Merging Hol With Set Theory

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Merging Hol With Set Theory

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Author : Michael J. C. Gordon
language : en
Publisher:
Release Date : 1994

Merging Hol With Set Theory written by Michael J. C. Gordon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Computer programs categories.

Abstract: "Set theory is the standard foundation for mathematics, but the majority of general purpose mechanized 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 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, whereas type theory may appear inaccessable [sic] 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 ZF-like sets: (i) HOL is used without any additions besides V; (ii) an embedding of the HOL logic into V is provided; (iii) HOL axiomatic theories are not automatically translated into set-theoretic definitional theories. These approaches are illustrated with two examples: the construction of lists and a simple lemma in group theory."

Theorem Proving In Higher Order Logics

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Author :
language : en
Publisher:
Release Date : 1998

Theorem Proving In Higher Order Logics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Automatic theorem proving categories.

Higher Order Logic Theorem Proving And Its Applications

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Author :
language : en
Publisher:
Release Date : 1995

Higher Order Logic Theorem Proving And Its Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Automatic theorem proving categories.

Theorem Proving In Higher Order Logics

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Author : Joakim von Wright
language : en
Publisher: Springer
Release Date : 1996-08-07

Theorem Proving In Higher Order Logics written by Joakim von Wright and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-07 with Computers categories.

This book constitutes the refereed proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics, TPHOL '96, held in Turku, Finland, in August 1996. The 27 revised full papers included together with one invited paper were carefully selected from a total of 46 submissions. The topics addressed are theorem proving technology, proof automation and decision procedures, mechanized theorem proving, extensions of higher order logics, integration of external tools, novel applications, and others. All in all, the volume is an up-to-date report on the state of the art in this increasingly active field.

A Comparison Of Hol St And Isabelle Zf

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Author : Sten Agerholm
language : en
Publisher:
Release Date : 1995

A Comparison Of Hol St And Isabelle Zf written by Sten Agerholm and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Automatic theorem proving categories.

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 first 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."

Theorem Proving With The Real Numbers

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Author : John Robert Harrison
language : en
Publisher:
Release Date : 1996

Theorem Proving With The Real Numbers written by John Robert Harrison and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Automatic theorem proving categories.

Abstract: "This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few 'discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of floating point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We describe the rigorous definitional construction of the real numbers, using a new version of Cantor's method, and the formalization of a significant portion of real analysis. We also describe an advanced derived decision procedure for the 'Tarski subset' of real algebra as well as some more modest but practically useful tools for automating explicit calculations and routine linear arithmetic reasoning. Finally, we consider in more detail two interesting application areas. We discuss the desirability of combining the rigour of theorem provers with the power and convenience of computer algebra systems, and explain a method we have used in practice to achieve this. We then move on to the verification of floating point hardware. After a careful discussion of possible correctness specifications, we report on two case studies, one involving a transcendental function. We aim to show that a theory of real numbers is useful in practice and interesting in theory, and that the 'LCF style' of theorem proving is well suited to the kind of work we describe. We hope also to convince the reader that the kind of mathematics needed for applications is well within the abilities of current theorem proving technology."

Proceedings Of The First Isabelle Users Workshop

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Author : Lawrence C. Paulson
language : en
Publisher:
Release Date : 1995

Proceedings Of The First Isabelle Users Workshop written by Lawrence C. Paulson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Computers categories.

Modular Reasoning In Isabelle

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Author : Florian Kammüller
language : en
Publisher:
Release Date : 1999

Modular Reasoning In Isabelle written by Florian Kammüller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Automatic theorem proving categories.

Abstract: "This work is concerned with modules for higher order logic theorem provers, in particular Isabelle. Modules may be used to represent abstract mathematical structures. This is typical for applications in abstract algebra. In Chapter 1, we set out with the hypothesis that for an adequate representation of abstract structures we need modules that have a representation in the logic. We identify the aspects of locality and adequacy that are connected to the idea of modules in theorem provers. In Chapter 2, we compare module systems of interactive theorem provers and their applicability to abstract algebra. Furthermore, we investigate a different family of proof systems based on type theory in Section 2.4. We validate our hypothesis by performing a large case study in group theory: a mechanization of Sylow's theorem in Chapter 3. Drawing from the experience gained by this large case study, we develop a concept of locales in Chapter 4 that captures local definitions, pretty printing syntax, and local assumptions. This concept is implemented and released with Isabelle version 98-1. However, this concept is alone not sufficient to describe abstract structures. For example, structures like groups and rings need a more explicit representation as objects in the logic. A mechanization of dependent [sigma]-types and [pi]-types as typed sets in higher order logic is produced in Chapter 5 to represent structures adequately. In Chapter 6, we test our results by applying the two concepts we developed in combination. First, we reconsider the Sylow case study. Furthermore, we demonstrate more algebraic examples. Factorization of groups, direct product of groups, and ring automorphisms are constructions that form themselves groups, which is formally proved. We also discuss the proof of the full version of Tarski's fixed point theorem. Finally, we consider how operations on modules can be realized by structures as dependent types. Locales are used in addition; we illustrate the reuse of theorems proved in a locale and the construction of a union of structures."

British Reports Translations And Theses

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Author : British Library. Document Supply Centre
language : en
Publisher:
Release Date : 1995

British Reports Translations And Theses written by British Library. Document Supply Centre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Dissertations, Academic categories.

Issue for Mar. 1981 contains index for Jan.-Mar. 1981 in microfiche form.

Overnight Inheritance Marriages And Mergers Book 2 Mills Boon Desire

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Author : Rachel Bailey
language : en
Publisher: HarperCollins UK
Release Date : 2023-12-07

Overnight Inheritance Marriages And Mergers Book 2 Mills Boon Desire written by Rachel Bailey and has been published by HarperCollins UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-07 with Fiction categories.

A fortune isn’t the only thing she inherited...