Audenaert, P.

Hoogewijs, Albert

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Ghent University Academic Bibliography

Contributed Papers 110Albert HoogewijsFormath: Higher-order logic revisedjoint work with Pieter AudenaertHOL (Higher-order logic) systems [3] are a family of interactive theoremproving tools, widely used for creating formal specifications of systems,and for proving properties about them. They have been deployed inboth industry and academia to support formal reasoning in many areas,including hardware and software verification. The underlying logic andbasic facilities are completely general. In principle they can be used tosupport any project that can be defined in higher-order logic, an ex-pressive logic originally developed as a foundation for mathematics. In[1] Audenaert extends this family with one more descendant: Formath.When formal methods are used to increase the reliability of software sys-tems, the result directly depends on the correctness of the proof systemthat supports the application of the formal methods. It is shown that For-math is equiconsistent to Hol-4 and Hol-Light. Formath stands out fromthe latter, in using a deduction calculus based on sequents of the formΓ1 ` Γ2, where Γ1 and Γ2 represent finite sets of formulas, and in usinga pert constant CEXT of type (α→ β) → (α→ β) → α in the formula-tion of the Extensionality axiom : f(CEXT fg) = g(CEXT fg) ` f = g.Note that CEXT fg represents a term t such that ft differs from gt (ifsuch a t exists). Hence Extensionality reads as follows: two functions areequal if they coincide on their “difference”. In [1] Formath is used forthe specification and verification of Alfred programs (see [2]).References[1] P. Audenaert, Specificatie en Verificatie van Functionele Programmatuur inHogere-Orde-Logica. PhD-thesis, UGent 2004.[2] A. Hoogewijs and P. Audenaert, Combinatory Logic, a Bridge to Verified Pro-grams, The Bulletin of Symbolic Logic (to be published).[3] http://www.dcs.gla.ac.uk/~tfm/hol-bib.htmlGhent University, Galglaan 2, B-9000 Gent, Belgium

Formath: Higher-order logic revised

Formath: higher-order logic revised

https://biblio.ugent.be/publication/302130/file/451760

Formath: Higher-order logic revised

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Ghent University Academic Bibliography

Ghent University Academic Bibliography