue(x: Int): Unit = {
require(size < Int.MaxValue, "queue size limit")
val fresh = new QueueNode(x, null)
if (last == null) first = fresh
else last.next = fresh
last = fresh
size += 1
}
def dequeue(): Int = {
require(first != null, "empty queue")
val answer = first.value
first = first.next
size -= 1
if (first == null) last = null
answer
}
def clear(): Unit = {
first = null
last = null
size = 0
}
def isEmpty: Boolean = size == 0
def length: Int = size
}Appending links the fresh node after the old tail, or establishes both endpoints when empty. Removing the head preserves the tail unless the final node was removed, in which case both endpoints become null. Clearing only discards the endpoint references; it need not visit or overwrite unreachable nodes. Thus all operations are in the usual pointer-operation/allocation cost model, with later garbage collection excluded from an individual operation's bound. The representation invariant and abstraction function show the specified sequence changes, including empty/singleton transitions.
Use a fixed-size count array and protected hooks defining a stable character-to-slot mapping. The default hooks count the ASCII lowercase interval. The document must start empty, and all subsequent edits must pass through the mixin methods, as they do for
new DocImp with CharCountPlugin.trait CharCountPlugin extends Doc {
protected def firstCounted: Char = 'a'
protected def numberCounted: Int = 26
protected def slot(ch: Char): Int = {
val k = ch.toInt - firstCounted.toInt
if (0 <= k && k < numberCounted) k else -1
}
private lazy val totals = Array.fill(numberCounted)(0)
abstract override def insert(pos: Int, ch: Char): Unit = {
val k = slot(ch)
super.insert(pos, ch)
if (k >= 0) totals(k) += 1
}
abstract override def delete(pos: Int): Char = {
val removed = super.delete(pos)
val k = slot(removed)
if (k >= 0) totals(k) -= 1
removed
}
def count(ch: Char): Int = {
val k = slot(ch)
require(k >= 0, "character is outside the counted alphabet")
totals(k)
}
}The additional representation invariant is that each array slot equals the number of corresponding characters in the current document. Initially all counts are zero. Each successful underlying edit changes exactly one relevant count, while a failed position check throws before any count is changed. Returning the actual deleted character lets deletion adjust the correct slot.
count takes time for the fixed alphabet, as do the mixin's additions to edit cost. The lazy array avoids reading subclass-overridden size hooks during trait construction; the hooks must remain stable. An extension can override the interval hooks, or override slot with another fixed finite mapping. This is stackable modification by a trait: abstract override permits the method to call the next implementation of super, supplied here by DocImp.[ref]With the completed default trait from part (a), the expression is well-typed and creates the empty complete multiset, provided the type
T is in scope. Every member has a concrete default, entries is empty, and every count is zero.A mixin is reusable behavior supplied by a trait and composed into a class in object-oriented programming. Scala allows only one direct superclass, so mixins allow several independently reusable capabilities without multiple concrete-class inheritance. A trait can provide implemented methods and require abstract members from its host class.
trait Named {
def name: String
}
trait Greeting extends Named {
def greeting: String = "Welcome, " + name
}
class Account(val name: String)
class WelcomedAccount(name: String) extends Account(name) with Greeting
val example = new WelcomedAccount("reader")
assert(example.greeting == "Welcome, reader")Here the single superclass supplies
name, and the mixin supplies the derived greeting. The same behavior can be mixed into another unrelated host that satisfies Named. Mixin composition uses a defined linearization and requires incompatible concrete member conflicts to be resolved; it does not make arbitrary combinations of concrete superclasses legal.[ref]Class Composition with Mixins in the Scala documentation. A class has one superclass and can include several traits
Scala 2026-10-24
A programming language supporting object-oriented programming and functional programming. Its traits support reusable mixin behavior, while type variance controls how parameterized types participate in subtyping. The Scala 2 and Scala 3 language versions differ in some syntax and typing details; examples should state the version relevant to a particular claim. Official documentation: docs.scala-lang.org
Trait 2026-10-24
A reusable type and collection of members that can be composed into a class in object-oriented programming. In Scala, a trait can declare required members and provide concrete implementations. Several traits can contribute mixin behavior to one class, subject to linearization and member-conflict rules.