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HOL Light QE. (English) Zbl 1511.68307

Avigad, Jeremy (ed.) et al., Interactive theorem proving. 9th international conference, ITP 2018, held as part of the federated logic conference, FloC 2018, Oxford, UK, July 9–12, 2018. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 10895, 215-234 (2018).
Summary: We are interested in algorithms that manipulate mathematical expressions in mathematically meaningful ways. Expressions are syntactic, but most logics do not allow one to discuss syntax. \(\mathrm{CTT}_\mathrm{qe}\) is a version of Church’s type theory that includes quotation and evaluation operators, akin to quote and eval in the Lisp programming language. Since the HOL logic is also a version of Church’s type theory, we decided to add quotation and evaluation to HOL Light to demonstrate the implementability of \(\mathrm{CTT}_\mathrm{qe}\) and the benefits of having quotation and evaluation in a proof assistant. The resulting system is called HOL Light QE. Here we document the design of HOL Light QE and the challenges that needed to be overcome. The resulting implementation is freely available.
For the entire collection see [Zbl 1391.68001].

MSC:

68V15 Theorem proving (automated and interactive theorem provers, deduction, resolution, etc.)
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