Lifting functions in scala

Question

I want to define lifting with implicits. Suppose we have a function A => B, I want to define how to lift it to Maybe, i.e. Maybe[A] => Maybe[B].

This can be simply done with implicit conversions. However, if I want to do the same with functions with two or more parameters, I have a problem. The only solutionI know is to duplicate the code.

I want to implement such lifting for arbitrary functions with any number of parameters without duplication. Is this possible in Scala?

Answer 1

If F has a functor instance available, it's possible to lift any function A => B to F[A] => F[B].

If F has an applicative functor instance available, it's possible to lift any function A => B => C => .. => Z to F[A] => F[B] => F[C] => .. => F[Z]. Essentially, applicative functor is a generalization of functor for arbitrary arity.

You can learn about functor and applicative functors here and here. There is also this excellent talk which covers these ideas.

Scalaz library provides these abstractions (and more!).

import scalaz._
import Scalaz._

scala> val foo: Int => String = _.toString
foo: Int => String = <function1>

scala> foo.lift[Option]
res0: Option[Int] => Option[String] = <function1>

scala> res0(Some(3))
res1: Option[String] = Some(3)

scala> res0(None)
res2: Option[String] = None

scala> val add: (Int, Int) => Int = _ + _
add: (Int, Int) => Int = <function2>

scala> add.lift[Option]
res3: (Option[Int], Option[Int]) => Option[Int] = <function2>

scala> res3(Some(2), Some(1))
res4: Option[Int] = Some(3)

scala> res3(Some(2), None)
res5: Option[Int] = None

scala> res3(None, None)
res6: Option[Int] = None

Scalaz pimps lift method on Function2, Function3 etc because curried functions being syntactially heavier are used less often. Behind the scenes, the lifting happens with Function1s (i.e. curried functions).

You might also want to take a look at Scalaz source code.