Representing code algebraically

Question

I have a number of small algorithms that I would like to write up in a paper. They are relatively short, and concise. However, instead of writing them in pseudo-code (à la Cormen or even Knuth), I would like to write an algebraic representation of them (more linear and better LaTeX rendering) . However, I cannot find resources as to the best notation for this, if there is anything: e.g. how do I represent a loop? If? The addition of a tuple to a list?

Has any of you encountered this problem, and somehow solved it?

Thanks.

EDIT: Thanks, people. I think I did a poor job at phrasing the question. Here goes again, hoping I make it clearer: what is the common notation for talking about loops and if-then clauses in a mathematical notation? For instance, I can use $acc \leftarrow acc \cup \langle i,i+1 \rangle$ to represent the "add" method of a list.

Answer 1

I see if-expressions in mathematical notation fairly often. The usual thing for a loop is a recurrence relation, or equivalently, a function defined recursively.

Here's how the Ackermann function is defined on Wikipedia, for instance:

This picture is nice because it feels mathematical in flavor and yet you could clearly type it in almost exactly as written and have an implementation. It is not always possible to achieve that.

Other mathematical notations that correspond to loops include ∑-notation for summation and set-builder notation.

I hope this answers your question! But if your aim is to describe how something is done and have someone understand, I think it is probably a mistake to assume that mathematicians would prefer to see equations. I don't think they're interchangeable tools (despite Turing equivalence). If your algorithm involves mutable data structures, procedural code is probably going to be better than equations for explaining it.