Towards pointer algebra

We show that the well-known unfold/fold transformation strategy is also fruitful for the (formal) derivation of correct pointer algorithms. The key to this extension is an algebra of partial maps which allows convenient description and manipulation of pointer structures at the functional level

Derivation of graph and pointer algorithms

We introduce operators and laws of an algebra of formal languages, a subalgebra of which corresponds to the algebra of (multiary) relations. This algebra is then used in the formal specification and derivation of some graph and pointer algorithms

Calculating a garbage collector

In this paper we give a calculational account of a garbage collection algorithm. There have been a number of papers with a similar programme. However, these treatments either were not completely formal or suffered from using an inconvenient representation of the problem. With this paper we want to introduce partial maps and their algebraic properties as a vehicle for treating pointer structures, as dealt with in garbage collection, both conveniently and formally. Moreover, we want to develop the algorithms to a level which can actually be transcribed directly into machine code allowing the use of overwriting and the like; this was not achieved in most of the papers cited. It also turns out that the theory of finite maps allows very concise high-level specifications of the subproblems involved in garbage collection