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Abstract: . The majority of general purpose mechanised proof assistants support versions of typed higher order logic, even though set theory is the standard foundation for mathematics. For many applications higher order logic works well and provides, for specification, the benefits of type-checking that are well-known in programming. However, there are areas where types get in the way or seem unmotivated. Furthermore, most people with a scientific or engineering background already know set theory, ... (Update)
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BibTeX entry: (Update)
@misc{ gordon-set,
author = "Michael J.C. Gordon",
title = "Set Theory, Higher Order Logic or Both?",
url = "citeseer.ist.psu.edu/328122.html" }
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505 Implementing Mathematics with the Nuprl Proof Development Sy.. - Constable - 1986
419 A formulation of the simple theory of types (context) - Church - 1940
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44 An analysis of Girard's paradox - Coquand - 1986
40 volume 133 of Studies in Logic and The Foundations of Mathem.. (context) - Nederpelt, Geuvers et al. - 1994
37 The Coq proof assistant user's guide - version (context) - Dowek, Felty et al. - 1993
34 Specifying and verifying fault-tolerant systems - Lamport, Merz - 1994
18 Exploring abstract algebra in constructive type theory (context) - Paul - 1994
11 a specification language based on type theory (context) - Hanna, Daeche et al. - 1989
9 Formalising a model of the -calculus in HOL-ST (context) - Agerholm - 1994
8 Abstract Hardware Limited (context) - Finn, Fourman et al. - 1993
7 Experiments with ZF Set Theory in HOL and Isabelle - Agerholm, Gordon - 1995
5 The enhanced HDM system for specification and verification (context) - Melliar-Smith, Rushby - 1985
4 Mechanizing set theory (context) - Corella - 1991
4 but available by anonymous FTP from menaik (context) - Rudnicki, of et al. - 1992
3 Merging HOL with set theory (context) - Gordon - 1994
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