Experiments with ZF Set Theory in HOL and Isabelle

Sten Agerholm, Mike Gordon

Abstract


Most general purpose proof assistants support versions of
typed higher order logic. Experience has shown that these logics are capable
of representing most of the mathematical models needed in Computer
Science. However, perhaps there exist applications where ZF-style
set theory is more natural, or even necessary. Examples may include
Scott's classical inverse-limit construction of a model of the untyped lambda-calculus
(D_inf) and the semantics of parts of the Z specification notation.

This paper compares the representation and use of ZF set theory within
both HOL and Isabelle. The main case study is the construction of D_inf.
The advantages and disadvantages of higher-order set theory versus first-order
set theory are explored experimentally. This study also provides a
comparison of the proof infrastructure of HOL and Isabelle.

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DOI: http://dx.doi.org/10.7146/brics.v2i37.19940
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ISSN: 0909-0878 

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