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sudori part 3

I’m hacking on a small project called sudori, an experimental sbt. The initial goal is to port the macro to Scala 3. It’s an exercise to take the macro apart and see if we can build it from the ground up. This an advanced area of Scala 2 and 3, and I’m finding my way around by trial and error. This is part 3.

It’s been a while since I wrote part 2, but in between I’ve written intro to Scala 3 macros, which is sort of a sudori prequel.

a letter from a reader

After part 2, I got a very helpful comment from Guillaume Martres, an EFPL Scala team member.

map, take 2

To recap the lambda expansion problem, to create a lambda expression we have to know the list of parameters upfront listed in MethodType(...). This means that we can’t create a placeholder symbol and mutably grow a lambda expression we do in sbt 1.x. Two workarounds that I proposed were:

This shows up in the context of rewriting setting macro into map etc:

someKey := { name.value + "!" }

This will expand to something like:

someKey <<=, (q1: String) => { q1 + "!" })

The general strategy would be:

  1. walk the tree once and collect all occurrences of x.value into inputs
  2. when there’s a single input, we’ll know to generate map with a lambda expression with a single parameter accepting q1: String
  3. walk the tree second time to replace all occurrences of x.value with a reference to a parameter

Here’s how we can perform step 1:

import scala.collection.mutable.ListBuffer

val inputBuf = ListBuffer[Input]()

// Called when transforming the tree to add an input.
//  For `qual` of type F[A], and a `selection` qual.value.
def record(name: String, tpe: TypeRepr, qual: Term, replace: Term) =
  convert[A](name, qual) transform { (tree: Term) =>
    inputBuf += Input(tpe, qual, freshName("q"))
val tx = transformWrappers(expr.asTerm, record)

See sudori part 1 on transformWrappers for details, but in this case it does the matching on x.value. The branching in step 2 looks like this:

def makeApp(body: Term, inputs: List[Input]): Expr[i.F[Effect[A]]] = inputs match
  case Nil      => pure(body)
  case x :: Nil => genMap(body, x)
  case xs       => ???

val tr = makeApp(inner(tx), inputBuf.toList)

The lambda creation part of genMap looks like this:

val lambda = Lambda(
  owner = Symbol.spliceOwner,
  tpe = tpe,
  rhsFn = (sym, params) => {
    val param = params.head.asInstanceOf[Term]
    // Called when transforming the tree to add an input.
    //  For `qual` of type F[A], and a `selection` qual.value,
    //  the call is addType(Type A, Tree qual)
    // The result is a Tree representing a reference to
    //  the bound value of the input.
    def substitute(name: String, tpe: TypeRepr, qual: Term, replace: Term) =
      convert[A](name, qual) transform { (tree: Term) =>
    transformWrappers(body.asTerm.changeOwner(sym), substitute)
).asExprOf[a => A1]

Note transformWrappers(...) is called again, this time with substitute instead of record. Since we no longer need to initialize a var, we no longer need Zero typeclass or null.asInstanceOf[A] either.


Consider the following setting expression:

someKey := {
  name.value + version.value + "!"

This will expand to something like:

someKey <<= i.mapN((wrap(name), wrap(version)), (q1: String, q2: String) => {
  q1 + q2 + "!"

This is the core feature and the tricky part of build.sbt settings macro. For one thing, mapN would have to be polymorphic in some way because a setting block in build.sbt could contain an arbitrary number of x.value, and when this macro was written for sbt 0.13, Scala 2.10 still had tuple 22 limitation. In sbt 0.13, mapN was defined as follows:

def app[K[L[x]], Z](in: K[M], f: K[Id] => Z)(implicit a: AList[K]): M[Z]


To abstract the arity problem, Mark Harrah created a typeclass called AList in 2012.

 * An abstraction over a higher-order type constructor `K[x[y]]` with the purpose of abstracting
 * over heterogeneous sequences like `KList` and `TupleN` with elements with a common type
 * constructor as well as homogeneous sequences `Seq[M[T]]`.
trait AList[K[F[x]]] {
  def transform[F1[_], F2[_]](value: K[F1], f: F1 ~> F2): K[F2]

  def traverse[F1[_], F2[_], P[_]](value: K[F1], f: F1 ~> (F2  P)#l)(implicit np: Applicative[F2]): F2[K[P]]

  def foldr[F1[_], A](value: K[F1], f: (F1[_], A) => A, init: A): A

  def toList[F1[_]](value: K[F1]): List[F1[_]] =
    foldr[F1, List[F1[_]]](value, _ :: _, Nil)

  def apply[F1[_], C](value: K[F1], f: K[Id] => C)(implicit a: Applicative[F1]): F1[C] =, traverse[F1, F1, Id](value, idK[F1])(a))

If I were to guess what “A” stands for here, it would be arity-generic. Given an arbitrary effect type F[_], AList holds on to them (F[A1], F[A2], etc) and fold them up if needed. There an instance of AList for empty, single, Tuple2[A1, A2], Tuple3[A1, A2, A3], Tuple11, and a data structure called KList, which is an HList that only holds on to F[a].

Mark wrote a series of blog posts on KList on Apocalisp in 2010:

One use of KList and the transform and down methods from 8b is to implement methods like zipWith for arbitrary tuple lengths.

I think zipWith is what we’d call mapN today. Fast forward to Scala 3, we might not need to create this abstraction because the built-in Tuple has improved.


For an introduction to Tuple’s arity-generic capability, see Vincenzo Bazzucchi’s Tuples bring generic programming to Scala 3:

In Scala 3, tuples gain power thanks to new operations, additional type safety and fewer restrictions, pointing in the direction of a construct called Heterogeneous Lists (HLists), one of the core data structures in generic programming.

… Scala 3 introduces types *:, EmptyTuple and NonEmptyTuple but also methods head and tail which allow us to define recursive operations on tuples.

For more detailed understanding of what’s going on under the hood, Tuple and runtime.Tuples are interesting reads. The key feature is that it lets us pretend as if tuples are constructed as nested pairs, even though internally it is using traditional Tuple2, Tuple3, etc.

As an example of arity-generic operation, .map is interesting.

scala> (1, "foo").map([A] => (a: A) => Option(a))
val res0: Option[Int] *: Option[String] *: EmptyTuple = (Some(1),Some(foo))

scala> (1, "foo", false).map([A] => (a: A) => Option(a))
val res1: Option[Int] *: Option[String] *: Option[Boolean] *: EmptyTuple = (Some(1),Some(foo),Some(false))

Here we see that .map() accepts a poly function, and returns (Option[Int], Option[String]) for the first and (Option[Int], Option[String], Option[Boolean]) for the next. The type signature of .map looks like this:

inline def map[F[_]](f: [t] => t => F[t]): Tuple.Map[this.type, F]

where Tuple.Map is a match type defined as follows:

/** Converts a tuple `(T1, ..., Tn)` to `(F[T1], ..., F[Tn])` */
type Map[Tup <: Tuple, F[_ <: Union[Tup]]] <: Tuple = Tup match {
  case EmptyTuple => EmptyTuple
  case h *: t => F[h] *: Map[t, F]

This Tuple.Map is for all intents and purposes same as Mark’s KList.

TupleUtil (AList for Tuple.Map)

If we can provide an implementation similar to AList for Tuple.Map, then that would give us somewhat direct translation of app.


For the purpose of this macro, I think the traverse in AList can be simplified to:

trait TupleUtil:

  def traverse[F1[_], F2[_]: Applicative, Tup <: Tuple](
      value: Tuple.Map[Tup, F1],
      f: [a] => F1[a] => F2[a]
  ): F2[Tup]
end TupleUtil

The instance looks like this:

object TupleUtil:
  def nil[Tup <: Tuple] = EmptyTuple.asInstanceOf[Tup]

  lazy val tuple: TupleUtil = new TupleUtil {
    override def traverse[F1[_], F2[_]: Applicative, Tup <: Tuple](
        value: Tuple.Map[Tup, F1],
        f: [a] => F1[a] => F2[a]
    ): F2[Tup] =
      val F2 = summon[Applicative[F2]]
      value match
        case _: Tuple.Map[EmptyTuple, F1] => F2.pure(nil[Tup])
        case (head: F1[x] @unchecked) *: (tail: Tuple.Map[Tail[Tup], F1] @unchecked) =>
          val tt = traverse[F1, F2, Tail[Tup]](tail, f)
          val g = (t: Tail[Tup]) => (h: x) => (h *: t).asInstanceOf[Tup]
          F2.apply[x, Tup](, tt), f(head))

end TupleUtil

The only weird thing I’m doing above is that using @unchecked to tell the compiler that Tuple.Map[Tupe, F1] is same thing as F1[x] *: Tuple.Map[Tail[Tup], F1].

traverse is so versatile people have been saying “The answer is traverse” since 2014:

In our case, given a tuple of (F1[A1], F1[A2], F1[A3], ...), traverse converts into F2[(A1, A2, A3)]. In other words, it’s able to make the relationship between F1 and tuple inside out. One quintessential usage of this idea is Future.sequence where List[Future[A]] becomes List[Future[A]], except in this case we have a heterogenous list.


Once we have traverse, mapN can be implemented on top of that.

def idPoly[F1[_]] = [a] => (p: F1[a]) => p

def mapN[F1[_]: Applicative, A, Tup <: Tuple](value: Tuple.Map[Tup, F1], f: Tup => A): F1[A] =
  summon[Applicative[F1]].map(f, traverse[F1, F1, Tup](value, idPoly[F1]))

Here’s how the test looks like:

test("mapN") {
  val tuple = (
    Future {
      println("started 1")
    Future {
      println("started 2")
  val f = (arg: (Int, String)) => arg._1.toString + "|" + arg._2
  val actual = tupleUtil.mapN[Future, String, (Int, String)](tuple, f)
  val result = Await.result(actual, Duration.Inf)
    result.toString == "1|foo"

In this example mapN is used to run two futures in parallel and aggregate the result.

Constructing tuples

Now that we’ve figured out mapN, let’s look into creating tuples programmatically using the list of Input we’ve collected.

To make a tuple, Expr provides a convenient API to do so, which automatically creates a tuple using the right runtime class:


Note that these input#term do not contain A, but i.F[A] instead, so the tuple of inputs would be Tuple.Map[(A1, A2, ...), i.F].


To generate mapN we end up using the raw Reflection API to manipulate the trees directly. This is because we need to pass br.inputTupleTypeRepr as a type parameter, but when you convert it into asType, I couldn’t quite convince the compiler that it satisfies <: Tuple.

def genMapN(body: Term, inputs: List[Input]): Expr[i.F[Effect[A]]] =
  def genMapN0[A1: Type](body: Expr[A1]): Expr[i.F[A1]] =
    val br = makeTuple(inputs)
    val lambdaTpe =
      MethodType(List("$p0"))(_ => List(br.inputTupleTypeRepr), _ => TypeRepr.of[A1])
    val lambda = ....
    val tupleMapRepr = TypeRepr
      .appliedTo(List(br.inputTupleTypeRepr, TypeRepr.of[i.F]))
    tupleMapRepr.asType match
      case '[tupleMap] =>
          .unique(instance.asTerm, "mapN")
          .appliedToTypes(List(br.inputTupleTypeRepr, TypeRepr.of[A1]))
          .appliedToArgs(List(typed[tupleMap](br.tupleExpr.asTerm), lambda))

  eitherTree match
    case Left(_) =>
    case Right(_) =>

The lambda part looks like this:

val lambdaTpe =
  MethodType(List("$p0"))(_ => List(br.inputTupleTypeRepr), _ => TypeRepr.of[A1])
val lambda = Lambda(
  owner = Symbol.spliceOwner,
  tpe = lambdaTpe,
  rhsFn = (sym, params) => {
    val p0 = params.head.asInstanceOf[Term]
    def substitute(name: String, tpe: TypeRepr, qual: Term, replace: Term) =
      convert[A](name, qual) transform { (tree: Term) =>
        val idx = inputs.indexWhere(input => input.term == qual)
          .unique(Ref(p0.symbol), "apply")
    transformWrappers(body.asTerm.changeOwner(sym), substitute, sym)

This constructs a lambda expression that takes a tuple as input and returns Effect[A]. Inside the lambda expression, we use transformWrappers to substitute wrapInit(...) with $p0(idx).

Overall, this can be used as follows:

test("getMapN") {
  val actual = contMapNMacro[Int]({
    val x = ContTest.wrapInit(List(1))
    val y = ContTest.wrapInit(List(2))
    x + y + 3
  assert(actual == List(6))

// This compiles away
def wrapInit[A](a: List[A]): A = ???

One of the key points is .changeOwner(sym) is called on body.asTerm so the symbols like val x and val y are re-owned by the lambda. For instance, the above example would expand as follows:

instance.mapN((wrapInit(List(1)), wrapInit(List(2))), ($p0: (Int, Int)) => {
  val x = $p0(0)
  val y = $p0(1)
  x + y + 3

With this macro, we now have Applicative do, which automatically lifts imperative code into parallel task processing code. This is analogous to async/await, but implemented as a user-land feature using a macro.