About CVC4
CVC4 is an automatic theorem prover for Satisifiability Modulo Theories (SMT) (for a more formal introduction to SMT see the following book chapter Satisfiability Modulo Theories ). Technically, it is an automated validity checker for a many-sorted (i.e., typed) first-order logic with built-in theories. It can be used to prove the validity (or, dually, the satisfiability) of with respect to several built-in logical theories and their combination.
CVC4 currently has support for the following theories:
- equality over free (aka uninterpreted) function and predicate symbols
- real and integer linear arithmetic
- bit-vectors
- arrays
- tuples
- records
- user-defined inductive data types.
CVC4 has a wide variety of features including:
- support for quantifiers through heuristic instantiaion;
- an interactive text-based interface;
- a rich C++ API for embedding in other systems;
- model generation abilities;
- source compatibility with much of the CVC3 API via a "compatibility library";
- essentially no limit on its use for research or commercial purposes (see license).
Web site
For more information and the latest news about CVC4, visit the CVC4 web site.
Decision Procedures
- Architecture
- See the CVC4 tool paper.
- Arithmetic
- Linear arithmetic is roughly an implementation of [yices.csl.sri.com/sri-csl-06-01.pdf Integrating Simplex with DPLL(T)]. A technical report is planned to explain our extensions.
- Integers are currently handled in an equational solver based on A Practical Approach to Satisfiability Modulo Linear Integer Arithmetic.
- Non-linear arithmetic support is rudimentary to non-existant. Currently, it is handled by abstracting monomials as unique new variables. We plan on implementing Solving Non-Linear Arithmetic this spring.
- Arrays
- Arrays are implemented in a manner inspired by the Generalized, efficient array decision procedures paper with a few major modifications.
- Bitvectors
- Bitvectors is implemented primarily via a lazy schema for bitblasting. See Anders Franz�en's thesis chapter 3.
- Combination
- Theory combination is based on the care graph framework described in both Being careful about theory combination and Sharing is Caring: Combination of Theories.
- Datatypes
- CVC4 implements An Abstract Decision Procedure for a Theory of Inductive Data Types.
- Quantifiers
- An overall description of the quantifier framework is given here [1].
- Rewrite rules [citation?]
- Finite model finding is described in this presentation.
- SAT Solver
- The main sat solver is based on minisat v2.2.0.
- Additionally, we use justification and relevancy to limit what gets sent to each theory. [citation?]
- Uninterpreted functions
- UF (without cardinality) is handled in a manner inspired by Simplify's tech report.
- UF + cardinality is described this presentation and is used for finite model finding.
History of CVC
The Cooperating Validity Checker series has a long history. The Stanford Validity Checker (SVC) came first in 1996, incorporating theories and its own SAT solver. Its successor, the Cooperating Validity Checker (CVC), had a more optimized internal design, produced proofs, used the Chaff SAT solver, and featured a number of usability enhancements. Its name comes from the cooperative nature of decision procedures in Nelson-Oppen theory combination, which share amongst each other equalities between shared terms. CVC Lite, first made available in 2003, was a rewrite of CVC that attempted to make CVC more flexible (hence the "lite") while extending the feature set: CVC Lite supported quantifiers where its predecessors did not. CVC3 was a major overhaul of portions of CVC Lite: it added better decision procedure implementations, added support for using MiniSat in the core, and had generally better performance.
CVC4 is the new version, the fifth generation of this validity checker line that is now celebrating sixteen years of heritage. It represents a complete re-evaluation of the core architecture to be both performant and to serve as a cutting-edge research vehicle for the next several years. Rather than taking CVC3 and redesigning problem parts, we've taken a clean-room approach, starting from scratch. Before using any designs from CVC3, we have thoroughly scrutinized, vetted, and updated them. Many parts of CVC4 bear only a superficial resemblance, if any, to their correspondent in CVC3.
However, CVC4 is fundamentally similar to CVC3 and many other modern SMT solvers: it is a DPLL(T) solver, with a SAT solver at its core and a delegation path to different decision procedure implementations, each in charge of solving formulas in some background theory.
The re-evaluation and ground-up rewrite was necessitated, we felt, by the performance characteristics of CVC3. CVC3 has many useful features, but some core aspects of the design led to high memory use, and the use of heavyweight computation (where more nimble engineering approaches could suffice) makes CVC3 a much slower prover than other tools. As these designs are central to CVC3, a new version was preferable to a selective re-engineering, which would have ballooned in short order.
