Tools on Rewriting

Isabelle is a generic proof assistant. It allows mathematical formulas to be expressed in a formal language and provides tools for proving those formulas in a logical calculus. The main application is the formalization of mathematical proofs and in particular formal verification, which includes proving the correctness of computer hardware or software and proving properties of computer languages and protocols.
Last updated: 20171027 19:34:01...

MINLOG is an interactive proof system developed by Helmut Schwichtenberg and members of the logic group at the University of Munich. MINLOG is based on first order natural deduction calculus. It is intended to reason about computable functionals, using minimal rather than classical or intuitionistic logic. The main motivation behind MINLOG is to exploit the proofsasprograms paradigm for program development and program verification. Proofs are in fact treated as first class objects which can be normalized. If a formula is existential then its proof can be used for reading off an instance of it, or changed appropriately for program development by proof transformation. To this end MINLOG is equipped with tools to extract functional programs directly from proof terms. This also applies to nonconstructive proofs, using a refined Atranslation. The system is supported by automatic proof search and normalization by evaluation as an efficient term rewriting device.
The case studies contain material from the following publications: ... Schwichtenberg and H. Tsuiki. (In D. Probst and P. Schuster (eds), Concepts of Proof in Mathematics, Philosophy, and Comput...

PVS is a verification system: that is, a specification language integrated with support tools and a theorem prover. It is intended to capture the stateoftheart in mechanized formal methods and to be sufficiently rugged that it can be used for significant applications. PVS is a research prototype: it evolves and improves as we develop or apply new capabilities, and as the stress of real use exposes new requirements.
Last modified: Wed 05 Feb 2014 23:49 UTC...

ACL2 is a very large, multipurpose system. You can use it as a programming language, a specification language, a modeling language, a formal mathematical logic, or a semiautomatic theorem prover, just to name its most common uses.
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CITP is a tool for proving inductive properties of software systems specified with constructor based logics. CITP is equipped with a default proof strategy for the automated verification of Observational Transitional Systems (OTS), but the area of applications is not restricted to OTS. The proof strategy can be customised by the user, or the basic tactics can be applied stepbystep. The Kernel of CITP is implemented in Core Maude. The interface of CITP is implemented in Full Maude.

The aim of the system daTac is to do automated deduction in firstorder logic with equality. Its speciality is to apply deductions modulo some equational properties of operators, such as commutativity or associativitycommutativity (AC). The deduction techniques implemented, based on resolution, paramodulation and term rewriting, have been proved refutationally complete.

iProver is an instantiationbased theorem prover which is based on InstGen calculus, complete for firstorder logic. One of the distinctive features of iProver is a modular combination of instantiation and propositional reasoning. In particular, any stateofthe art SAT solver can be integrated into our framework. iProver incorporates stateoftheart implementation techniques such as indexing, redundancy elimination, semantic selection and saturation algorithms. Redundancy elimination implemented in iProver include: dismatching constraints, blocking nonproper instantiations and propositionalbased simplifications. In addition to instantiation, iProver implements ordered resolution calculus and a combination of instantiation and ordered resolution.
New version: iProver v0.99 (CASCJ6, 2012) to be released in a few days!!! ... Easy to install: We assume OCaml v3.12 >= is installed. ... iProver won the (effectively propositional) EPR division...

E is a a purely equational theorem prover for full firstorder logic. That means it is a program that you can stuff a mathematical specification (in firstorder format) and a hypothesis into, and which will then run forever, using up all of your machines resources. Very occasionally it will find a proof for the hypothesis and tell you so...