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Reduction types and intensionality in the lambda-calculus

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Wright, David Amson (1992) Reduction types and intensionality in the lambda-calculus. PhD thesis, University of Tasmania.

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Abstract

In this thesis I introduce a new approach to the automated analysis of the
reduction behaviour of A-calculus terms. This new approach improves on earlier
analysers in several ways, not least in its treatment of higher-order terms and
polymorphism, two notably troublesome issues.
In addition, this thesis introduces a stronger notion of reduction behaviour
than strictness. This concept, called strong head neededness, forms the basis for
a new notation for describing the reduction behaviour of terms. This notation
is a kind of type, elements of which are built using a Boolean algebra of function
type constructors. Thus the form of the methodology proposed is that of a type
system.
Consideration is given to a variety of type assignment systems for the new
type system. This supports the hypothesis that the approach proposed is suitable
as a framework for building a range of analyses. Having established this
framework it is then a matter of engineering to determine the appropriate trade
off between information derived and performance achieved.
An investigation is conducted into the formal semantics of all the constructs
introduced. In particular, the investigation proves a range of soundness and
completeness results. Also examined is the semantics of the new notion of type
and the development of a model for reduction types. The model is of interest in
its own right, as it gives further insight into the reduction behaviour of A-terms.
The thesis includes detailed implementations of all the type assignment
systems and ascertains the correctness of these implementations.

Item Type: Thesis (PhD)
Keywords: Lambda calculus, Functional programming languages
Copyright Holders: The Author
Copyright Information:

Copyright 1992 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s).

Additional Information:

Thesis (Ph.D.)--University of Tasmania, 1993. Includes bibliographical references (p. [202]-207)

Date Deposited: 04 Feb 2015 23:21
Last Modified: 11 Mar 2016 05:55
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