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Logic + control: On program construction and verification

Published online by Cambridge University Press:  19 June 2017

WŁODZIMIERZ DRABENT
WŁODZIMIERZ DRABENT*
Affiliation:
Institute of Computer Science, Polish Academy of Sciences, Warsaw IDA, Linköping University, Linköping, Sweden (e-mails: drabent@ipipan.waw.pl)
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Abstract

This paper presents an example of formal reasoning about the semantics of a Prolog program of practical importance (the SAT solver of Howe and King). The program is treated as a definite clause logic program with added control. The logic program is constructed by means of stepwise refinement, hand in hand with its correctness and completeness proofs. The proofs are declarative – they do not refer to any operational semantics. Each step of the logic program construction follows a systematic approach to constructing programs which are provably correct and complete. We also prove that correctness and completeness of the logic program is preserved in the final Prolog program. Additionally, we prove termination, occur-check freedom and non-floundering.

Our example shows how dealing with “logic” and with “control” can be separated. Most of the proofs can be done at the “logic” level, abstracting from any operational semantics.

The example employs approximate specifications; they are crucial in simplifying reasoning about logic programs. It also shows that the paradigm of semantics-preserving program transformations may be not sufficient. We suggest considering transformations which preserve correctness and completeness with respect to an approximate specification.

Keywords

logic programmingdeclarative programmingprogram completenessprogram correctnessspecificationprogram transformationflounderingoccur-check
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 18 , Issue 1 , January 2018 , pp. 1 - 29
Copyright
Copyright © Cambridge University Press 2017 

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