-*- mode: outline; coding: utf-8; -*-

* Info/links.

See

  http://en.wikipedia.org/wiki/Automated_theorem_proving


* proofgeneral.

  $ sudo apt-get install proofgeneral
  $ sudo apt-get install proofgeneral-coq
  $ sudo apt-get install proofgeneral-misc
  $ sudo apt-get install proofgeneral-doc
  $ sudo apt-get install proofgeneral-minlog

or build from source:

  $ make clean
  $ make compile EMACS=xemacs
  $ cat ~/.emacs
...
(load-file "dir/generic/proof-site.el")
...

See

  http://proofgeneral.inf.ed.ac.uk/

* Isabelle.

Isabelle 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
application is the formalization of mathematical proofs and in particular
formal verification, which includes proving the correctness of computer
hardware or software and proving properties of computer languages and
protocols.

See

  http://isabelle.in.tum.de/overview.html
  http://en.wikipedia.org/wiki/Isabelle_(theorem_prover)

* IsarMathLib.

The goal of the project is to create a library of formalized mathematics,
similar to the Mizar Mathematical Library, but written for the Isabelle/Isar
theorem prover (ZF logic).

See

  http://savannah.nongnu.org/projects/isarmathlib
  http://lists.nongnu.org/mailman/listinfo/isarmathlib-devel

** http://isarmathlib.org/

This site is an experimental HTML rendering of fragments of the IsarMathLib
project. IsarMathLib is a library of mathematical proofs formally verified by
the Isabelle theorem proving environment. The formalization is based on the
Zermelo-Fraenkel set theory.

** Tiddly Formal Math.

This site is an experimental TiddlyWiki rendering of fragments of the
IsarMathLib project. IsarMathLib is a library of mathematical proofs formally
verified by the Isabelle theorem proving environment. The formalization is
based on the Zermelo-Fraenkel set theory.

See

  http://formalmath.tiddlyspot.com/

* HOL Light.

HOL Light is a computer program to help users prove interesting mathematical
theorems completely formally in higher order logic. It sets a very exacting
standard of correctness, but provides a number of automated tools and
pre-proved mathematical theorems (e.g. about arithmetic, basic set theory and
real analysis) to save the user work. It is also fully programmable, so users
can extend it with new theorems and inference rules without compromising its
soundness.

Ocalm.

See

  http://www.cl.cam.ac.uk/~jrh13/hol-light/index.html

* ACL2.

ACL2 (A Computational Logic for Applicative Common Lisp) is a software system
consisting of a programming language, an extensible theory in a first-order
logic, and a mechanical theorem prover. ACL2 is designed to support automated
reasoning in inductive logical theories, mostly for the purpose of software
and hardware verification. The input language and implementation of ACL2 are
built on Common Lisp. ACL2 is free, open source (GPL) software.

  $ sudo apt-get install acl2

See

  http://www.cs.utexas.edu/users/moore/acl2/
  http://en.wikipedia.org/wiki/ACL2

* PVS Specification and Verification System

Old (1992). Many article in 199x.

The system is implemented in Common Lisp, and is released under the GNU
General Public License (GPL).

See

  http://pvs.csl.sri.com/
  http://en.wikipedia.org/wiki/Prototype_Verification_System
  http://www-formal.stanford.edu/clt/ARS/Entries/pvs

* The TPTP Problem Library for Automated Theorem Proving.

The TPTP (Thousands of Problems for Theorem Provers) is a library of test
problems for automated theorem proving (ATP) systems. The TPTP supplies the
ATP community with:

 * A comprehensive library of the ATP test problems that are available today,
   in order to provide an overview and a simple, unambiguous reference
   mechanism.
 * A comprehensive list of references and other interesting information for
   each problem.
 * Arbitrary size instances of generic problems (e.g., the N-queens problem).
 * A utility to convert the problems to existing ATP systems' formats.
 * General guidelines outlining the requirements for ATP system evaluation.
 * Standards for input and output for ATP systems.

The principal motivation for the TPTP is to support the testing and evaluation
of ATP systems, to help ensure that performance results accurately reflect the
capabilities of the ATP system being considered. A common library of problems
is necessary for meaningful system evaluations, meaningful system comparisons,
repeatability of testing, and the production of statistically significant
results. The TPTP is such a library.

See

  http://www.cs.miami.edu/~tptp/

* SPASS.

An Automated Theorem Prover for First-Order Logic with Equality.

See

  http://www.spass-prover.org/index.html

* Competition.

See

  http://www.cs.miami.edu/~tptp/CASC/
  http://www.cs.albany.edu/~nvm/cade.html

* Conference.

IJCAR is a series of conferences on the topics of automated reasoning,
automated deduction, and related fields. It is organized semi-regularly as a
merger of other meetings. IJCAR replaces those independent conferences in the
years it takes place. The conference is organized by CADE Inc., and CADE has
always been one of the conferences partaking in IJCAR.

See

  http://www.ijcar.org/
  http://en.wikipedia.org/wiki/International_Joint_Conference_on_Automated_Reasoning

* Top 100.

  http://www.cs.ru.nl/~freek/100/
                (winner)
  http://personal.stevens.edu/~nkahl/Top100Theorems.html
                (orig list)
  http://www.cse.unsw.edu.au/~kleing/top100/#5
                (Isabelle)