Passing functions for all applicable types around

Question

I followed the advice found here to define a function called square, and then tried to pass it to a function called twice. The functions are defined like this:

Answer 1

Here's a session from the Scala REPL.

Welcome to Scala version 2.8.0.final (Java HotSpot(TM) 64-Bit Server VM, Java 1.6.0_20).
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scala> def square[T : Numeric](n: T) = implicitly[Numeric[T]].times(n, n)
square: [T](n: T)(implicit evidence$1: Numeric[T])T

scala> def twice2[T](f: T => T)(a: T) = f(f(a))
twice2: [T](f: (T) => T)(a: T)T

scala> twice2(square)(3)
:8: error: could not find implicit value for evidence parameter of type
 Numeric[T]
       twice2(square)(3)
              ^

scala> def twice3[T](a: T, f: T => T) = f(f(a))
twice3: [T](a: T,f: (T) => T)T

scala> twice3(3, square)
:8: error: could not find implicit value for evidence parameter of type
 Numeric[T]
       twice3(3, square)

scala> def twice[T](a: T)(f: T => T) = f(f(a))
twice: [T](a: T)(f: (T) => T)T

scala> twice(3)(square)
res0: Int = 81

So evidently the type of "twice(3)" needs to be known before the implicit can be resolved. I guess that makes sense, but I'd still be glad if a Scala guru could comment on this one...