[This is part of a series on generating every string in a language. The previous part is here . The next part is here .] Suppose we want to come up with a CFG for numbers with additions. Consider this very simple grammar with only one nonterminal. We...

[This is part of a series on generating every string in a language. The previous part is here . The next part is here .] We can now enumerate every binary tree and every arbitrary tree of a given size, and therefore we can enumerate all of them, period...

[This is part of a series on generating every string in a language. The previous part is here . The next part is here .] Last time we talked about how the number of binary trees with n nodes is C(n), where C(n) is the nth Catalan number. I asked if there...

[This is the first part of a series on generating every string in a language. The next part is here .] The other day I wrote a little algorithm that did some operation on binary trees. I wanted to test it. I whipped up a few little test cases and it seemed...

My copy of Essential C# 4.0 just arrived, and it looks great. I was one of the technical reviewers of this book. Some books are a pain to edit, but the Essential C# series is one of my favourites. It totally lives up to its name; it really does give you...

Yet another amusing question from StackOverflow : is there a difference between “return something;” and “return (something);” in C#? In practice , there is no difference. In theory there could be a difference. There are three interesting points...

The DateTime struct represents dates as a 64 bit number that measures the number of “ticks” since a particular start date. Ten million ticks equals one second. That’s a quite high degree of precision . You can represent dates and times to sub-microsecond...

I was amused to read this post about an arithmetic bug which accidentally turned into an AI feature (found via Raymond’s recent link clearance .) It reminded me of a story that my friend Lars told me about working on a certain well-known first-person...

As I’m sure you know by now, we are done implementing C# 4. We’ve added support for interoperability with dynamic languages and legacy object models, named and optional parameters, the ability to “link” against interfaces from a Primary Interop Assembly...