Infinite Cheese Fractal using WPF 3D and F#

I always liked fractals, because they look like objects from another world, but on the other side if you look at some things in our world you can see many similarities with fractals (but not quite as ideal with the infinite level of precision). One of my favorite fractals is 3D version of Sierpinski carpet [1], which itself is based on very famous Cantor set. Quite long time ago I thought that it would be nice to implement animation of flying through this fractal, but I was never good in 3D graphics and it looked like a lot of work, so I never get to doing it. Luckily, now with F#, which makes it very easy to write the code to generate the fractal and with WPF 3D, which can be easily used to animate the fractal, I finally had everything I needed to do it, so here it is!

Asynchronous Programming in C# using Iterators

In this article we will look how to write programs that perform asynchronous operations without the typical inversion of control. To briefly introduce what I mean by 'asynchronous' and 'inversion of control' - asynchronous refers to programs that perform some long running operations that don't necessary block a calling thread, for example accessing the network, calling web services or performing any other I/O operation in general. The inversion of control refers to the code structure that you have to use when writing a code that explicitly passes a C# delegate as a callback to the asynchronous method (typically called BeginSomething in .NET). The asynchronous method calls the delegate when the operation completes, which reverses the way you write the code - instead of encoding the control flow using typical language constructs (e.g. while loop) you have to use global variables and write your own control mechanism.

The funny thing about this article is that it could have been written at least 3 years ago when a beta version of Visual Studio 2005 and C# 2.0 became first available, but it is using iterators in a slightly bizarre way, so it is not easy to realize that this is possible. Actually, I will use some C# 3.0 methods in the article as well, but only extension methods and mainly just to keep the code nicer. As with my earlier article about building LINQ queries at runtime, I realized that it can be done in C# when I was playing with the F# solution (called F# Asynchronous Workflows), where this approach is very natural, so I will shortly mention the F# implementation as well.

F# Overview (IV.) - Language Oriented Programming

In the fourth article of the F# overview series, I will shortly describe how I understad the language oriented paradigm and how the F# language can be used for developing libraries using this paradigm. We will look how discriminated unions relate to this paradigm and at three specific features that support this paradigm, namely active patterns, computation expressions and quotations.

Defining precisely what the term language oriented programming means in context of the F# language would be difficult, so I will instead explain a few examples that will demonstrate how I understand it. In general, the goal of language oriented programming is to develop a language that would be suitable for some (more specific) class of tasks and use this language for solving these tasks. Of course, developing a real programming language is extremely complex problem, so there are several ways for making it easier. As the most elementary example, you can look at XML files (with certain schema) as language that are processed by your program and solve some specific problem (for example configuring the application). As a side note, I should mention that I'm not particularly happy with the term ‘language’ in this context, because the term can be used for describing a wide range of techniques from very trivial constructs to a complex object-oriented class libraries, but I have not seen any better term for the class of techniques that I’m going to talk about.

F# Overview (III.) - Imperative and Object-Oriented Programming

In the third part of the F# Overview article series, we will look at language features that are mostly well known, because they are present in most of the currently used programming languages. Indeed, I'm talking about imperative programming, which is a common way for storing and manipulating application data and about object oriented programming which is used for structuring complex programs.

In general, F# tries to make using them together with the functional constructs described in the previous part [^] as natural as possible, which yields several very powerful language constructs.

F# Overview (II.) - Functional Programming

In the second part of the F# overview we will look at functional programming, which is probably the most important paradigm used with the F# language, because F# is built on the same grounds as many functional languages. We will first examine the standard F# data types, which are useful to allow the functional programming style and we will also look at a few functional tricks.

As already mentioned in the Introduction for this article series, F# is a typed functional language, by which I mean that types of all values are determined during the compile-time. However, thanks to the use of a type inference, the types are explicitly specified in the code very rarely as we will see in the following examples. Basic data types (aside from a standard set of primitive numeric and textual types that are present in any .NET language) available in F# are tuple, discriminated union, record, array, list, function and object. In the following quick overview, we will use the F# interactive, which is a tool that compiles and executes the entered text on the fly.

F# Overview (I.) - Introduction

In my bachelor thesis I included a short introduction that covered all of the important aspects of the F# programming language and I thought that it may be useful to extend it a little bit to cover also a topics that were not important for my thesis and post it as an article, so there is one and relatively short article that introduces all the interesting F# features. The article got however a bit longer than I expected, so I decided to split it into a three parts that would introduce three different paradigms that are supported by F#. Of course, this series won't teach you everything about F#, but it tries to cover the main F# design goals and (hopefully) presents all the features that make F# interesting and worth learning. In this first part I will shortly introduce F# and the supported paradigms that will be discussed in the upcoming articles.

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