Is there a generic way to invert the order of the arguments of a curried function?

Question

I was wondering if you can write a generic function that takes a curried function and then inverts the arguments, like this:

def foo(a: String)(b: Boolean)(c: Int): String
val bar = invert(foo _)
foo("baz")(false)(12) must be equalTo(bar(12)(false)("baz"))

The below is working as long as you add implicit inverters for the specific cases you want to address. But I am more interested in the more general case – that is, the case that deals with any number of curried arguments.

trait Inverter[V, W] {
  def invert(v: V): W
}

implicit def function2Inverter[X, Y, Z] = 
  new Inverter[(X, Y) => Z, (Y, X) => Z] {
    def invert(v: (X, Y) => Z) = {
      def inverted(y: Y, x: X) = v(x, y)
      inverted _
    }
  }

implicit def curried2Inverter[X, Y, Z] = 
  new Inverter[X => Y => Z, Y => X => Z] {
    def invert(v: (X) => (Y) => Z) = {
      def inverted(y: Y)(x: X) = v(x)(y)
      inverted _
    }
  }

def invert[V, W](v: V)(implicit inverter: Inverter[V, W]): W = 
  inverter.invert(v)

Oh, and I would love to have a solution that works with Scala 2.9 as well.

Answer 1

TL;DR: Use this gist. Explanation of the same follows:

First, define a type class (and cases) to partially apply a function with the last parameter:

trait PopLast[A, Last, Rem] {
  def pop(f: A, v: Last): Rem
}

trait LowPrioPopLast {
  implicit def popEnd[A,B] = new PopLast[A => B, A, B] {
    def pop(f: A => B, v: A) = f(v)
  }  
}

object PopLast extends LowPrioPopLast {
  implicit def popOne[A, B, C, Last, IRem](
    implicit iPop: PopLast[B => C, Last, IRem]) = 
      new PopLast[A => B => C, Last, A => IRem] {
        def pop(f: A => B => C, v: Last) = { a: A => iPop.pop(f(a), v) }
      }
}

Then, create the inverter type class: recursively do partial application of last parameter and invert the result.

trait Inverter[A] {
  type Out
  def invert(f: A): Out 
}

trait LowPrioInverter {
  implicit def invertEnd[A,B] = new Inverter[A => B] {
    type Out = A => B
    def invert(f: A => B) = f
  }
}

object Inverter extends LowPrioInverter {
  implicit def invertStep[A, Last, Rem](implicit pop: PopLast[A, Last, Rem],
    inv: Inverter[Rem]) = new Inverter[A] {
      type Out = Last => inv.Out
      def invert(f: A) = { a: Last => inv.invert(pop.pop(f, a)) }
  }
}

Finally, encapsulate into a function:

def invert[A](f: A)(implicit inv: Inverter[A]) = inv.invert(f)

And there we go:

def foo(a: String)(b: Boolean)(c: Int): String = "bar"
val bar = invert(foo _)
// bar: Int => Boolean => String => String

bar(1)(true)("foo")

Answer 2

1) Extract type information from your function to HList (from shapeless) Ts and type argument Res.

For Int => String => Long => String Ts is Int :: String :: Long :: HNil and Res is String:

import shapeless.{HList, HNil, ::}

trait TypeExtractorAux[A, R, Ts <: HList, Res]

trait LowPriorityTypeExtractorAux{
  implicit def apply1[A, R]: TypeExtractorAux[A, R, A :: HNil, R] = new TypeExtractorAux[A, R, A :: HNil, R]{}
}

object TypeExtractorAux extends LowPriorityTypeExtractorAux{
  implicit def applyN[A1, A2, R, TsNext <: HList, Res](implicit te: TypeExtractorAux[A2, R, TsNext, Res]): TypeExtractorAux[A1, A2 => R, A1 :: TsNext, Res] =
    new TypeExtractorAux[A1, A2 => R, A1 :: TsNext, Res]{}
}

2) Convert curried function to Ts => Res:

trait FunctionConverterAux[Ts <: HList, Res, A, R]{
  def apply(f: A => R): Ts => Res
}

object FunctionConverterAux{
  implicit def apply1[L, Res]: FunctionConverterAux[L :: HNil, Res, L, Res] =
    new FunctionConverterAux[L :: HNil, Res, L, Res]{
      def apply(f: L => Res): L :: HNil => Res = hl => f(hl.head)
    }

  implicit def applyN[L1, L2, Rt <: HList, Res, R](implicit fc: FunctionConverterAux[L2 :: Rt, Res, L2, R]): FunctionConverterAux[L1 :: L2 :: Rt, Res, L1, L2 => R] =
    new FunctionConverterAux[L1 :: L2 :: Rt, Res, L1, L2 => R]{
      def apply(f: L1 => L2 => R): L1 :: L2 :: Rt => Res = hl => fc(f(hl.head))(hl.tail)
    }
}

For Int => String => Long => String result is Int :: String :: Long :: HNil => String

3) Invert Ts using shapeless.HList.ReverseAux and collect all arguments to HList. You'll get Ts. Then apply your Ts => Res function to HList of arguments:

trait ArgumentsGetterAux[Prev <: HList, Rest <: HList, NR, Ts, Res]{
  def apply(p: Prev, f: Ts => Res): NR
}

object ArgumentsGetterAux{
  implicit def applyHNil[Prev <: HList, L, Res]: ArgumentsGetterAux[Prev, L :: HNil, L => Res, L :: Prev, Res] =
    new ArgumentsGetterAux[Prev, L :: HNil, L => Res, L :: Prev, Res]{
      def apply(p: Prev, f: L :: Prev => Res): L => Res = l => f(l :: p)
    }

  implicit def applyHList[Prev <: HList, L1, R <: HList, NR, Ts, Res](implicit aga: ArgumentsGetterAux[L1 :: Prev, R, NR, Ts, Res]): ArgumentsGetterAux[Prev, L1 :: R, L1 => NR, Ts, Res] =
    new ArgumentsGetterAux[Prev, L1 :: R, L1 => NR, Ts, Res]{
      def apply(p: Prev, f: Ts => Res): L1 => NR = l => aga(l :: p, f)
    }
}

invert method:

import shapeless.HList.ReverseAux

def invert[A, R, Ts <: HList, Res, RevTs <: HList, NR](f: A => R)(
    implicit te: TypeExtractorAux[A, R, Ts, Res],
             r: ReverseAux[Ts, RevTs],
             ag: ArgumentsGetterAux[HNil, RevTs, NR, Ts, Res],
             fc: FunctionConverterAux[Ts, Res, A, R]
  ): NR = ag(HNil, fc(f))

Usage:

scala> invert((i: Int) => (s: String) => (l: Long) => s"i: $i; s: $s; l: $l")
res0: Long => (String => (Int => String)) = <function1>

scala> res0(666L)("str")(1)
res1: String = i: 1; s: str; l: 666