Ideal Streams

Abstract:
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 to give a simplified semantics for finite and infinite streams, based on the ideal completion. We show how some essential operations on streams and notions concerning correctness are expressed and show the use of the underlying algebra in reasoning about streams. Moreover, we give a simple treatment of non-determinacy. The approach is illustrated with the specification and correctness proof for the alternating bit protocol. 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.