Alt-Ergo

Alt-Ergo, an automatic solver for mathematical formulas, is mainly used in formal program verification. It operates on the principle of satisfiability modulo theories (SMT). Development was undertaken by researchers at the Paris-Sud University, Laboratoire de Recherche en Informatique, Inria Saclay Ile-de-France, and CNRS. Since 2013, project management and oversight has been conducted by OCamlPro company. It is released under the free and open-source software CeCILL-C license.

Design choices
Alt-Ergo employs a specialized input language with prenex polymorphism, designed to reduce the number of axioms requiring quantification and to simplify the complexity of problems. While Alt-Ergo offers partial support for the SMT-LIB 2 language, its efficiency with SMT files is comparatively limited.

Main components
The core architecture of Alt-Ergo comprises three main elements: a depth-first search (DFS)-based SAT solver, a quantifiers instantiation engine that uses e-matching, and an assembly of decision procedures for a range of built-in theories. These components collectively enable Alt-Ergo's abilities in automatic formula solving.

Built-in theories
Alt-Ergo implements (semi-)decision procedures for the following theories:
 * Empty theory
 * Linear integer arithmetic
 * Linear rational arithmetic
 * Non-linear arithmetic
 * Floating point arithmetic
 * Polymorphic arrays
 * Enumerated data types
 * AC symbols
 * Record data types

Industrial uses
Several verification platforms are built on Alt-Ergo:
 * Why3, a platform for deductive program verification, uses Alt-Ergo as main prover
 * CAVEAT, a C-verifier developed by CEA and used by Airbus; Alt-Ergo was included in the qualification DO-178C of one of its aircraft
 * Frama-C, a framework to analyse C-code, uses Alt-Ergo in the Jessie and WP plugins (dedicated to deductive program verification)
 * SPARK, uses Alt-Ergo (behind GNATprove) to automate the verification of some assertions in Spark 2014
 * Atelier-B can use Alt-Ergo instead of its main prover (raising success from 84% to 98% on ANR Bware project benchmarks)
 * Rodin, a B-method framework developed by Systerel, can use Alt-Ergo as a back-end
 * Cubicle, an open source model checker to verify safety properties of array-based transition systems
 * EasyCrypt, a toolset for reasoning about relational properties of probabilistic computations with adversarial code
 * BWARE
 * Cafein
 * FUI Hi-Lite
 * Decert
 * ADT Alt-Ergo
 * A3PAT