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Logic and Foundations
LF Logical Framework
Af2 Proof Assistant
- A type system based on second order intuitionistic logic.
- A successor to the proof editor Alf with a graphical user interface, being developed at the Programming Logic Group at Chalmers. Available for download.
The HOL Theorem Proving System
- The system documented originated at the Laboratory for Applied Logic of Brigham Young University and features higher-order, classical, natural deduction with tactics.
- Homepage of the theorem prover environment developed by Larry Paulson at Cambridge University and Tobias Kipkow at TU Munich.
- A web-based proof assistant. It assists with proofs in first order hidden logic, using OBJ3 as a reduction engine. The most important inference rules in first order logic and hidden equational logic are implemented, including induction and coinduction, generates proof documentation for the web, supports distributed cooperative proving.
The LEGO Proof Assistant
- A powerful tool for interactive proof development in the natural deduction style. It supports refinement proof as a basic operation. The system design emphasizes removing the more tedious aspects of interactive proofs.
MetaPRL logical programming environment
- The next generation of the NuPrl proof development system. The main new features of MetaPRL include: 1) Modularity. Programs and logics are developed as modules that define computational, heuristic, and mathematical properties. 2) Speed. MetaPRL is more than two orders of magnitude faster than NuPrl.
NuPrl Proof Development System
- A powerful tactic-based proof assistant, developed over the last 15 years at Cornell University. Features include: very expressive logical language based on Martin-Lof type theory, extensive library of formal mathematics and automata theory, possibility of an extraction a certified program from the constructive proof of its formal specification, graphical proof editor. NuPrl was successfully used in verifying components of the Ensemble group communications system.
The Practice of Logical Frameworks
- Comprehensive survey article by Frank Pfenning (1996) discussing the history of work on logical frameworks and their current open problems.
- Emacs based generic interface for theorem provers.
- A proof-assistant for Pure Type Systems (PTSs), representing different logics and programming languages. A basic knowledge of Pure Type Systems and the Curry-Howard-de Bruijn isomorphism is required. (This isomorphism says how you can interpret types as propositions.)
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