Declaring functions two ways. What is the distinction?

Question

Are these two function declarations effectively different?

If not, why do they have different toString values?

scala> def f: (Int) => Int = x=> x*x
f: (Int) => Int

scala> def f(x: Int) = x*x
f: (Int)Int

Answer 1

The first is a no-argument method f1 that returns a Function1[Int, Int].

scala> def f1: (Int => Int) = (x: Int) => x * x
f1: (Int) => Int

The second is a one argument method f2 that takes an an Int and returns an Int.

scala> def f2(x: Int): Int = x * x
f2: (x: Int)Int

You can invoke f1 and f2 with the same syntax, although when you call f1(2) it is expanded to f1.apply(2).

scala> f1
res0: (Int) => Int = <function1>

scala> f1(2)
res1: Int = 4

scala> f1.apply(2)
res2: Int = 2

scala> f2(2)
res3: Int = 4

Finally, you can 'lift' the method f2 to a function as follows.

scala> f2
<console>:6: error: missing arguments for method f2 in object $iw;
follow this method with `_' if you want to treat it as a partially applied funct
ion
       f2
       ^

scala> f2 _
res7: (Int) => Int = <function1>

scala> (f2 _).apply(2)
res8: Int = 4

Exercise: What is the type of f1 _?

Answer 2

These are methods declarations, not function declarations. The first method returns a function, the second returns an Int and has nothing to do with functions.

See this question.