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\title{Isabelle: An Overview}
\author{Lawrence C. Paulson}

\date{October 2003}

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Isabelle~\cite{isa-tutorial} is a generic proof assistant.  It allows mathematical formulas to be expressed in a 
formal language and provides tools for proving those formulas in a
logical calculus. The main potential application in industry is
\emph{formal verification}, which includes proving the 
correctness of computer hardware or software and proving 
properties of computer languages and protocols. Among its research
applications are the formalization of mathematical proofs.

Compared with similar tools, Isabelle's distinguishing feature is its flexibility. Most proof assistants
are built around a single formal calculus, typically higher-order logic.
Isabelle has the capacity to
accept a variety of formal calculi. The distributed version
supports higher-order logic but also axiomatic set theory and several other
formalisms. Isabelle provides excellent notational support: 
new notations can be introduced, using normal mathematical symbols.

The main limitation of all such systems is that proving theorems
requires much effort
from an expert user. Isabelle incorporates some tools to improve
the user's productivity by automating some parts of the proof process.
In particular, Isabelle's \emph{classical reasoner} can perform long
chains of reasoning steps to prove formulas. The \emph{simplifier} 
can prove certain arithmetic facts and can reason about equations.

Isabelle is closely integrated with the 
\hfootref{http://www.cl.cam.ac.uk/users/lcp/papers/protocols.html}{Proof General} user interface, which greatly eases the task of interacting with 
Isabelle. Proof General is open-source software under the GNU General Public
License. Using Isabelle without Proof General would be difficult.

Isabelle is distributed with large theories of formalized mathematics, 
including elementary number theory (for example, Gauss's law of quadratic reciprocity), analysis (basic properties of limits, derivatives and integrals) and algebra (up to Sylow's theorem). Also provided are numerous 
examples arising from research into formal verification. The total size of
the distribution (program sources and documentation) is about 5.4MB.

\paragraph*{Sponsorship.}
Isabelle is a joint project between Cambridge and the Technical University
of Munich, Germany. Prof.\ Tobias Nipkow leads the German team; other significant contributors at Munich include Dr. Markus Wenzel, Dr. Gerwin Klein and Mr.\ Stefan Berghofer.
The development of Isabelle at Cambridge was funded by the following grants:
\begin{itemize}
\item \emph{Supporting Logics} (6/1986--11/1989). SERC grant GR/E0355.7
\item \emph{Logical Frameworks: Design, Implementation and Experiment} (6/1989--3/1992). ESPRIT Basic Research Action 3245
\item \emph{Types for Proofs and Programs}: ESPRIT Basic Research Action 6453 (9/1992--8/1995) 
\item \emph{Combining HOL with Isabelle} (9/1992--8/1995). EPSRC grant GR/H40570
\item \emph{Mechanising Temporal Reasoning} (11/1995--4/1999). EPSRC grant reference GR/K57381
\item \emph{Authentication Logics: New Theory and Implementations} (1/1996--6/1999). EPSRC grant GR/K77051
\item \emph{Compositional Proofs of Concurrent Programs} (10/1999--6/2003). EPSRC grant GR/M75440 (RG28587)
\item \emph{Verifying Electronic Commerce Protocols} (10/2000--9/2003). EPSRC grant GR/R 01156/01 (NRAG/002)
%\item \emph{Automation for Interactive Proof} (2/2004--1/2007).
%EPSRC grant GR/S57198/01 (NRAG/071)
\end{itemize}
Lawrence Paulson was the Principal Investigator on all of these grants.
The Munich side had support from German sponsors.
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