Higher Logics

My day job is has stuck me with C#, but I try to make the best of it, as evidenced by my FP# and Sasa C# libraries. One thing that still gets in my way more than it should is O/R mapping. No other mapper I've come across encourages a true object-oriented application structure. Granted, I've only really used NHibernate, and I had built my own mapper before that was even available, but I've read up quite a bit on the the other mappers. By true OO structure, I mean that all application objects are only constructed from other application objects, which doesn't involve dependencies on environment-specific code (ie. if you're running under ASP.NET, Windows forms, Swing, etc.). A pure structure encourages a proper separation between core application code, and display and controller code, which allows more flexible application evolution. Instead, controller logic often manually constructs application objects, passing in default arguments to properly initialize the required

Calculating permutations has some fairly nifty algorithms out there. I recently ran into a permutation problem for which I couldn't find an existing algorithm. I admit that I didn't look too hard though. Basically, I needed the permutations of the elements of a set of size N over K slots. However, the permutations should include duplicate elements from the set, as K > N is valid configuration. This corresponds to N K permutations. Most algorithms I found did not permit duplicate elements. As an example of an application for such a permutation algorithm, imagine the set of all function signatures of arity K-1 over N types. This corresponds to K slots with N possible choices for each slot. I devised a fairly simple implementation of such a permutation algorithm. Essentially, N forms the base of an arbitrary-precision integer of size K. In other words, we have an array of elements with a maximum of N which index our set. To permute, we simply increment the first element and pr