Specification and Verification I

Lecturer: Prof. M.J.C. Gordon (mjcg@cl.cam.ac.uk)

No. of lectures: 12

Prerequisite course: Logic and Proof

This course is a prerequisite for Specification and Verification II.

Aims

The aim of the course is to motivate and illustrate the use of rigorous methods and mechanised tools for reasoning about the functional behaviour of imperative programs. A goal is to show the similarities and differences between hardware and software verification.

Lectures

• Program specification. Partial and total correctness. Hoare notation. [2 lectures]

• Program verification. Axioms and rules of Floyd-Hoare logic. Discussion of soundness and completeness. [4 lectures]

• Mechanised program verification. Annotation. Verification condition generation. [3 lectures]

• Program refinement. Definition of the refinement relation. Derivation of laws. [1 lecture]

• Semantic embedding. Deep versus shallow embedding. Shallow embedding of Hoare notation in higher order logic. Programming logic as a special case of general logic. [2 lectures]

Objectives

At the end of the course students should have an understanding of some aspects of the following topics:

• partial and total correctness

• Hoare notation

• axioms and rules of Floyd-Hoare logic

• soundness and completeness

• mechanised program verification using verification conditions

• program refinement

• weakest preconditions

• semantic embedding in higher order logic

• limitations of program verification

• problems of reasoning about C programs

Recommended books

None (comprehensive notes supplied).