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Side effects and aliasing can have simple axiomatic descriptions

Editor: Susan L. Graham Author:

Hans-Juergen BoehmAuthors Info & Claims

ACM Transactions on Programming Languages and Systems (TOPLAS), Volume 7, Issue 4

Pages 637 - 655

https://doi.org/10.1145/4472.4474

Published: 01 October 1985 Publication History

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Abstract

We present a different style of axiomatic definition for programming languages. It is oriented toward imperative languages, such as Algol 68, that do not distinguish between statements and expressions. Rather than basing the logic on a notion of pre- or postcondition, we use the value of a programming language expression as the underlying primitive.

A number of language constructs are examined in this framework. We argue that this style of definition gives us a significantly different view of the notion of “easy axiomatixability.” Side effects in expressions as well as aliasing between variables are shown to be “easily axiomatizable” in our system.

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Side effects and aliasing can have simple axiomatic descriptions

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Reviews

Reviewer: Frank George Pagan

The axiomatic approach to the formal definition of programming language semantics was founded by Hoare [1] and has been extended and refined over the years by numerous people. The author argues that the well-known difficulties pertaining to the axiomatizability of various language features are a result of keeping too close to Hoare's (precondition/postcondition) style of specification. He proposes an alternative style which is applicable to “expression-oriented” languages such as ALGOL 68, where any construct can both yield a value (like an expression) and cause a side effect (like a statement). The proposed method is based on a metalinguistic primitive for talking about the value of an expression; viz., &angl0; a &angr0; denotes the value of the expression a. The notation &angl0; a &angr0; t, where t is a metaexpression, represents the value of t after executing a. The semantics of each kind of expression is defined by a “value axiom” and an “effect axiom.” For example, the value axiom &angl0; a+ b &angr0; = &angl0; a &angr0; + &angl0; a; b &angr0; states that, for any subexpressions a and b, the value of a+ b in the current state is the value of a in the current state plus the value of b in the state that will exist after a is executed. The effect axiom &angl0; a+ b &angr0; t= &angl0; a; b &angr0; t states that the side effects of a+ b consist of the side effects caused by first executing a and then executing b. The paper develops the formal system in some detail and describes how it can be used to verify the correctness of programs. In the conclusion, the author lists the weaknesses of the system as (1) lack of a firm notion of completeness, and (2) inability to deal with nondeterminism (which implies that the method could not actually be used to define ALGOL 68). He suggests that different axiomatic formalisms should be used with different kinds of programming languages. The reviewer would add that the biggest weakness seems to be the restriction to expression-oriented languages (a rather small minority of languages) and the consequent inability to ameliorate the difficulties of axiomatically characterizing the more common languages. The paper implicitly assumes a knowledge of axiomatic semantics and will be of definite interest to scholars in that area. Although the mathematical difficulty is not excessive, this reviewer did find certain parts of the discussion to be overly terse and hard to follow.

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cover image ACM Transactions on Programming Languages and Systems

ACM Transactions on Programming Languages and Systems Volume 7, Issue 4

Oct. 1985

185 pages

ISSN:0164-0925

EISSN:1558-4593

DOI:10.1145/4472

Editor:
Susan L. Graham

Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1985

Published in TOPLAS Volume 7, Issue 4

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Mossakowski TSchröder LGoncharov S(2010)A generic complete dynamic logic for reasoning about purity and effectsFormal Aspects of Computing10.1007/s00165-010-0153-422:3(363-384)Online publication date: 1-May-2010
https://dl.acm.org/doi/10.1007/s00165-010-0153-4
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Leavens GAbrial JBatory DButler MCoglio AFisler KHehner EJones CMiller DPeyton-Jones SSitaraman MSmith DStump AJarzabek SSchmidt DVeldhuizen T(2006)Roadmap for enhanced languages and methods to aid verificationProceedings of the 5th international conference on Generative programming and component engineering10.1145/1173706.1173740(221-236)Online publication date: 22-Oct-2006
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Linguistic side effects

Axiomatic bootstrapping: a guide for compiler hackers

Derivation of axiomatic definitions of programming languages from algorithmic definitions

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