## HOL-Omega

 swMATH ID: 6581 Software Authors: Homeier, Peter V. Description: The HOL-Omega logic A new logic is posited for the widely used HOL theorem prover, as an extension of the existing higher order logic of the HOL4 system. The logic is extended to three levels, adding kinds to the existing levels of types and terms. New types include type operator variables and universal types as in System $$F$$. Impredicativity is avoided through the stratification of types by ranks according to the depth of universal types. The new system, called HOL-Omega or $$mathrm{HOL} _{omega }$$, is a merging of HOL4, HOL2P, and major aspects of System $$F _{omega }$$ from Chapter 30 of [{it B. C. Pierce}, Types and programming languages. Cambridge: MIT Press (2002)]. This document presents the abstract syntax and semantics for the kinds, types, and terms of the logic, as well as the new fundamental axioms and rules of inference. As the new logic is constructed according to the design principles of the LCF approach, the soundness of the entire system depends critically and solely on the soundness of this core. Homepage: http://trustworthytools.com/id17.html Related Software: HOL; Isabelle; Coq; Lifting; Transfer; HOL Light; Isabelle/HOL; HOL Zero; ML; Haskell; Agda; Matita; Archive Formal Proofs; Density Compiler; Locales; Berlekamp Zassenhaus; Nuprl; Mizar; seL4; Isar Cited in: 9 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
The HOL-Omega logic. Zbl 1252.68257
Homeier, Peter V.
2009
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### Cited by 13 Authors

 4 Popescu, Andrei 3 Kunčar, Ondřej 3 Lochbihler, Andreas 1 Arthan, Rob D. 1 Blanchette, Jasmin Christian 1 Bouzy, Aymeric 1 Guéneau, Armaël 1 Homeier, Peter V. 1 Kumar, Ramana 1 Myreen, Magnus O. 1 Norrish, Michael 1 Schneider, Joshua P. 1 Traytel, Dmitry

### Cited in 1 Serial

 3 Journal of Automated Reasoning

### Cited in 2 Fields

 9 Computer science (68-XX) 1 Category theory; homological algebra (18-XX)