Λrrow Analysis supports the addition of invariants to types, but what happens when you already have a type and want to add information relative to it? And when may that situation arise?

Inline classes

Sometimes there’s a particular invariant we repeat over and over in our code. For example, a list not being empty, or a number being positive:

fun average(xs: List<Int>): Int {
  pre(xs.isNotEmpty()) { "list not empty" }

fun increment(x: Int): Int {
  pre(x > 0) { "non-negative" }
  return (x + 1).post({ it > 0 }) { "positive" }

In those cases it might be worth defining a new type where the invariant is encoded once and for all. Here we show those types corresponding to non-empty lists and positive numbers:

value class NonEmptyList<A>(val value: List<A>) {
  init { require(value.isNotEmpty()) { "not empty" } }

value class Positive(val value: Int) {
  init { require(value > 0) { "positive" } }

That way your pre- and post-conditions are encoded in the types themselves. Alas, in many cases you need to access the underlying value or apply the constructor manually.

fun average(xs: NonEmptyList<Int>): Int = TODO()

fun increment(x: Positive): Positive {
  return Positive(x.value + 1)

The good news is that the performance won’t suffer. The @JvmInline value at the beginning of the NonEmptyList and Positive classes declare those as inline classes. The Kotlin compiler substituted (“inlines”) any usage of inline classes by their underlying value, avoiding any additional heap allocations.


Declaring wrappers to encode invariants become increasingly important when working with collection types (lists, sets, maps). Imagine we want to define a function which increments a list of positive values:

// previous version of increment
fun increment(x: Int): Int {
  pre(x > 0) { "non-negative" }
  return (x + 1).post({ it > 0 }) { "positive" }

fun List<Int>.example() = map { increment(it) }

This will not work, as the analysis cannot guarantee that the value passed to increment inside map is indeed positive. Alas, there is no way to define a pre-condition which talks about all the elements in the list (technically, that would involve quantifiers, and this is not supported by the logic in Λrrow Analysis.) The solution is to use the corresponding wrapper type:

fun List<Positive>.example() = map { increment(it.value) }

Note that in this case we didn’t have to change our definition of increment to take Positive values. Instead, by unwrapping with it.value the condition it.value > 0 becomes available to the analysis, making the call to increment correct.

One important pattern in this case is the replacement of filters with operations that introduce the wrapper types. For example, the following is not accepted by Λrrow Analysis, because it is unaware of the predicate in filter.

fun moreExample(xs: List<Int>) = xs.filter { it > 0 }.example()

This case can be worked around by replacing filter with mapNotNull. Instead of simply removing the undesired elements, we also wrap the good ones in Positive.

fun moreExample(xs: List<Int>) = xs.mapNotNull {
  if (it > 0) Positive(it) else null

In the future we aim to introduce support for attaching invariants to types “on the spot”. Other analyzers, like LiquidHaskell, support this features by means of refinement types.

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