Book ChapterDOI
Theory Interpretation in Simple Type Theory
William M. Farmer
- pp 96-123
TLDR
Although the method is based on a nonclassical version of simple type theory, it is intended as a guide for theory interpretation in classical simple type theories as well as in predicate logics with partial functions.Abstract:
Theory interpretation is a logical technique for relating one axiomatic theory to another with important applications in mathematics and computer science as well as in logic itself. This paper presents a method for theory interpretation in a version of simple type theory, called lutins, which admits partial functions and subtypes. The method is patterned on the standard approach to theory interpretation in first-order logic. Although the method is based on a nonclassical version of simple type theory, it is intended as a guide for theory interpretation in classical simple type theories as well as in predicate logics with partial functions.read more
Citations
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BookDOI
MathDox : mathematical documents on the web
TL;DR: OMDoc: Open Mathematical Documents, an OMDoc Primer, and the RelaxNG Schemata for Mathematical Objects.
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OMDoc -- An Open Markup Format for Mathematical Documents [version 1.2]: Foreword by Alan Bundy (Lecture Notes in Computer Science)
TL;DR: In contrast to the OMDoc format, this report is a total re-write, it closes many documentation gaps, clarifies various remaining issues and adds a multitude of new examples.
Journal ArticleDOI
MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems
Michael Kohlhase,Andreas Franke +1 more
TL;DR: The data model of the MB ase system, a web-based, distributed mathematical knowledge base, is described, a mathematical service in MathWeb that offers a universal repository of formalized mathematics where the formal representation allows semantics-based retrieval of distributed mathematical facts.
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The open theory standard theory library
TL;DR: The core contribution of this paper is the presentation of a standard theory library for higher order logic represented as an OpenTheory package, and the process of instrumenting the HOL Light theorem prover to extract a standardized version of its core theory development.
Journal ArticleDOI
Mechanically verified proof obligations for linearizability
TL;DR: This article defines simulation-based proof conditions for linearizability and applies them to two concurrent implementations, a lock-free stack and a set with lock-coupling, and employs a theorem prover to mechanize the proofs.
References
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Book
A mathematical introduction to logic
TL;DR: A comparison of first- and second-order logic in the case of SETs shows that the former is more likely to be correct and the latter is less likely.
Journal ArticleDOI
A Formulation of the Simple Theory of Types
TL;DR: A formulation of the simple theory oftypes which incorporates certain features of the calculus of λ-conversion into the theory of types and is offered as being of interest on this basis.