\section{Introduction}
\label{sec:intro}
Compilers and interpreters are among the most complex pieces of software
written to date. Due to the rapid technological development of the last
decades, programming languages have become increasingly complex, semantically
speaking. It has become impossible for a programmer to keep in mind the impact
of their changes on the generated machine code. Developers now constantly rely on assumptions about how
the language that they write in works. Intuitive semantics may change over
time, however, and proper definitions are required now that our world relies so
principally on software.

Nowadays, programming languages have semantical specifications as the main link
between programmers and compiler designers. This solves the problem on the
programmer's side. However, now that programming languages become increasingly
complex, another problem occurs on the compiler designer's side: the
specification has become too complex to efficiently translate it into
imperative code, and writing a correct compiler or interpreter is no longer a
trivial task.

Functional programming languages offer writers of code processing systems tools
to efficiently work with semantical specifications --- indeed, functional
programs can be used as the very specification themselves~\citep{fpasspec}.
However, we will not go this far. While functional programs are indeed better
suitable for semantic specifications than natural language, mathematical
notation gives even more freedom. We therefore suggest tools for the
implementation of these mathematical definitions in a functional style.

Using a high level of abstraction, the gap between specification and
implementation is closed, allowing for quicker correctness checks and better
maintainable code.  The connections between functional languages and
mathematics let us \emph{prove} properties about code processing systems (for
example, their correctness with respect to a specification).

\input{intro-org}
\input{intro-while}
