Define new type whose domain is subset of another type in Scala

Question

Using the example of even numbers, I would like to define the Even type whose domain is even integers using the function val isEven(i: Int): Boolean = i % 2 == 0

How would I do this in Scala 3 using the opaque keyword...

opaque type Even = ??? // use Int and filter using isEven or if that does not work,

type Even = ???

The rationale is to use functions as a building block to create new types, rather that complicating matters by using newtype as scala-even-type-number or using Refined Types

Answer 1

Something like the following:

object Evens:
  opaque type Even = Int

  object Even:
    def apply(i: Int): Even = if i % 2 == 0 then i else sys.error(s"$i is odd")
    def unsafe(i: Int): Even = i
    def safe(i: Int): Option[Even] = Option.when(i % 2 == 0)(i)

  extension (x: Even)
    def toInt: Int = x
    def +(y: Even): Even = x + y
    def *(y: Int):  Even = x * y
    def half: Int = x / 2
end Evens

import Evens.*
// val x: Even = 2 // doesn't compile
val x: Even = Even(2)
// val x: Even = Even(3) // RuntimeException: 3 is odd

https://docs.scala-lang.org/scala3/book/types-opaque-types.html

https://docs.scala-lang.org/scala3/reference/other-new-features/opaques.html

If you'd like Even(3) to fail at compile time rather than runtime then replace def apply(i: Int): Even = ... with one of the following implementations

import scala.compiletime.{error, erasedValue, constValue, codeOf, summonFrom}
import scala.compiletime.ops.int.%
import scala.compiletime.ops.any.{==, ToString}

inline def apply[I <: Int with Singleton](inline i: I): Even =
  inline erasedValue[I % 2] match
    case _: 0 => i
    case _    => error(codeOf(i) + " is odd")

inline def apply[I <: Int with Singleton](inline i: I): Even =
  inline if constValue[I % 2] == 0 then i else error(codeOf(i) + " is odd")

inline def apply[I <: Int with Singleton](inline i: I): Even = 
  inline erasedValue[I % 2 == 0] match
    case _: true => i
    case _       => error(constValue[ToString[I]] + " is odd")

inline def apply[I <: Int with Singleton](inline i: I): Even = 
  summonFrom {
    case _: (I % 2 =:= 0) => i
    case _                => error(constValue[ToString[I]] + " is odd")
  }

inline def apply(inline i: Int): Even =
  inline if i % 2 == 0 then i else error(codeOf(i) + " is odd")

https://docs.scala-lang.org/scala3/reference/metaprogramming/inline.html

https://docs.scala-lang.org/scala3/reference/metaprogramming/compiletime-ops.html