Reading Contracts

Question 1

What is used to model each program type in Java (i.e. int double, String, NaturalNumber, etc.)?

Answer 1

A mathematical type - every variable of a certain program type has a value from its mathematical model’s mathematical space/domain

Question 2

Mathematical type of boolean

Answer 2

boolean (true or false)

Question 3

Mathematical type of char

Answer 3

character (‘A’, ‘?’, ‘z’, …)

Question 4

Mathematical type of int

Answer 4

integer (-2147483648 through 2147483647)

Question 5

Mathematical type of double

Answer 5

real (about 15 significant digits)

Question 6

Mathematical type of String

Answer 6

string of character

Question 7

Mathematical type of NaturalNumber

Answer 7

integer (non-negative)

Question 8

Mathematical type of Queue<T>.</T>

Answer 8

String of T

Question 9

Mathematical type of Sequence<T></T>

Answer 9

String of T

Question 10

Mathematical type of Stack<T></T>

Answer 10

String of T

Question 11

Mathematical type of Set<T></T>

Answer 11

finite set of T

Question 12

Mathematical type of Map<K, V>

Answer 12

There are 2 ways to define the mathematical type of Map<K, V>:
1. finite set of ordered pairs of (K, V), with “function property” (i.e. the condition that no 2 pairs in the set have the same K value)
2. finite partial function from K to V

Question 13

What constitutes a method contract? (Only name the parts)

Answer 13

A precondition (requires clause) and a postcondition (ensures clause)

Question 14

Define precondition (requires clause)

Answer 14

A precondition (requires clause) is the part of a contract of a method that defines the responsibility of the program “calling” (using) that method (client code)

Question 15

Define postcondition (ensures clause)

Answer 15

A postcondition (ensures clause) is the second part of a method that defines the responsibility of the program that implements that method (implementation code in the method body)

Question 16

What does a contract mean/define/state?

Answer 16

When a method is called, if the precondition of its contract is true, then the method will terminate (i.e. return to the calling program) and when the method “does” return/terminate, the postcondition of its contract will be true.
If the precondition is not true, then the method may do “anything” - it can perform as intended, or it may not (including (not) terminate).

Question 17

Set Notation (Mathematical)

Answer 17

Curly braces {a, b, …}; the set with no elements { } is called the empty set

Question 18

String Notation (Mathematical)

Answer 18

Angle brackets <a, b, …>; the string with no elements < > is called the empty string; <x> is not the same as the element x by itself.</x>

Question 19

Tuple Notation (Mathematical)

Answer 19

Parentheses (a, b, …); a tuple “may” contain different program/mathematical types of elements, order of an element identifies which element is which type/item, but the order itself may be arbitrary.

Question 20

‘*’ symbol (Mathematical)

Answer 20

It can mean either of the two:
1. Concatenation between two “strings”
2. Multiply between two integers

Question 21

Entries of a string (Mathematical)

Answer 21

The entries of a string are all the unique bits/items/elements of the string, taken as a set (entries of a string are considered by taking unique elements of the string without any duplicates and sorting them in any order. For instance, if you have a string of integers, and there are three occurrences of the integer 2, take 2 as only one entry of the string and not the n occurrences of the same integer as separate (n) entries of the string).

Question 22

Perms of a string (Mathematical)

Answer 22

The perms of a string (permutation) means a string with all the same elements, in possibly a different order.

Question 23

Rev() of a string (Mathematical)

Answer 23

Reverse of the string.

Question 24

Substring notation (Mathematical)

Answer 24

s[x, y); the syntax s[x, y) means the substring of s that begins at position x and ends at position y - 1 (before y).
If x >= y, then s[x, y) = < > (empty string)

Question 25

Universal quantification

Answer 25

Universal quantification is the part of a method contract that defines something (main-assertion) is true for every (for all) combination of values (quantified-variables) that satisfy a certain property (restriction-assertion).

Question 26

Explain the Java representation of universal quantification

Answer 26

for all quantified-variables
where (restriction-assertion)
(main-assertion)

Question 27

Existential quantification

Answer 27

Existential quantification is the part of a method contract that states something (assertion) is true for some (there exists) combination of values (quantified-variables).

Question 28

Explain the Java representation of existential quantification

Answer 28

there exists quantified-variables
(assertion)

Question 29

Is this universal or existential quantification: “Every non-empty string has positive length.” Also, show a Java representation.

Answer 29

Universal;

for all s: string of T
where (s /= < >)
(|s| > 0)

Question 30

Is this universal or existential quantification: “Some positive integer is odd.” Also, show a Java representation.

Answer 30

Existential;

there exists n, k: integer
(n > 0 and n = k * 2 + 1)

Question 31

|x| notation (Mathematical)

Answer 31

It can mean 3 things:

1. If x is a Set, |x| is the size of the set x.
2. If x is a String, |x| is the length of the string x.
3. If x is a NUMERIC value, |x| is the absolute value.