1. Modular Decomposition, Abstraction and Specifications
EECE 309: Software Design
Modular Decomposition, Abstraction and Specifications

2. Decomposition
Goal: Create small programs that interact with one another in simple, well-defined ways, to reduce complexity
Criteria for good decomposition
Sub-problems at the same level of detail
Each can be solved independently
Can be combined to solve the original problem

3. Decomposition Example
Large Unsolved Problem
SP2
SP3
SP4
SP5
SP6
SP1
Combined solution

4. What often happens in practice ?
Large Unsolved Problem
SP1
SP2
SP3
SP7
SP4
SP5
SP9
Combined solution ?

5. Learning Objectives Define abstraction and types of abstraction
List the standard elements of specification
Write specifications in the standard format
Differentiate between “good” and “bad” specifications
Develop implementations to satisfy a specification

6. Abstraction A way to do decomposition productively Definitions:
Application of many-to-one mapping
Simplification of the problem that hides irrelevant details, characteristics
Grouping of related entities into distinct categories without worrying about the details

7. Abstraction Types By Parameterization By Specification
Abstracts from the identity of the data
By Specification
Abstracts from implementation details to the behavior users can depend on
Isolates modules from one another’s implementations
Provides a clear contract between the user and the implementer of module

8. Abstraction by Parameterization
Write the procedure once, but change its parameters
Generalizes modules so they can be used many times
Fundamental technique used in programming
Example: Recipe for making pasta (Serves 2 people)
Step 1: Boil 2 cups of water in a sauce-pan
Step 2: Add 6 cups of pasta when water comes to a boil
Step 3: Sautee 5 grams of vegetables in an another pan
Step 4: Mix the sauteed vegetables with the cooked pasta
Step 5: Add pasta sauce, cheese and salt to taste
But, what if we wanted to make pasta for 5 people ?
Should we develop a new recipe from scratch ?

9. Abstraction by Specification
Hide implementation details of a module and focus instead on what it does (rather than how it does it)
Specify the behavior that module’s users can depend on
Can generalize across multiple implementations
Change module’s behavior without changing its usage
Example: Recipe for making pasta (Serves 2)
Step 1: Boil 2 cups of water in a sauce-pan
Step 2: Add 6 cups of pasta when water comes to a boil
Step 3: Sautee 5 grams of vegetables in an another pan
Step 4: Mix sauteed vegetables with the cooked pasta
Step 5: Add pasta sauce, cheese and salt to taste

10. Benefits of Abstraction by Specification
Locality -- the implementation of an abstraction can be read or written without needing to examine the implementations of any other abstractions.
2. Modifiability -- an abstraction can be re-implemented without requiring changes to any abstractions that use it.

11. Learning Objectives Define abstraction and types of abstraction
List the standard elements of specification
Write specifications in the standard format
Differentiate between “good” and “bad” specifications
Develop implementations to satisfy a specification

12. Specification
Tells the client of an abstraction what the client is expected to do
Tells the implementer of an abstraction what implementation must do to satisfy the client
Contract between client and implementer
Client will rely only on behavior in specification
Implementer only needs to provide this behavior
Implementer is free to change implementation

13. Specifications: Formal Vs Informal
Formal Specs
Informal Specs
Written in a mathematically precise language
Have only one meaning or a finite set of meanings
Can be understood by humans and machines
Automated tools can check code against specifications
Written in an informal language (English)
Have different meanings depending on the reader
Can be understood only by humans (for the most part)
Manual effort needed to check code against specs
In this class, we will write informal specifications, but you will write formal specs in the assignments

14. Recipes: Analogy
A good specification is like a recipe and has the following components:
What is being done ?
What is required ?
How to do it ?
Are there things that one needs to look for ?
Any other things to note
Recipes are written in a standard format defined by the Chef’s Association.

15. How to write procedural specifications ?
Choose a name for the procedure that is descriptive
Procedural specifications should consist of:
REQUIRES: What does the procedure need ?
MODIFIES: What data does the procedure modify ?
EFFECTS: What does the procedure produce at the end ?
The code for the procedure is not part of its specification, but must match the specification

16. Procedural Specifications
Factorial: Fact(n) = 1 * 2 *3 …. * n * (n- 1)
static int Fact(int n) {
// REQUIRES: n >= 0
// MODIFIES: None (this can be dropped)
// EFFECTS: Returns the factorial of n
// where fact(n) = 1 * 2 * … * n … }

17. Multiple Implementations
Using Iteration
Using recursion
public static int fact(int N ) { int result = 1; for (int i =1; i<=N; i++) { result = result * i; } return result;
public static int fact(int N) { int result; if (N==0) result = 1; else result = N * fact(N – 1); return result; }
Both implementations satisfy the specification.
(Do they have the same behavior (why or why not) ?)

18. Learning Objectives Define abstraction and types of abstraction
List the standard elements of specification
Write specifications in the standard format
Differentiate between “good” and “bad” specifications
Develop implementations to satisfy a specification

19. Sorting Routine: Informal Spec
Take an array as argument, sort it in place
What kind of arrays do we want to handle ?
Arrays of ints (primitive type)
Array should be non-null
No need to say that array elements are non-null
public static void sort( int[] a ) {
// REQUIRES:
// MODIFIES:
// EFFECTS:

20. REQUIRES clause
Should only capture the requirements on array that are not implied by the type signature
Do not need to say anything about the types of the arguments, unless they cannot be inferred
Do not mention the return type of the procedure
public static void sort( int[] a ) {
// REQUIRES: Array a not be Null }

21. MODIFIES Clause
Modifies clause only specifies what objects (on heap) are modified by the procedure
Does not include return value of procedure
Does not say anything about how it is modified
public static void sort( int[] a ) {
// REQUIRES: Array a not be Null
// MODIFIES: Array a

22. EFFECTS Clause Specifies the EFFECT of the procedure on the caller
Include both return value and heap objects
Include any exceptions thrown by the procedure
Must say what modifications are made and how
public static void sort( int[] a ) {
// REQUIRES: Array a not be Null
// MODIFIES: Array a
// EFFECTS: Rearranges the elements of a in
// ascending order (i.e., lowest to highest)

23. Group Activity
Write a specification for the sort program that sorts an array of String objects (in alphabetical order)
public static void sort( String[] a ) {
// REQUIRES:
// MODIFIES:
// EFFECTS:

24. One Solution: Group Activity
public static void sort( String[] a ) {
// REQUIRES: a is not NULL &&
// Elements of a are not NULL
// MODIFIES: Array a
// EFFECTS: Re-arranges the elements of array a
// in alphabetical order (i.e., lowest to highest)
// Uses String.compareTo for determining order

25. Group Activity (continued)…
How would your specification change if the sort procedure needs to return a new array ?

26. Learning Objectives Define abstraction and types of abstraction
List the standard elements of specification
Write specifications in the standard format
Differentiate between “good” and “bad” specifications
Develop implementations to satisfy a specification

27. Procedural Specifications: Example 1
public class Vectors {
//OVERVIEW: Provides useful standalone procedures
// for manipulating vectors
public static void removeDuplicates ( Vector v ) {
// REQUIRES: No element of vector v is null
// MODIFIES: v
// EFFECTS: Removes all duplicate elements from v;
// uses equals method to determine duplicates.
// The order of the remaining elements may change }

28. Procedural Specification: Example 2
Does the following implementation satisfy the specification ?
public static void removeDuplicates ( Vector v )
// REQUIRES: No element of vector v is null
// MODIFIES: v
// EFFECTS: Removes all duplicate elements from v;
// uses equals method to determine duplicates.
// The order of the remaining elements may change
v.clear(); }

29. Procedural Specifications: Example 3
public class Vectors {
//OVERVIEW: Provides useful standalone procedures
// for manipulating vectors
public static void removeDuplicates ( Vector v ) {
// REQUIRES: No element of vector v is null
// MODIFIES: v
// EFFECTS: Removes all duplicate elements from v;
// uses the equals method to determine duplicates.
// The order of the remaining elements may change
// but the set of elements formed by the new vector is
// identical to the set of elements formed by the old one }

30. What’s the problem ? The original specification was too weak
Any implementation could satisfy it, even incorrect ones
The specification should be sufficiently restrictive to allow only correct implementations
If it is important to you, then write it down
From the point of view of the client
Make sure you can use the specification

31. Remember … Specifications are many-to-one mappings
Many implementations may satisfy a specification
But some may be wrong because the specification is not restrictive enough !
A specification is like a contract. If the implementer can get away by doing less and yet satisfy the specification, they may choose to !
It is your responsibility to put it in the specification

32. Learning Objectives Define abstraction and types of abstraction
Write specifications in the standard format
Write precise specifications that are sufficiently restrictive, but not too restrictive
Differentiate between “good” and “bad” specifications
Develop implementations to satisfy a specification

33. What makes a good specification ?
Sufficiently restrictive
Minimally constraining
Clear – no room for ambiguity
These guidelines are necessarily vague, so let us see some examples

34. Sufficiently Restrictive
public static int search (int[] a, int x) // REQUIRES: a is not null
// EFFECTS: Examines each of a[0], a[1], ... , in order and
returns the index of the element that equals to x.
What’s wrong with the above specification ?
What if there is more than one element equal to x ?
What if there is no element equal to x ?
How will you fix these issues ?

35. Minimally Constraining
Do you really care that the procedure examines each element in turn ?
Also, do you need the first element that equals x ?
Precludes non-linear implementations such as binary search
public static int search (int[] a, int x) // REQUIRES: a is not null
// EFFECTS: Examines each of a[0], a[1], ... , in some order and
// returns the index of an element that equals to x.
// If no such element is found, it returns - 1

36. Note the use of i.e. to indicate redundancy
Clarity
The above specification is NOT clear. Do we return an element whose index is x, or do we return the index of an element that equals x. This is the problem with natural language. So we need to be more clear.
public static int search (int[] a, int x) // REQUIRES: a is not null
// EFFECTS: Examines each of a[0], a[1], ... , in some order and
// returns the index of an element that equals to x.
// i.e., returns an i, such that a[i] = x and 0 <=i <a.length
// if no such element is found, it returns -1.
Note the use of i.e. to indicate redundancy

37. Learning Objectives Define abstraction and types of abstraction
List the standard elements of specification
Write specifications in the standard format
Differentiate between “good” and “bad” specifications
Develop implementations to satisfy a specification

38. Implementation Do NOT handle cases in the REQUIRES clause
EFFECTS clause is satisfied only if REQUIRES holds
Do NOT modify entities not in MODIFIES clause
Do only what the EFFECTS clause says, no more
Clients should rely upon specification, not implementation
If EFFECTS clause is underspecified, then it’s a problem in the specification and needs to be fixed

39. Group Activity - 1
Develop implementation for the specification below (write legibly on a separate sheet)
public static int search (int[] a, int x) // REQUIRES: a is not null
// EFFECTS: Examines each of a[0], a[1], ... , and returns
// the index of any array element that equals to x.
// i.e., returns an i, such that a[i] = x and 0 <=i <a.length
// If no such element is found, returns -1.

40. Group Activity - 2
Write the implementation of a procedure replace that uses search and has the following specification:
public static void replace(int[] a, int x, int y) {
// MODIFIES: a
// EFFECTS: Replaces all instances of element
// x in the array a[] with that of y }