In scala, a named function is defined as:
scala> def addOne(x: Int): Int = x+1
addOne: (x: Int)Int
scala> :type addOne
(x: Int)Int
And an anonymous one as:
scala> val addOne = (x:Int) => x+1
addOne: Int => Int = <function1>
scala> :type addOne
Int => Int
Why do their types look different?
Why can't a named function be passed as an argument to another function?
Shouldn't both be treated uniformly from type and first-order behavior point of views?
def addOne(x: Int): Int is not a function in scala. It's a method of some object.
Functions like val addOne = (x:Int) => x+1 are objects of type FunctionN (in this case Function1) with method apply.
One can use method as function in scala - compiler can create a function from method, for instance:
scala> List(1, 2, 3).map((1).+) // or just `1+`
res0: List[Int] = List(2, 3, 4)
In this case method + of object 1 is used as function x => (1).+(x).
scala> List(1, 2, 3).foreach(println)
1
2
3
Method println of object Predef is used as function s => Predef.println(s).
Since version 2.10 you can't use :type on methods:
scala> def addOne(x: Int): Int = x+1
addOne: (x: Int)Int
scala> :type addOne
<console>:9: error: missing arguments for method addOne;
follow this method with `_' if you want to treat it as a partially applied function
addOne
^
