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Two frameworks of theories and their implementation in Isabelle

from Frameworks

Published online by Cambridge University Press:  04 August 2010

By
Peter Aczel ,
David P. Carlisle  and
Nax Mendler
Edited by
Gerard Huet  and
G. Plotkin
Peter Aczel
Affiliation:
Computer Science Department Manchester University Manchester, M13 9PL
David P. Carlisle
Affiliation:
Computer Science Department Manchester University Manchester, M13 9PL
Nax Mendler
Affiliation:
Computer Science Department Manchester University Manchester, M13 9PL
Gerard Huet
Affiliation:
Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt
G. Plotkin
Affiliation:
University of Edinburgh
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Summary

Abstract

In this paper we describe a version of the LTC (Logical Theory of Constructions) framework, three Martin-Löf type theories and interpretations of the type theories in the corresponding LTC theories. Then we discuss the implementation of the above in the generic theorem prover Isabelle. An earlier version of the LTC framework was described by Aczel and Mendler in.

Introduction

In the notion of an open-ended framework of deductive interpreted languages is formulated, and in particular an example is given of a hierarchy of languages Li in the LTC framework. In the first part of this three part paper, sections 2 to 4, we review this hierarchy of languages and then discuss some issues concerning the framework, which lead to another hierarchy of languages, LTC0, LTC1, LTCW. In the second part, sections 5 and 6, we give three type theories, TT0, TT1, and TTW, and their interpretations in the corresponding LTC language. In the final part, sections 7 to 9, we document the implementation of the LTC hierarchy in the generic theorem prover, Isabelle, developed by Larry Paulson at Cambridge. We also describe a programme for verifying, in Isabelle, the interpretations of the type theories TT0, TT1 and TTW.

The basic LTC framework is one that runs parallel to the ITT framework. ITT stands for “Intuitionistic Theory of Types”, see. It is a particular language from the latter framework that has been implemented in the Cornell Nuprl System.

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Logical Frameworks , pp. 3 - 39
Publisher: Cambridge University Press
Print publication year: 1991

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