Z3 Theorem Prover

Z3, also known as the Z3 Theorem Prover, is a satisfiability modulo theories (SMT) solver developed by Microsoft.^[2]

Z3 Theorem Prover

Original author(s)	Microsoft Research
Developer(s)	Microsoft
Initial release	2012; 12 years ago (2012)
Stable release	4.13.3[1]  / 11 October 2024; 44 days ago (11 October 2024)
Repository	github.com/Z3Prover/z3
Written in	C++
Operating system	Windows, FreeBSD, Linux (Debian, Ubuntu), macOS
Platform	IA-32, x86-64, WebAssembly, arm64
Type	Theorem prover
License	MIT License
Website	github.com/Z3Prover

Overview

Z3 was developed in the Research in Software Engineering (RiSE) group at Microsoft Research Redmond and is targeted at solving problems that arise in software verification and program analysis. Z3 supports arithmetic, fixed-size bit-vectors, extensional arrays, datatypes, uninterpreted functions, and quantifiers. Its main applications are extended static checking, test case generation, and predicate abstraction.^{[citation needed]}

Z3 was open sourced in the beginning of 2015.^[3] The source code is licensed under MIT License and hosted on GitHub.^[4] The solver can be built using Visual Studio, a makefile or using CMake and runs on Windows, FreeBSD, Linux, and macOS.

The default input format for Z3 is SMTLIB2. It also has officially supported bindings for several programming languages, including C, C++, Python, .NET, Java, and OCaml.^[5]

Examples

Propositional and predicate logic

In this example propositional logic assertions are checked using functions to represent the propositions a and b. The following Z3 script checks to see if ${\displaystyle {\overline {a\land b}}\equiv {\overline {a}}\lor {\overline {b}}}$:

(declare-fun a () Bool)
(declare-fun b () Bool)
(assert (not (= (not (and a b)) (or (not a)(not b)))))
(check-sat)

Result:

unsat

Note that the script asserts the negation of the proposition of interest. The unsat result means that the negated proposition is not satisfiable, thus proving the desired result (De Morgan's law).

Solving equations

The following script solves the two given equations, finding suitable values for the variables a and b:

(declare-const a Int)
(declare-const b Int)
(assert (= (+ a b) 20))
(assert (= (+ a (* 2 b)) 10))
(check-sat)
(get-model)

Result:

sat
(model 
  (define-fun b () Int
    -10)
  (define-fun a () Int
    30)
)

Awards

In 2015, Z3 received the Programming Languages Software Award from ACM SIGPLAN.^[6][7] In 2018, Z3 received the Test of Time Award from the European Joint Conferences on Theory and Practice of Software (ETAPS).^[8] Microsoft researchers Nikolaj Bjørner and Leonardo de Moura received the 2019 Herbrand Award for Distinguished Contributions to Automated Reasoning in recognition of their work in advancing theorem proving with Z3.^[9][10]

See also

• Free and open-source software portal

• Formal verification

References

1. "Release 4.13.3". 11 October 2024. Retrieved 27 October 2024.
2. "Using the SMT solver Z3" (PDF). Archived from the original (PDF) on 2020-11-17. Retrieved 2019-12-01.
3. "Microsoft's Visual Studio timeline and Z3 Theorem Prover, Google Cloud Launcher, Facebook's Fresco—SD Times news digest: March 27, 2015". March 27, 2015.
4. "GitHub - Z3Prover/z3: The Z3 Theorem Prover". December 1, 2019 – via GitHub.
5. Bjørner, Nikolaj; de Moura, Leonardo; Nachmanson, Lev; Wintersteiger, Christoph (2019). "Programming Z3". Programming Z3. Archived from the original on February 9, 2023. Retrieved May 21, 2023.
6. "Programming Languages Software Award". www.sigplan.org.
7. Microsoft Z3 Theorem Prover Wins Award
8. ETAPS 2018 Test of Time Award
9. The inner magic behind the Z3 theorem prover - Microsoft Research
10. Herbrand Award

Further reading

• Leonardo De Moura; Nikolaj Bjørner (2008). "Z3: an efficient SMT solver". Tools and Algorithms for the Construction and Analysis of Systems. 4963: 337–340.
• The inner magic behind the Z3 theorem prover

External links

• Official website
• Z3 online playground