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

Approximating least fixpoints

I try to come up with general techniques for approximating least fixpoints from below and greatest fixpoints from above. In this, I try to place as few restrictions as possible on the underlying partial orders; in particular, I avoid the use of linear orders. The approach is intended to abstract and thus generalise approximation techniques used in [10,1]. I hope that I am not falling into Einstein’s trap with this note

Refining ideal behaviours

This paper provides some mathematical properties of behaviours of systems, where the individual elements of a behaviour are modeled by ideals of a suitable partial order. It is well-known that the associated ideal completion provides a simple way of constructing algebraic cpos. An ideal can be viewed as a set of consistent finite or compact approximations of an object which itself may even be infinite. We introduce a special way of characterising behaviours through sets of relevant approximations

Algebraic calculation of graph and sorting 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 sorting algorithms. This study is part of an attempt to single out a framework for program development at a very high level of discourse, close to informal reasoning but still with full formal precision

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

Lazy Kleene Algebra

We propose a relaxation of Kleene algebra by giving up strictness and right-distributivity of composition. This allows the subsumption of Dijkstra's computation calculus, Cohen's omega algebra and von Wright's demonic refinement algebra. Moreover, by adding domain and codomain operators we can also incorporate modal operators. Finally, it is shown that the predicate transformers form lazy Kleene algebras again, the disjunctive and conjunctive ones even lazy Kleene algebras with an omega operation

Shorter paths to graph algorithms

AbstractWe illustrate the use of formal languages and relations in compact formal derivations of some graph algorithms