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Experiments with ZF Set Theory in HOL and Isabelle
 IN PROCEEDINGS OF THE 8TH INTERNATIONAL WORKSHOP ON HIGHER ORDER LOGIC THEOREM PROVING AND ITS APPLICATIONS, LNCS
, 1995
"... 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 ZFstyle set theory is more natural, ..."
Abstract

Cited by 13 (1 self)
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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 ZFstyle set theory is more natural, or even necessary. Examples may include Scott's classical inverselimit construction of a model of the untyped  calculus (D1 ) and the semantics of parts of the Z specification notation. This paper
Merging HOL with Set Theory  preliminary experiments
, 1994
"... Set theory is the standard foundation for mathematics, but the majority of general purpose mechanised proof assistants support versions of type theory (higher order logic). Examples include Alf, Automath, Coq, EHDM, HOL, IMPS, LAMBDA, LEGO, Nuprl, PVS and Veritas. For many applications type theory w ..."
Abstract

Cited by 11 (1 self)
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Set theory is the standard foundation for mathematics, but the majority of general purpose mechanised proof assistants support versions of type theory (higher order logic). Examples include Alf, Automath, Coq, EHDM, HOL, IMPS, LAMBDA, LEGO, Nuprl, PVS and Veritas. For many applications type theory works well and provides, for specification, the benefits of typechecking that are wellknown 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, whereas type theory may appear inaccessable and so be an obstacle to the uptake of proof assistants based on it. This paper describes some experiments (using HOL) in combining set theory and type theory; the aim is to get the best of both worlds in a single system. Three approaches have been tried, all based on an axiomatically specified type V of ZFlike sets: (i) HOL is used without any additions besides V; (ii) an emb...