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The equivalence of sequential and associate information structure models

Authors:

Clement McGowan,

Peter WegnerAuthors Info & Claims

ACM SIGPLAN Notices, Volume 6, Issue 2

Pages 191 - 216

https://doi.org/10.1145/1115880.1115888

Published: 01 February 1971 Publication History

Abstract

Interpreters for programming languages may be defined in terms of the information structures (data structures) generated during program execution. This paper develops a class of proof techniques for proving equivalence between two classes of programming language interpreters referred to as <u>associative interpreters</u> and <u>sequential interpreters</u>. The relation between associative and sequential interpreters is briefly illustrated first for arithmetic expression evaluation and then for lambda calculus evaluation, and the strategy for proving equivalence is briefly described. The proof technique is worked out in detail both for arithmetic expression evaluation and for lambda calculus evaluation. The relatively trivial case of arithmetic expression evaluation is considered in detail in order to illustrate the basic structure of the proof in a context familiar to the uninitiated. The proof of equivalence of associative and sequential lambda calculus interpreters demonstrates a nontrivial equivalence proof and at the same time provides valuable insights into the relation between mathematical definitions of the lambda calculus and practical implementations of the lambda calculus. It is shown that an understanding of lambda calculus interpretation in turn provides insights into interpretation mechanisms for block structure languages like ALGOL 60.

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The equivalence of sequential and associate information structure models
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Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 6, Issue 2

February 1971

416 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/1115880

Issue’s Table of Contents

Copyright © 1971 Copyright is held by the owner/author(s).

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

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Publication History

Published: 01 February 1971

Published in SIGPLAN Volume 6, Issue 2

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