next up previous
Next: About this document ...

A Z Specification for a Queue
Eric C. Cyr (ecyr@clemson.edu)

Let $ELEMENT$ be the set of all possible items you want in your queue. Boolean is a place holder for boolean values.
\begin{zed}[ELEMENT]\\ Boolean ::= True \vert False \end{zed}

This is the schema for Queue. All that Queue contains is a set of partial functione mapping the natural numbers to the items in the queue. The predicate gurantees that the doman of "items" is the emptyset or {1..n} where n is an integer greater then or equal to 1.
\begin{schema}{Queue} items: \nat \pfun ELEMENT \where \forall x:\nat \vert x > 1 @ x \in \dom items \implies x-1 \in \dom items \end{schema}

The initialize for a Queue, make sure it is empty to begin with.
\begin{schema}{InitQueue} Queue' \where items' = \emptyset \end{schema}

Return "True" if the priority queue is empty and "False" otherwise.
\begin{schema}{IsEmpty} \Xi Queue \\ result!: Boolean \where result!=True \iff \char93 items = 0 \\ result!=False \iff \char93 items > 0 \end{schema}

The join operation is the similar to what enqueue typically does.
\begin{schema}{Join} \Delta Queue \\ theItem?: ELEMENT \where items' = items \cup \{ \char93 items+1 \mapsto theItem? \} \end{schema}

The Leave operation is the same as dequeue, it simply returns the value with index 1 and shifts everything down.
\begin{schema}{Leave} \Delta Queue \\ theItem!: ELEMENT \where items \neq \... ...vert x \mapsto y \in items \land x > 1 @ \\ \t1 x-1 \mapsto y ~\} \end{schema}


Brian Malloy 2002-04-22