functional programming - Using partial functions in Scala - how does it work?

Question

I'm new to Scala, I'm using 2.9.1, and I'm trying to get my head around how to use partial functions. I have a basic understanding of curried functions, and I know that partial functions are kind of like curried functions where they are only 2nary or some such. As you can tell I'm a bit green at this.

It does seem that in certain cases like XML filtering, being able to partial functions would be highly advantageous, so I'm hoping get a better understanding of how to use them.

I have a function that uses the RewriteRule structure, but I need it to work with two arguments, whereas the RewriteRule structure only takes one, OR a partial function. I think this is one of the cases I'm thinking about it being helpful.

Any advice, links, words of wisdom etc. welcome!

The answers so far are excellent, and have cleared up a few fundamental misconceptions I have. I think they also explain where I'm struggling - I think maybe posting a new question being a bit more specific will help, so I'll do that too.

Answer 1

A partial function is a function that is valid for only a subset of values of those types you might pass in to it. For example:

val root: PartialFunction[Double,Double] = {
  case d if (d >= 0) => math.sqrt(d)
}

scala> root.isDefinedAt(-1)
res0: Boolean = false

scala> root(3)
res1: Double = 1.7320508075688772

This is useful when you have something that knows how to check whether a function is defined or not. Collect, for instance:

scala> List(0.5, -0.2, 4).collect(root)   // List of _only roots which are defined_
res2: List[Double] = List(0.7071067811865476, 2.0)

This is not going to help you place two arguments where you really want one.

In contrast, a partially applied function is a function where some of its arguments have already been filled in.

def add(i: Int, j: Int) = i + j
val add5 = add(_: Int,5)

Now you only need one argument--the thing to add 5 to--instead of two:

scala> add5(2)
res3: Int = 7

You can see from this example how to use it.

But if you need to specify those two arguments, this still won't do it--say you want to use map, for instance, and you need to give it a function of one argument, but you want it to add two different things. Well, then you can

val addTupled = (add _).tupled

which will partially apply the function (really, just create a function out of the method, since nothing has been filled in) and then combine the separate arguments into a tuple. Now you can use this in places that require a single argument (assuming that the type is correct):

scala> List((1,2), (4,5), (3,8)).map(addTupled)
res4: List[Int] = List(3, 9, 11)

In contrast, currying is different yet again; it turns functions of the form (A,B) => C into A => B => C. That is, given a function of multiple arguments, it will produce a chain of functions that each take one argument and return a chain one shorter (you can think of it as partially applying one argument at a time).

val addCurried = (add _).curried

scala> List(1,4,3).map(addCurried)
res5: List[Int => Int] = List(<function1>, <function1>, <function1>)

scala> res5.head(2)   // is the first function, should add 1
res6: Int = 3

scala> res5.tail.head(5)   // Second function should add 4
res7: Int = 9

scala> res5.last(8)  // Third function should add 3
res8: Int = 11