SE-381 Week 3 Lecture 1

Faculty schedule system example (FacSched01)

System maintains information on teaching assignments

What can you figure out from reading it?

[Section 1]

Variable declarations

Funny looking "P" - like an array or set?

Course described as "within" a set

Idea that we're keeping track of professors and sections they teach

Wierd arrows in state schema

[Section 2]

Formal way -- e.g., add professor to list with set union

Cardinality of relationships -- e.g., professors to sections

Funny "P" notation

Funny triangles in "delete professor"

Differences between ":" and "::=", etc.

"dom" and "ran"?

Z types

Given sets (basic types)

Example: PROF, COURSE, SECTION

Free types

Sets (that are also types) defined by enumerating values

Similar to an "enum" in C++ (not in Java)

Example: academic departments

More advanced kinds of free type definitions not covered here

Z operators

Arithmetic operators (text, pages 72 & 301)

Set operators (text, pages 73 & 300)

Also see Z "reference card"

Axiomatic descriptions

Used to define "global" variables (and functions)

Components

Above the line -- variable name : type (or set)

Declaration note . . .

Variable value is drawn from set of values (maybe a type)

mycourse : COURSE

Be careful when "set" expression is complex

Below the line -- predicates

What is a predicate, anyway?

What if there is more than one predicate?

Implicitly, they are ANDed together logically

What if there are no predicates (no line)?

Default predicate = "true"

Normalized declarations

Simple declarations are "variable : type"

Possibly followed by predicates "below the line"

Meaning

Variable's type is "type"

Variable's value is drawn from the full set represented by "type"

Declarations can also be "variable : set" (also with predicates)

If "set" is not a type, then . . .

Variable's type is the type of "set"

There is an implicit predicate that the variable's value is in "set"

Normalized declarations make explicit the implicit type and predicates

Declaration notes

A particular "global" variable has only one value throughout a Z specification

Unlike a C++ data object, which can take on different values at different times

There is no time in Z !! . . .

Well, there are ways to represent "before" and "after" states . . .

In Z notation itself, the ordering of declarations does not matter . . .

. . . but in Z/EVES, variables need to be defined before use, and . . .

. . . ordering of declarations and other elements may affect how the theorem prover works

Schemas

Z mechanism for encapsulating "state" (and related operations)

What does "state" (and "state variables") mean, anyway?

Notation looks something like an axiomatic description

Above the line: declarations

Below the line: predicates

Additional features

Top and bottom lines enclosing the schema content

Schema name in the top line

Types of schemas

State schema

Declarations: state variables for the schema

Predicates: invariants (what's an invariant?)

To be continued . . .