Data and processes in computing: Introduction

Introduction
This unit provides an introduction to data and processes in software, and provides a basis that enables these fundamental ideas to be developed in a clear and precise way. It has two main aims. The first is to illustrate how we can describe ways in which data may be structured and processed. The second is to introduce you to some vocabulary and concepts that help us to do this. The material is accessible to anyone with a little experience of the use of symbols in presenting ideas.
Section 1 provides a brief introduction to the unit. It contains some new language that will be explained more fully in later sections. Read this section without spending too much time on it. The most important material in this unit is that in Sections 2 and 4. Section 3 includes some ideas that are relatively difficult. You should read this section, but do not spend a great deal of time on it. Section 5 is of a similar length to Sections 2 and 4.
Overall, do not allow yourself to spend too long on any section while you are studying this unit. You can always come back and reread material here if you find later that you need a more thorough understanding of some point.

The unit introduces you to:
  ways in which data may be stored and processed;
  language notation and concepts that enable discussion of these in a precise way.
  It enables you to do the following:
  distinguish between different forms of data, and use notations introduced in the unit to show different forms of data;
  appreciate that fine details may be important when interpreting formal notation (for example, different types of brackets may be used to distinguish between different forms of data);
  interpret a given function description;
  recognise correct syntax in formal expressions, in particular, that:
  a function requires the correct number and type of inputs;
  function inputs must satisfy any precondition on the function;
  in an expression, brackets need to be used in a way that makes it possible to interpret the expression in a unique way, and binary operations and functions in the expression need to be combined in a way which is consistent with their signatures and preconditions.