Abstract
This report provides detailed background of our development of the rational type expression, concrete syntax, regular type expression, and a Common Lisp implementation which allows the programmer to declarative express the types of heterogeneous sequences in a way which is natural in the Common Lisp language. We present a brief theoretical background in rational language theory, which facilitates the development of rational type expressions, in particular the use of the Brzozowski derivative and deterministic automata to arrive at a solution which can match a sequence in linear time. We illustrate the concept with several motivating examples, and finally explain many details of its implementation.