Module Identifier CS33310  
Academic Year 2000/2001  
Co-ordinator Dr Mark Ratcliffe  
Semester Semester 2  
Pre-Requisite CS21020 or CS22120, CS22120  
Course delivery Lecture   22 lectures  
  Seminars / Tutorials   (Up to) 4 workshops  
Assessment Exam   2 Hours   80%  
  Course work   Two pieces   20%  
  Supplementary examination   Will take the same form, under the terms of the Department's policy    

General description
The module introduces students to the use of mathematically formal methods for the specification of software. As background to the formal methods in software engineering, students are introduced to formal logic and some of its other applications in Computer Science.

This module aims to introduce students to the use of formal methods in software specification. It develops the underlying ideas by presenting mathematical logic in a formal way, illustrating a number of different logics, and by showing some of the other applications of logic in Computer Science.

Learning outcomes
On successful completion of this course students should understand:

1. The Traditional Approach to Specification - 1 Lecture
Problems of incompleteness, inconsistency and ambiguity. Practical problems (volume of paperwork, etc.)

2. Formal Specifications - 1 Lecture
The advantages and disadvantages of formal specification. Algebraic and operational specifications.

3. VDM as a Specification Language - 4 Lectures
Introduction and history. The VDM specification language. Data types in VDM. Proof using the data types. An example specification.

4. The Logic of Partial Functions - 2 Lectures
Proof in the three valued logic of partial functions. Differences from the traditional two valued logic. Applications to formal methods, in particular VDM.

5. VDM as a Formal Development Method - 3 Lectures
Stages and processes in the development of a software design using VDM. Data reification and operation decomposition.

6. Correctness Proofs - 3 Lectures
Programming proof rules and their application in the specification of computer systems.

7. Outstanding Problems and Other Methods - 2 Lectures
Formal specification of systems with concurrency. Modularisation of formal specifications. Safety and reliability issues. Other specification languages, Z and GYPSY (briefly). ANNA and SPARK.

8. Temporal Logic - 2 Lectures
Specification of time dependent systems. The operators always , sometimes , next and until . Extension of VDM to include temporal logic.

9. Logic Applications in Computing - 4 Lectures
Resolution theorem proving. Logic programming and Prolog. Multi-valued logics, Fuzzy logic, and reasoning with uncertainty.

Reading Lists
** Should Be Purchased
R.D. Dowsing, V.J. Rayward-Smith, and C.D. Walter. (1986) A First Course in Formal Logic and its Application in Computer Science. Computer Science Texts, Blackwell Scientific Publications
C.B. Jones. (1990) Systematic Software Development Using VDM. 2nd. International Series in Computer Science. Prentice-Hall
** Consult For Futher Information
J G P Barnes. (1997) High Integrity Ada: The SPARK Approach. Addison-Wesley
D. Bjorner, C.A.R Hoare, and H. Langmaack, editors. (1990) VDM '90: VDM and Z - Formal Methods in Software Development [volume 428 of LNCS]. Springer-Verlag
J.M. Spivey. (1992) The Z Notation: A Reference Manual. 2nd. International Series in Computer Science. Prentice-Hall
J. Woodcock and M. Loomes. (1988) Software Engineering Mathematics. Pitman