This is a repo that I will use to develop my Bernoulli data type concept, which is a general framework for understanding and constructing a lot of interesting new data types and compuational trade-offs. It can also be used as a foundation for constructing oblivious programs as a composition of oblivious data types / obvious functions.

I doubt any of it will compile – I actually hadn’t looked at this in years, while I battled sickness and cancer, but now that I’m feeling better, I’m revisting some old projects. Look at my repo for other things I’m working on, and https://metafunctor.com for my personal web site.

Here are some markdown files in the repo. I’ve throw it all into Doxygen, but I haven’t had time to make it work properly yet. Here are the files:

• Bernoulli Map for info on the most generic type, which can be used to in theory model any computable function. We also show how even traditional algorithms, like the Miller-Rabin primality test, can be understood in th framework of the Bernoulli model.
  • The random approximate values over algebraic types
    • I’m not sure if this is correct. The markdown files I have should be more up to date and more correct, so stick with this for grokking the concept. This PDF is more for historical purposes, and to show how I was thinking about it at the time.
• Bernoulli Bool for an example of the simplest Bernoulli type, useful for understanding.
• Bernoulli Set for information on the most common kind of Bernoulli data type. The Bloom filtr is a special case. Here are some PDF files related to this:
  • Bernoulli sets: a model for modeling sets with random errors and corresponding random binary classification measures.
    • A lot of the material in this section is obsolete, but there is still a lot of good information here.
  • An algebra of random approximate sets with derivations of higher-order random approximate sets induced by set-theoretic operations on random approximate sets with corresponding random binary classification measures.
    • Again, a lot of obsolete content. Much of this comes prior to my generalization of the result for Bernoulli types, and before I had a proper appreciation for the correct definition. However, as a separate result, if we ignore some of the details, it has a lot of interesting information.
• Codec for more information codecs. I will eventually use this to describe how to automatically generate any Bernoulli map, including Cipher maps (Oblivious data type). The idea will be to use the universal Bernoulli map constructor
• Regular Type for more information about regular types, and how the Bernoulli model fails this basic requirement in many ways. It’s not intended as a criticism, because in some ways it’s desirable (say in the oblivious type use-case), only to explain why some predicates like equality are not necessarily accurate (equality itself return a Bernoulli Boolean).

See the API Documentation for more details, but there isn’t much there yet. I’ll be working on the code + doxygen comments soon.