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\title{Auto2 prover}
\author{Bohua Zhan}
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\begin{abstract}
  Auto2 is a saturation-based heuristic prover for higher-order logic,
  implemented as a tactic in Isabelle.

  This entry contains the instantiation of auto2 for Isabelle/HOL,
  along with two basic examples: solutions to some of the Pelletier's
  problems, and elementary number theory of primes.
\end{abstract}

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\section{Introduction}

Auto2 \cite{zhan16} is a proof automation tool implemented in
Isabelle. It uses a saturation-based approach to proof search:
starting with a list of initial assumptions, it iteratively adds facts
that can be derived from these assumptions, with the aim of ultimately
deriving a contradiction. Users can add their own proof procedures to
auto2 in the form of \emph{proof steps}, in order to implement
domain-specific knowledge. Auto2 can be instantiated to both
Isabelle/HOL (for ordinary usage) and Isabelle/FOL (for formalization
of mathematics based on set theory).

This AFP entry contains the instantiation of auto2 to Isabelle/HOL,
and two basic applications:

\begin{itemize}
\item Pelletier's problems: solutions to some of the problems in
  Pelletier's collection of problems for testing automatic theorem
  provers \cite{pelletier}. Auto2 is not intended to compete with
  ATPs. In our examples, we merely show how to use the prover to solve
  some of the problems, sometimes with hints.

\item Elementary number theory: theory of prime numbers up to the
  infinitude of primes and unique factorization. This example follows
  the development in HOL/Computational\_Algebra/Primes.thy in the
  Isabelle distribution.

\end{itemize}

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