Lifting methods to function values in Scala

Question

Does the Scala library provide any support for lifting a method of a given type to a function value?

For example, suppose I want to lift String.length. I can write

val f: String => Int = _.length

or

val f = { s: String => s.length }

However, this syntax is not always ideal (particularly in the midst of a larger expression). I think I'm looking for something that will enable expressions like

Lift[String](_.length)
Lift[Option[Int]].lift(_.filter)

and I have in mind something like this:

class Lift[T] {                                                          
   def apply[R](f: T => R): T => R = f

   def lift[A, R](f: (T) => (A) => R): (T, A) => R = 
         f(_)(_) 
   def lift[A1, A2, R](f: (T) => (A1, A2) => R): (T, A1, A2) => R =
         f(_)(_,_)
   // ... etc. ...
}
object Lift {
   def apply[T] = new Lift[T]
}

Question 1: Does the standard library (or any library) provide something like this?

Question 2: If not, is it possible to write it in such a way that Option.filter can be lifted as above (rather than as Lift[Option[Int]].lift[Int => Boolean, Option[Int]](_.filter))? Without supplying the type parameters on the lift method I get the following error:

error: missing parameter type for expanded function ((x$1) => x$1.filter)
       Lift[Option[Int]].lift(_.filter)
                              ^

Update:

Apparently, the problem I'm running in to has something to do with the overloaded lift method. If I rename the overloads, I can lift Option.filter without all the extra type parameters.

Answer 1

What is the problem with

(_: String).length
(_: Option[Int]).filter _

?

Answer 2

I finally came up with a solution that I'm happy with. This version supports simple syntax and a single entry point to the API, while also providing control over the form of the lifted function (i.e. uncurried, partly curried, or fully curried).

Examples:

I'll use the following class definition in the examples below:

class Foo {
   def m1: Int = 1
   def m2(i: Int): Int = i
   def m3(i: Int, j: Int): Int = i + j
}

The simplest form of lifting is to return the method as a partially applied function, equivalent to invoking ((_: Foo).method _):

scala> lift[Foo](_.m1)                         // NOTE: trailing _ not required
res0: (Foo) => Int = <function1>

scala> lift[Foo](_.m2 _)                       // NOTE: trailing _ required
res1: (Foo) => (Int) => Int = <function1>

scala> lift[Foo](_.m3 _)
res2: (Foo) => (Int, Int) => Int = <function1> // NOTE: the result is partly curried

By importing some implicits, one can request curried or uncurried forms:

scala> {                        
     | import CurriedLiftables._
     | lift[Foo](_.m3 _)        
     | }
res3: (Foo) => (Int) => (Int) => Int = <function1>

scala> {                          
     | import UncurriedLiftables._
     | lift[Foo](_.m3 _)          
     | }
res4: (Foo, Int, Int) => Int = <function3>

Implementation:

class Lift[T] {
   def apply[R,F](f: T => R)(implicit e: (T => R) Liftable F): F = e.lift(f)
}
object lift {
   def apply[T] = new Lift[T]
}

class Liftable[From, To](val lift: From => To)

class DefaultLiftables {
   implicit def lift[F]: F Liftable F = new Liftable(identity)
}
object Liftable extends DefaultLiftables

class UncurriedLiftable1 extends DefaultLiftables {
   implicit def lift1[T, A, R]: (T => A => R) Liftable ((T, A) => R) = 
      new Liftable( f => f(_)(_) )
}
class UncurriedLiftable2 extends UncurriedLiftable1 {
   implicit def lift2[T, A1, A2, R]: (T => (A1, A2) => R) Liftable ((T, A1, A2) => R) = 
      new Liftable ( f => f(_)(_,_) )
}
// UncurriedLiftable3, UncurriedLiftable4, ...
object UncurriedLiftables extends UncurriedLiftable2

class CurriedLiftable2 extends DefaultLiftables {
   implicit def lift2[T, A1, A2, R]: (T => (A1, A2) => R) Liftable (T => A1 => A2 => R) =
      new Liftable( f => (x: T) => (a1: A1) => (a2: A2) => f(x)(a1, a2) )
}
// CurriedLiftable3, CurriedLiftable4, ...
object CurriedLiftables extends CurriedLiftable2

---

My previous solution required a separate lift method for each arity:

import Lift._
val f1 = lift0[String](_.length)
val f2 = lift1[Option[Int]](_.filter)
val f3 = lift2[Either[String, Int]](_.fold)

Implementation:

class Lift0[T] {
   def apply[R](f: T => R): T => R = f
}
class Lift1[T] {
   def apply[A, R](f: (T) => (A) => R): (T, A) => R = 
      f(_)(_) 
}
class Lift2[T] {
   def apply[A1, A2, R](f: (T) => (A1, A2) => R): (T, A1, A2) => R =
      f(_)(_,_)
}
// ... etc. ...

object Lift {
   def lift0[T] = new Lift0[T]
   def lift1[T] = new Lift1[T]
   def lift2[T] = new Lift2[T]
   // ... etc. ...
}

Answer 3

Passing in filter as partially applied method seems to do the job:

scala> class Lift[T] {                                        
     |    def apply[R](f: T => R): T => R = f
     | }
defined class Lift

scala> object Lift {
     |    def apply[T] = new Lift[T]
     | }
defined module Lift

scala> val ls = Lift[String](_.length)
ls: (String) => Int = <function1>

scala> val los = Lift[Option[Int]](_.filter _)     
los: (Option[Int]) => ((Int) => Boolean) => Option[Int] = <function1>