Type-Checking of Heterogeneous Sequences in Common Lisp

  We introduce the abstract concept of \textit{rational type
    expression} and show its relationship to rational language theory.
  We further present a concrete syntax, regular type
    expression, and a Common Lisp implementation thereof which allows the programmer
  to declaratively express the types of heterogeneous sequences in a way
  which is natural in the Common Lisp language.  The implementation uses
  techniques well known and well founded in rational language theory,
  in particular the use of the Brzozowski derivative and deterministic
  automata to reach 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.