Assignment 3 Solution

(10 pts) Complete the following algebraic specification for an abstract data type describing a queue of cars at an intersection by providing axioms.



algebra QueueOfCars

imports Integer, Boolean;

introduces

sorts Queue, Car;

operations

New: → Queue;

CarArrives: Car x Queue → Queue;

CarDeparts: Queue → Queue;

IsEmpty: Queue → Boolean;

NumberOfCars: Queue → Integer;

Longer: Queue x Integer → Boolean;

FirstCar: Queue → Car;

Equal: Queue x Queue → Boolean;

WhichQueue: Queue x Queue x Car → Integer;

Position: Car x Queue → Integer;

constrains New, CarArrives, CarDeparts, IsEmpty, NumberOfCars, Longer, FirstCar, Equal, WhichQueue, Position, so that Queue generated by [New, CarArrives]




IMPORTANT NOTES




Description of the operations:

CarArrives adds a car to the end of a queue
CarDeparts removes a car from the front of a queue (the other side than the one where we add cars)
IsEmpty returns true if a queue of cars is empty and false otherwise
Longer returns true if a queue is longer than the integer and false otherwise (assume that the integer is never negative)
NumberOfCars returns the number of cars in the queue
FirstCar returns the car from the front of the queue without deleting it
Equal returns true if number of cars in two queues is equal and false otherwise
WhichQueue examines two queues and returns 1 if a given car is in the first queue, 2 if the car is in the second queue, and 0 if the car is not in the queues.
Position examines if a given car is in a queue and returns the number of cars that are in front of this car in the queue (closer to the front of the queue) or -1 if this car is not in the queue
You should provide only the axioms (including the for all and end statements)
Be precise in terms of both syntax and symbols that you use
Assume that error constant is available

Assume that applying CarDeparts to empty queue generates error
Assume that applying FirstCar to empty queue generates error
Assume that = = and + operators are defined for the sort Integer
Write neatly (preferably using a word processor)
Due Dates and Notes




Your assignment must be received by 11:00 pm MST, November 1 (Thursday), 2018. Your assignment should be submitted via eClass.