Comparison of Systems
See also: Dependent type#Comparison and Automated theorem proving#Comparison| Name | Latest version | Developer(s) | Implementation language | Features | |||||
|---|---|---|---|---|---|---|---|---|---|
| Higher-order logic | Dependent types | Small kernel | Proof automation | Proof by reflection | Program extraction | ||||
| ACL2 | 5.0 | Matt Kaufmann and J Strother Moore | Common Lisp | No | No | Yes | Yes | ||
| Agda | 2.3.0 | Ulf Norell (Chalmers) | Haskell | Yes | Yes | Yes | No | Partial | |
| Coq | 8.4 | INRIA | OCaml | Yes | Yes | Yes | Yes | Yes | Yes |
| HOL Light | repository | John Harrison | OCaml | Yes | No | Yes | Yes | No | Unknown |
| Isabelle/HOL | 2012 | Larry Paulson (Cambridge), Tobias Nipkow (München) and Makarius Wenzel (Paris-Sud) | Standard ML | Yes | No | Yes | Yes | Yes | Yes |
| LEGO | 1.3.1 | Randy Pollack (Edinburgh) | Standard ML | Yes | Yes | Unknown | Unknown | Unknown | Unknown |
| NuPRL | 5 | Cornell University | Common Lisp | Yes | Yes | Yes | Yes | Unknown | Yes |
| PVS | 5.0 | SRI International | Common Lisp | Yes | Yes | No | Yes | No | Unknown |
| Twelf | 1.7.1 | Frank Pfenning and Carsten Schürmann | Standard ML | Yes | Yes | Unknown | No | No | Unknown |
- 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 with a BSD-style license.
- 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
Read more about this topic: Proof Assistant
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