Implicit lifting in scala - scala

Question

I want to implicitly convert functions from A => B to List[A] => List[B].
I wrote the following implicit definition:
implicit def lift[A, B](f: A => B): List[A] => List[B] = ...
Unfortunately, when I write the following code, implicit aren't applied:
val plusOne: (List[Int]) => List[Int] = (x: Int) => (x + 1)
If I annotate the function with explicit time, it works fine.
Why? How can I fix it?
UPDATE. It seems that the problem is specific to anonymous functions. Compare:
#Test
def localLiftingGenerics {
implicit def anyPairToList[X, Y](x: (X, Y)): List[X] => List[Y] = throw new UnsupportedOperationException
val v: List[String] => List[Int] = ("abc", 239)
}
#Test
def localLiftingFuns {
implicit def fun2ListFun[X, Y](f: X => Y): List[X] => List[Y] = throw new UnsupportedOperationException
val v: List[String] => List[Int] = ((x: String) => x.length)
}
The first one is compiled well. The second one is marked as error

Answer 1

According to The Scala Language Specification / Expressions / Anonymous Functions (6.23):
If the expected type of the anonymous function is of the form
scala.Functionn[S1, …, Sn, R], the expected type of e is R ...
So, the result type of the function will be inferred as List[Int] unless you separate the function definition from the function value assignment (to get rid of the expected type):
val function = (x: Int) => (x + 1)
val plusOne: (List[Int]) => List[Int] = function
or specify the function type explicitly:
val plusOne: (List[Int]) => List[Int] = ((x: Int) => (x + 1)): Int => Int

Answer 2

(Scala 2.9.1-1 (Java HotSpot(TM) 64-Bit Server VM, Java 1.7.0_05)
A first observation: If you duplicate fun2ListFun and rename it to, e.g.,``fun2ListFun, you'll get
found : String => <error>
required: List[String] => List[Int]
Note that implicit conversions are not applicable because they are ambiguous:
both method fun2ListFun2 of type [X, Y](f: X => Y)List[X] => List[Y]
and method fun2ListFun of type [X, Y](f: X => Y)List[X] => List[Y]
are possible conversion functions from String => <error> to List[String] => List[Int]
val v: List[String] => List[Int] = ((x: String) => x.length)
It looks as if the compiler considers both implicits as applicable.
A second observation:
Splitting
val v: List[String] => List[Int] = ((x: String) => x.length) /* Error*/
into
val f = ((x: String) => x.length)
val v: List[String] => List[Int] = f /* Works */
makes the compiler happy.

Answer 3

The implicit conversion for the input value compiles. So we just have a problem for the output of the anonymous function
def localLiftingFuns {
implicit def fun2ListFun[X, Y](f: X => Y): List[X] => Y = throw new UnsupportedOperationException
val v: List[String] => Int = ((x: String) => x.length)
}
A possible fix using a second implicit conversion:
def localLiftingFuns {
implicit def fun2ListFun[X, Y](f: X => List[Y]): List[X] => List[Y] = throw new UnsupportedOperationException
implicit def type2ListType[X](x:X): List[X] = throw new UnsupportedOperationException
val v: List[String] => List[Int] = ((x: String) => x.length)
}
This version compiles.

Answer 4

Seems the compiler has hard time figuring what is going on with the type of the function. If you will give him a little help, it would work:
scala> implicit def lift[A,B](f: A => B) = (_:List[A]).map(f)
lift: [A, B](f: (A) => B)(List[A]) => List[B]
scala> val f: List[Int] => List[Int] = ((_:Int) + 1):(Int => Int)
f: (List[Int]) => List[Int] = <function1>