Model-based Specification-Software Engineering-Lecture 11 Slides-Computer Science, Slides of Software Engineering

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LECTURE 11: Z

Software Engineering

1 Introduction

• In this lecture, we introduce schemas, the most distinctive feature of the Z specification language.
• We show how a simple computer system can be specified in Z.

• The most fundamental operation we use is the assignment statement, ‘:=’... such statements change the state of a system.
• In Z, we represent the state space of a system as a collection of functions, sets, relations, sequences, bags, etc., together with a collection of invariant properties on these objects.
• These invariant properties describe regularities between state changes.
• How about operations? What level of abstraction to we deal with them? Lowest level would be assignment statement level. We start with more abstract descriptions.
• Operations are usually defined in terms of pre- and post- conditions.
• Operations define acceptable state transitions.

2 Schemas

• The Z schema is a 2-dimensional graphical notation for describing: - state spaces; - operations.
• Definition: A vertical-form schema is either of the form SchemaName Declarations Predicate 1 ; · · · ; Predicaten

or of the form SchemaName Declarations

• In the latter case, the predicate part is assumed to be ‘true’.

2.1 State Space Schemas

• Here is an example state-space schema, representing part of a system that records details about the phone numbers of staff. (Assume that NAME is a set of names, and PHONE is a set of phone numbers.) PhoneBook known : IP NAME tel : NAME → 7 PHONE dom tel = known
• The declarations part of this schema introduces two variables: known and tel.
• The value of known will be a subset of NAME, i.e., a set of names. This variable will be used to represent all the names that we know about — those that we can give a phone number for.
• The value of tel will be a partial function from NAME to PHONE, i.e., it will associate names with phone numbers.

• The declarations part is separated from the predicate part by the horizontal line.
• The predicate part contains the following invariant: The domain of tel is always equal to the set known.

• Return to the telephone book example, and consider the ‘lookup’ operation: we put a name in, and get a phone number out. - this operation accesses the PhoneBook schema; - it does not change it; - it takes a single ‘input’ — a name for which we want to find a phone number; - it produces a single output — a phone number. - it has the pre-condition that the name is known to the database.
• Here is a Z schema specifying the lookup operation: Find ΞPhoneBook name? : NAME phone! : PHONE name? ∈ known phone! = tel(name?)

This illustrates the following Z conventions:

• placing the name of the schema in the declarations part ‘includes’ that schema — it is as if the variables were declared where the name is;
• ‘input’ variable names are terminated by a question mark; -... the only input is name?
• ‘output’ variables are terminated by an exclamation mark; -... the only output is phone!
• the Ξ (Xi) symbol means that the PhoneBook schema is not changed;
• if we have written a ∆ (delta) instead of Ξ, it would mean that the PhoneBook schema did change.
• the pre-condition is that name? is a member of known;
• the post-condition is that phone! is set to tel(name?).

• EXERCISE. Rewrite this schema to get rid of post-condition, and allow overwriting of existing names.

3 CADIZ

• CADIZ is an automated checker and typesetter for Z specifications.
• It takes as its input a plain ASCII file, prepared using an ordinary text editor. This file contains various instructions describing Z schemas.
• It then performs some checks on this specification, and depending on what command-line options you gave, it will: - typeset your spec., producing a binary file with a .dit extension, which can be printed off with the printz command; - allow you to browse through the spec., and get feedback on certain parts of it.