Welcome back for another installment in my series on why I find Microsoft F# to be an exciting language for the .NET platform. If you're just joining us, below are links to the articles in the series so far.

1. The Interactive Environment
2. Type-safe Format Strings
3. Tuples
4. Breaking Up Tuples
5. Result Tuples

I have around 15-20 more articles planned, but I'm always looking for suggestions. If you have a topic idea for the series, feel free to email me at dustin AT diditwith.net.

One of the main reasons that I find F# to be so provocative is that it fully embraces three programming paradigms: functional, imperative and object-oriented. Of these, functional programming is the most favored, mostly due to its OCaml heritage. Because of this, we can't move any further in this series without introducing what functional programming is all about: functions!

In F#, a function declaration consists of the fun keyword, an argument, the -> operator and finally, the function body.

In the F# interactive environment, we can declare a function that takes an argument x and returns its increment like so:

If the -> operator looks strange to you, remember that it's just a divider that separates function arguments from function bodies.

The code above is somewhat equivalent to the following C# 3.0 lambda expression:

Or this VB 9.0 lambda expression:

The biggest difference is that the F# function does not need to be assigned to a .NET delegate (or expression tree) as the C# 3.0 and VB 9.0 lambda expressions do. This is an important point: F# functions are not delegates. They're something else entirely.

Another point of interest is F#'s type inference. We didn't specify a type for x in the function above, but F# determined that x is of type int and that the function returns an int. F# worked this out from the literal 1 that appears in the function body. 1 is an int. Therefore, x must be an int because it is being added together with 1. Finally, the function must return an int since its body returns the result of adding two ints, x and 1.

Because the literal that is added together with x is what triggers the type inference, changing the literal will change the type of the function. For example, changing 1 to 1.0 produces a function that increments floats.

This really isn't anything to write home about. After all, C# 3.0 and VB 9.0 handle type inference similarly for their respective lambda expressions. However, F#'s type inference algorithm is extremely advanced. As this series progresses, you'll see functions without any type annotations that the compiler will successfully type infer, leaving you scratching your head.

At this point, we've successfully declared a function in F#. Unfortunately, we can't use our function yet because it doesn't have a name. We've declared an anonymous function. So, how do we give our function a name? Well, let's back up a little bit to examine some syntax from a previous article.

The above example shows a variable, pair, being defined and assigned a value of (37, 5). The heart of this syntax is the keyword let.

Simply put, let binds a value to a name.

In F#, functions are values. That's a small thing to say, but it has enormous implications. Functions are treated in the same way as any other value. That means that functions can be passed as arguments to other functions, returned by other functions, contained within data structures and bound by names as variables.

Because functions are values, we can give our function the name inc using let.

And, we can call inc like so:

After learning to declare a function of one argument, the next logical step is to declare a function of two arguments. This is actually done with two functions. Consider the code below:

That might look a bit confusing at first. If so, look again carefully. We're declaring a function of one argument, x. This function's body is another function of one argument, y. The body of the inner function is x + y. To call our function, we pass the first argument. That returns the inner function to which we pass the second argument and finally receive the result of the calculation. In essence, calling add requires two function calls. Normally, this is done all at once, as below:

add is an example of a curried function. The idea behind currying is simply transforming a function of multiple arguments into a series of functions that each take one argument. That's all it is. It's not hard. In fact, you can even torture .NET delegates to curry functions in C#. Currying is a simple concept, but it's hard to grasp if you've never encountered it before.

An interesting property of curried functions is the ability to partially apply them. For example, if we pass 1 to our add function above but don't pass the second argument, we are left with a function of one argument that increments by 1. That is, we can define our inc function in terms of add:

Cool!

The reality of our add definition above is that it is far too verbose. It's easy to imagine the nested functions quickly getting out of control when functions of more arguments are declared. For this reason, F# provides a more concise way to declare functions of multiple arguments.

That's better. However, F# provides an even more concise syntax.

That's much better. Note that all three declarations of add are equivalent. Each syntax produces a curried function. In F#, we get currying for free. If you need to declare a function that isn't curried (e.g. to be called easily from C# or VB), you'd use a slightly different syntax. But, that's another article.

I should also point out that F# managed to infer the type of add as int -> int -> int even though there weren't any literals to trigger off of. In future articles, we'll see F#'s type inference algorithm work "miracles" like this over and over again.

Next time, we'll be looking at pattern matching and how it fits into F#. See you then!