shapeless HList to TupleN where the tuple shape need not exactly match the HList shape

Question

I would like to create the equivalent of:

def toTupleN[A1, ..., AN, L <: HList](l: L): TupleN[A1, ..., AN]

Code using toTupleN should compile only when there is exactly one N combination of values in l that the tuple could be created from. Anything else should generate a compile-time error. Available implicit conversions should be taken into account. Note that there are no restrictions on the size of l or the ordering of values in it.

Example:

val l = 23 :: (1, "wibble") :: (2, "wobble") :: "foo" :: HNil
// l: shapeless.::[Int,shapeless.::[(Int, String),shapeless.::[(Int, String),shapeless.::[String,shapeless.HNil]]]] = 23 :: (1,wibble) :: (2,wobble) :: foo :: HNil

val t2: (String, Int) = toTuple2(l)
// t2: (String, Int) = (foo,23)

val nope: (String, String) = toTuple2(l)
// Compiler error because no combination of l's values can create nope

val nein: ((Int, String)) = toTuple2(l)
// Another compiler error because there is more than one way l's values can create nein

This question arose from the answer to the following question. The more general machinery in this question could be used to both create data structures and call any standard function (whose arguments are of different types) using FunctionN#tupled.

Update:

Some examples to define the desired behavior with subtypes:

trait A
trait B extends A
trait C extends A

val a: A
val b: B
val c: C

toTuple2[(A, Int)](5 :: b :: HNil)      // (b, 5): subtypes match supertypes when there is no exact match
toTuple2[(A, Int)](5 :: b :: a :: HNil) // (a, 5): only one exact match is available
toTuple2[(A, Int)](5 :: a :: a :: HNil) // compile error: more than one exact match is available
toTuple2[(A, Int)](5 :: b :: c :: HNil) // compile error: more than one inexact match is available

Answer 1

I haven't been able to make target type inference work out quite the way you wanted, but as compensation I've generalized to an arbitrary product type via shapeless's Generic,

import shapeless._, ops.hlist._, test._

object Demo {
  trait UniqueSelect[L <: HList, M <: HList] {
    def apply(l: L): M
  }

  object UniqueSelect {
    implicit def hnil[L <: HList]: UniqueSelect[L, HNil] =
      new UniqueSelect[L, HNil] {
        def apply(l: L): HNil = HNil
      }

    implicit def hcons[L <: HList, H, T <: HList, S <: HList]
      (implicit
        pt: Partition.Aux[L, H, H :: HNil, S],
        ust: UniqueSelect[S, T]
      ): UniqueSelect[L, H :: T] =
      new UniqueSelect[L, H :: T] {
        def apply(l: L): H :: T = {
          val (h :: HNil, s) = pt(l)
          h :: ust(s)
        }
      }
  }

  def toProductUniquely[P <: Product] = new ToProductUniquely[P]
  class ToProductUniquely[P <: Product] {
    def apply[L <: HList, M <: HList](l: L)
      (implicit gen: Generic.Aux[P, M], up: UniqueSelect[L, M]): P =
        gen.from(up(l))
  }

  val l = 23 :: (1, "wibble") :: (2, "wobble") :: "foo" :: HNil

  val t2 = toProductUniquely[(String, Int)](l)
  typed[(String, Int)](t2)
  assert(t2 == ("foo", 23))

  illTyped("""
  toProductUniquely[(String, String)](l)
  """)

  illTyped("""
  toProductUniquely[Tuple1[(Int, String)]](l)
  """)
}

Update 1

Adding support for the selection being satisfied by subtypes of the requested types is fairly straightforward if we say that where we have types A and B <: A then the selection of A from A :: B :: HNil is ambiguous because both elements conform to A. This can be done by adding a SubtypeUnifier to the witnesses in the previous definition of hcons,

import shapeless._, ops.hlist._, test._

object Demo extends App {
  trait UniqueSelect[L <: HList, M <: HList] {
    def apply(l: L): M
  }

  object UniqueSelect {
    implicit def hnil[L <: HList]: UniqueSelect[L, HNil] =
      new UniqueSelect[L, HNil] {
        def apply(l: L): HNil = HNil
      }

    implicit def hcons[L <: HList, M <: HList, H, T <: HList, S <: HList]
      (implicit
        su: SubtypeUnifier.Aux[L, H, M],
        pt: Partition.Aux[M, H, H :: HNil, S],
        upt: UniqueSelect[S, T]
      ): UniqueSelect[L, H :: T] =
      new UniqueSelect[L, H :: T] {
        def apply(l: L): H :: T = {
          val (h :: HNil, s) = pt(su(l))
          h :: upt(s)
        }
      }
  }

  def toProductUniquely[P <: Product] = new ToProductUniquely[P]
  class ToProductUniquely[P <: Product] {
    def apply[L <: HList, M <: HList](l: L)
      (implicit gen: Generic.Aux[P, M], up: UniqueSelect[L, M]): P =
        gen.from(up(l))
  }

  class A
  class B extends A
  class C

  val ac = new A :: new C :: HNil
  val bc = new B :: new C :: HNil
  val abc = new A :: new B :: new C :: HNil

  // Exact match
  val tac = toProductUniquely[(A, C)](ac)
  typed[(A, C)](tac)

  // Subtype
  val tbc = toProductUniquely[(A, C)](bc)
  typed[(A, C)](tbc)

  // Exact match again
  val tabc = toProductUniquely[(B, C)](abc)
  typed[(B, C)](tabc)

  // Ambiguous due to both elements conforming to A
  illTyped("""
  toProductUniquely[(A, C)](abc)
  """)
}

Update 2

We can also accommodate a unification semantics which gives preference to exact match and then falls back to a unique subtype as described in your updated question. We do this by combining the instances from the two solutions above: the exact match instance from the first at normal priority and the subtype match instance at low priority,

import shapeless._, ops.hlist._, test._

object Demo extends App {
  trait UniqueSelect[L <: HList, M <: HList] {
    def apply(l: L): M
  }

  object UniqueSelect extends UniqueSelect0 {
    implicit def hnil[L <: HList]: UniqueSelect[L, HNil] =
      new UniqueSelect[L, HNil] {
        def apply(l: L): HNil = HNil
      }

    implicit def hconsExact[L <: HList, H, T <: HList, S <: HList]
      (implicit
        pt: Partition.Aux[L, H, H :: HNil, S],
        upt: UniqueSelect[S, T]
      ): UniqueSelect[L, H :: T] =
      new UniqueSelect[L, H :: T] {
        def apply(l: L): H :: T = {
          val (h :: HNil, s) = pt(l)
          h :: upt(s)
        }
      }
  }

  trait UniqueSelect0 {
    implicit def hconsSubtype[L <: HList, M <: HList, H, T <: HList, S <: HList]
      (implicit
        su: SubtypeUnifier.Aux[L, H, M],
        pt: Partition.Aux[M, H, H :: HNil, S],
        upt: UniqueSelect[S, T]
      ): UniqueSelect[L, H :: T] =
      new UniqueSelect[L, H :: T] {
        def apply(l: L): H :: T = {
          val (h :: HNil, s) = pt(su(l))
          h :: upt(s)
        }
      }
  }

  def toProductUniquely[P <: Product] = new ToProductUniquely[P]
  class ToProductUniquely[P <: Product] {
    def apply[L <: HList, M <: HList](l: L)
      (implicit gen: Generic.Aux[P, M], up: UniqueSelect[L, M]): P = gen.from(up(l))
  }

  trait A
  trait B extends A
  trait C extends A

  val a: A = new A {}
  val b: B = new B {}
  val c: C = new C {}

  // (b, 5): subtypes match supertypes when there is no exact match
  toProductUniquely[(A, Int)](5 :: b :: HNil)

  // (a, 5): only one exact match is available
  toProductUniquely[(A, Int)](5 :: b :: a :: HNil)

  // compile error: more than one exact match is available
  illTyped("""
  toProductUniquely[(A, Int)](5 :: a :: a :: HNil)
  """)

  // compile error: more than one inexact match is available
  illTyped("""
  toProductUniquely[(A, Int)](5 :: b :: c :: HNil)
  """)
}