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Reasoning about multi-stage programs*

Part of: JFP Research Articles

Published online by Cambridge University Press:  07 November 2016

JUN INOUE  and
WALID TAHA
JUN INOUE
Affiliation:
National Institute of Advanced Industrial Science and Technology, Ikeda, Osaka, Japan (e-mails: jun.inoue@aist.go.jp)
WALID TAHA
Affiliation:
Halmstad University, Halmstad, Halland, Sweden (e-mails: walid.taha@hh.se)
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Abstract

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We settle three basic questions that naturally arise when verifying code generators written in multi-stage functional programming languages. First, does adding staging to a language compromise any equalities that hold in the base language? Unfortunately it does, and more care is needed to reason about terms with free variables. Second, staging annotations, as the name “annotations” suggests, are often thought to be orthogonal to the behavior of a program, but when is this formally guaranteed to be true? We give termination conditions that characterize when this guarantee holds. Finally, do multi-stage languages satisfy useful, standard extensional properties, for example, that functions agreeing on all arguments are equivalent? We provide a sound and complete notion of applicative bisimulation, which establishes such properties or, in principle, any valid program equivalence. These results yield important insights into staging and allow us to prove the correctness of quite complicated multi-stage programs.

Information

Type
Articles
Information
Journal of Functional Programming , Volume 26 , 2016 , e22
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Cambridge University Press 2016

Footnotes

*

This work was supported by NSF CCF 0747431 award entitled “Multi-stage programming for object-oriented languages”, NSF CSR/EHS 0720857 award entitled “Building physically safe embedded systems”, NSF CPS 1136099 award entitled “A CPS Approach to Robot Design”, and Halmstad University.

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