Verification of Euclid programs

Abstract

The proof rules for the programming language Euclid are closely modelled on the axiomatic definition of Pascal. However, there is intended to be a much closer correspondence between the language as actually implemented and the proof rules. This has been achieved by a combination of language changes, more stringent requirements on the compiler, and modifications of the proof rules. Several novel features of Euclid were introduced specifically in response to problems and limitations of the Pascal definition.

Typical proof rules and proofs for programs using basic language constructs are very similar in Euclid and Pascal. We discuss some of these as a review of Hoare's methodology.

The proof rules for Euclid functions and procedures deviate from those for Pascal, and avoid some of their problems. We discuss the reasons for some of the changes.

Some parts of the Euclid language, such as modules and zones, were motivated by application or implementation considerations. These have been more difficult to axiomatize, and have proved to be some of the most troublesome parts of the language. We mention a few of the problem areas.

These notes should be read in conjunction with the published proof rules.