## A comparison of HOL-ST and Isabelle/ZF (1995)

Citations: | 2 - 2 self |

### BibTeX

@TECHREPORT{Agerholm95acomparison,

author = {Sten Agerholm},

title = {A comparison of HOL-ST and Isabelle/ZF},

institution = {},

year = {1995}

}

### OpenURL

### Abstract

The use of higher order logic (simple type theory) is often limited by its restrictive type system. Set theory allows many constructions on sets that are not possible on types in higher order logic. This paper presents a comparison of two theorem provers supporting set theory, namely HOL-ST and Isabelle/ZF, based on a formalization of the inverse limit construction of domain theory � this construction cannot be formalized in higher order logic directly. We argue that whilst the combination of higher order logic and set theory in HOL-ST has advantages over the rst order set theory in Isabelle/ZF, the proof infrastructure of Isabelle/ZF has better support for set theory proofs than HOL-ST. Proofs in Isabelle/ZF are both considerably shorter and easier to write. 1

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(Show Context)
Citation Context ...ombine the usefulness of higher order logic with the expressive power of set theory in a single system [5]. A prototype system, called HOLST, has been implemented by extending the existing HOL system =-=[4]-=- with axioms of ZF set theory (this is not a conservative extension). A larger case study on HOL-ST was presented in [1]. By formalizing the inverse limit construction of domain theory, which would no... |

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Citation Context ...do not give a detailed presentation of the formalization (see [1]). The version of the inverse limit construction employed here is based on categorical methods using embedding project pairs, see e.g. =-=[6, 11, 10]-=-. Comparing systems is di cult. The lack of some feature supported by one system does not mean that it could not be supported by another. In this paper, we have chosen to freeze time in the sense that... |

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Citation Context ...do not give a detailed presentation of the formalization (see [1]). The version of the inverse limit construction employed here is based on categorical methods using embedding project pairs, see e.g. =-=[6, 11, 10]-=-. Comparing systems is di cult. The lack of some feature supported by one system does not mean that it could not be supported by another. In this paper, we have chosen to freeze time in the sense that... |

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Citation Context ...ZF) set theory. Gordon has also been experimenting with mechanizing set theory in an attempt to combine the usefulness of higher order logic with the expressive power of set theory in a single system =-=[5]-=-. A prototype system, called HOLST, has been implemented by extending the existing HOL system [4] with axioms of ZF set theory (this is not a conservative extension). A larger case study on HOL-ST was... |

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Citation Context ...system, called HOLST, has been implemented by extending the existing HOL system [4] with axioms of ZF set theory (this is not a conservative extension). A larger case study on HOL-ST was presented in =-=[1]-=-. By formalizing the inverse limit construction of domain theory, which would not be possible in HOL directly [2], the case study demonstrated how one can make essential use of the additional expressi... |

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Citation Context ...nizing set theory. He has developed a very large amount of set theory in his Isabelle/ZF system [7, 8], which is an extension of a rst order logic instantiation of the genericstheorem prover Isabelle =-=[9]-=- with axioms of Zermelo-Fraenkel (ZF) set theory. Gordon has also been experimenting with mechanizing set theory in an attempt to combine the usefulness of higher order logic with the expressive power... |

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Citation Context ...n applying stronger type theories in theorem proving. Paulson has done a lot of pioneering work on mechanizing set theory. He has developed a very large amount of set theory in his Isabelle/ZF system =-=[7, 8]-=-, which is an extension of a rst order logic instantiation of the genericstheorem prover Isabelle [9] with axioms of Zermelo-Fraenkel (ZF) set theory. Gordon has also been experimenting with mechanizi... |

1 |
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(Show Context)
Citation Context ...n applying stronger type theories in theorem proving. Paulson has done a lot of pioneering work on mechanizing set theory. He has developed a very large amount of set theory in his Isabelle/ZF system =-=[7, 8]-=-, which is an extension of a rst order logic instantiation of the genericstheorem prover Isabelle [9] with axioms of Zermelo-Fraenkel (ZF) set theory. Gordon has also been experimenting with mechanizi... |

1 |
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Citation Context ...do not give a detailed presentation of the formalization (see [1]). The version of the inverse limit construction employed here is based on categorical methods using embedding project pairs, see e.g. =-=[6, 11, 10]-=-. Comparing systems is di cult. The lack of some feature supported by one system does not mean that it could not be supported by another. In this paper, we have chosen to freeze time in the sense that... |