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Joined 2026-09-21 Message
Incoming links: Stackable trait modification
The doubling mixin delegates with a transformed argument.For
trait DoublePlugin extends Stack {
override def push(x: Int): Unit = super.push(2 * x)
}A, the relevant Scala trait linearization is A, DoublePlugin, SumPlugin, Stack. A push first doubles the argument, then SumPlugin sees and sums that doubled value. The physical values are and the total is .For Equivalently,This is stackable trait modification: the order determines which arguments an outer mixin observes. In particular, the running-total specification from part (b) holds for
B, the Scala trait linearization is B, SumPlugin, DoublePlugin, Stack. SumPlugin sums the original argument, while its super.push doubles the stored value. The physical values are still , but the counter is . Hence the two lines printed are12
6A but does not survive the transforming inner mixin in B. With the given implementation, popping from B would subtract the doubled stored value, demonstrating why mixing individually sensible traits can break a combined representation invariant.Keep 26 cached counts, updating them after a successful delegated edit. Count exactly lowercase letters; the query alphabet does not make uppercase letters the same character.For an initially empty underlying document that stores inserted arguments unchanged, the representation invariant isInsertion increments precisely the inserted lowercase character's count. Deletion uses the returned character, avoiding an extra indexed read and decrementing the character actually removed. Updating after
trait CharTrackPlugIn extends Doc {
private val counts = Array.fill[Int](26)(0)
private def lower(x: Char): Boolean = 'a' <= x && x <= 'z'
abstract override def insert(x: Char, pos: Int): Unit = {
super.insert(x, pos)
if (lower(x)) counts(x - 'a') += 1
}
abstract override def delete(pos: Int): Char = {
val x = super.delete(pos)
if (lower(x)) counts(x - 'a') -= 1
x
}
def getCount(x: Char): Int = {
assert(lower(x))
counts(x - 'a')
}
}super means a rejected edit leaves the counts unchanged. Both the added update work and getCount use time complexity and fixed storage.The
abstract override methods implement a stackable trait modification: they require a concrete document implementation further along the delegation chain. The invariant above depends on subsequent layers preserving inserted characters. Part (d) deliberately composes a transforming layer that can break this assumption; that is the transform-sensitive trait frequency counter phenomenon.The rightmost trait intercepts insertion first. In
A, capitalization runs before counting, so the counter receives uppercase A and does not increment the lowercase count. In B, counting receives lowercase a, delegates to capitalization, and then increments the original lowercase argument's counter. Both concrete documents store uppercase A.The exact output isThis illustrates an order-sensitive stackable trait modification. In the second composition the cached count describes intercepted insertion arguments, and no longer the actual lowercase characters in the stored document. For example, deleting its uppercase
0
1A would not decrement the lowercase counter. A counter required to track actual contents under arbitrary transforming mixins would need a stronger composition contract or would inspect the stored character after insertion; such a change would alter the intended behavior of this example.Maintain one frequency count for each lowercase alphabet character. Update only after a successful delegated operation:For an initially empty underlying implementation that inserts the character it receives and returns the character actually deleted, the representation invariant isInsertion increases exactly one applicable frequency count, and deletion decreases the count of the returned character. Uppercase and nonletter characters contribute nothing. Exceptions from failed underlying operations leave the counters unchanged. The stackable trait modification uses
trait CharTrackPlugIn extends Doc {
private val counts = Array.fill[Int](26)(0)
private def lower(x: Char): Boolean = 'a' <= x && x <= 'z'
abstract override def insert(x: Char, pos: Int): Unit = {
super.insert(x, pos)
if (lower(x)) counts(x - 'a') += 1
}
abstract override def delete(pos: Int): Char = {
val old = super.delete(pos)
if (lower(old)) counts(old - 'a') -= 1
old
}
def getCount(x: Char): Int = {
assert('a' <= x && x <= 'z')
counts(x - 'a')
}
}abstract override because it delegates to a concrete implementation elsewhere in the mixin chain.[ref]The counters depend on the character seen by this trait. A later trait that transforms characters can break the stated underlying-operation assumption; part (d) deliberately exposes that order dependence.Apply capitalization before delegating insertion:Scala's
trait CapitalisePlugIn extends Doc {
abstract override def insert(x: Char, pos: Int): Unit = {
super.insert(x.toUpper, pos)
}
}Char.toUpper implements the hinted conversion and leaves ordinary nonletters unchanged. The stackable trait modification intercepts insertion without changing the position, result type or deletion behavior.