Proof assistant
From Wikipedia, the free encyclopedia
(Redirected from Interactive theorem proving)
In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by man-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer.
Contents |
[edit] Comparison
| Name | Latest version | Developer(s) | Implementation language | Features | |||||
|---|---|---|---|---|---|---|---|---|---|
| Higher-order logic | Dependent types | Small kernel | Proof automation | Proof by reflection | Program extraction | ||||
| ACL2 | 4.3 | Matt Kaufmann and J Strother Moore | Common Lisp | No | No | No | Unverified | No | |
| Agda | 2.3.0 | Ulf Norell (Chalmers) | Haskell | Yes | Yes | Yes | No | Partial | N/A |
| Coq | 8.3pl2 | INRIA | OCaml | Yes | Yes | Yes | Yes | Yes | Yes |
| Isabelle/HOL | 2011-1 | Larry Paulson (Cambridge), Tobias Nipkow (München) and Makarius Wenzel (Paris-Sud) | Standard ML | Yes | No | Yes | Yes | No | Yes |
| LEGO | 1.3.1 | Randy Pollack (Edinburgh) | Standard ML | Yes | Yes | ||||
| NuPRL | 5 | Cornell University | Common Lisp | ||||||
| PVS | 5.0 | SRI International | Common Lisp | Yes | Partial | No | Unverified | No | |
| Twelf | 1.7.1 | Frank Pfenning and Carsten Schürmann | Standard ML | Yes | Partial | Unknown | No | No | |
[edit] Other proof assistants
- ACL2 - a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer-Moore tradition.
- Coq - Which allows the expression of mathematical assertions, mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof of its formal specification.
- HOL theorem provers - A family of tools ultimately derived from the LCF theorem prover. In these systems the logical core is a library of their programming language. Theorems represent new elements of the language and can only be introduced via "strategies" which guarantee logical correctness. Strategy composition gives users the ability to produce significant proofs with relatively few interactions with the system. Members of the family include:
- HOL4 - The "primary descendant". Moscow ML based.
- HOL Light - A thriving "minimalist fork". OCaml based.
- Isabelle - With a BSD license. Based on Standard ML.
- ProofPower - Went proprietary, then returned to open source. Based on Standard ML.
- Jape - Java based.
- LEGO
- Matita - A light system based on the Calculus of Inductive Constructions.
- MINLOG - A proof assistant based on first-order minimal logic.
- Mizar - A proof assistant based on first-order logic, in a natural deduction style, and Tarski-Grothendieck set theory.
- PhoX - A proof assistant based on higher-order logic which is eXtensible.
- Prototype Verification System (PVS) - a proof language and system based on higher-order logic.
- TPS and ETPS - Interactive theorem provers also based on simply-typed lambda calculus, but based on an independent formulation of the logical theory and independent implementation.
- Typelab
- Yarrow
[edit] User interface
A popular front-end for proof assistants is the Emacs-based Proof General, developed at the University of Edinburgh.
[edit] See also
- Automated theorem proving
- Computer-assisted proof
- Proof verification
- QED manifesto
- Satisfiability Modulo Theories
[edit] References
- Frank Pfenning. "The Practice of Logical Frameworks"
- H. Geuvers. "Proof assistants: History, ideas and future".
- Freek Wiedijk. "The Seventeen Provers of the World"
[edit] External links
- "Introduction" in Certified Programming with Dependent Types.
- Introduction to the Coq Proof Assistant (with a general introduction to interactive theorem proving)
- Interactive Theorem Proving for Agda Users
- Catalogues
- Digital Math by Category: Tactic Provers
- Automated Deduction Systems and Groups
- Theorem Proving and Automated Reasoning Systems
- Database of Existing Mechanized Reasoning Systems
- NuPRL: Other Systems
- Specific Logical Frameworks and Implementations
- DMOZ: Science: Math: Logic and Foundations: Computational Logic: Logical Frameworks
 |
This computer science article is a stub. You can help Wikipedia by expanding it. |
 |
This mathematics-related article is a stub. You can help Wikipedia by expanding it. |
