EECE 310 Software Engineering Modular Decomposition Abstraction and

EECE 310: Software Engineering Modular Decomposition, Abstraction and Specifications

Lecture Outline • Modular Decomposition • Abstraction Kinds • Specifications • Procedural abstractions 2

Program Decomposition • Goal: Reducing complexity – Developing – Maintaining – Modifying – Understanding – Using • Based on recognition of useful abstractions 3

Decomposition • Goal: Create small programs that interact with one another in simple, well-defined ways • Criteria for good decomposition 1. Sub-problems at the same level of detail 2. Each can be solved independently 3. Can be combined to solve the original problem 4

Decomposition Example Large Unsolved Problem SP 1 SP 2 SP 3 SP 4 Combined solution SP 5 SP 6 5

What often happens in practice ? Large Unsolved Problem SP 1 SP 4 SP 5 SP 2 SP 3 SP 7 Combined solution ? SP 9 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

Lecture Outline • Modular Decomposition • Abstraction Kinds • Specifications • Procedural abstractions 8

Abstraction Kinds 1. By Parameterization – Abstracts from the identity of the data 2. 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 9

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 ? 10

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 11

Benefits of Abstraction by Specification 1. Locality -- the implementation of an abstraction can be understood (or written) without needing to examine the implementations of any other abstractions. 2. Modifiability -- an abstraction can be reimplemented without requiring changes to any abstractions that use it. 12

Lecture Outline • Modular Decomposition • Abstraction Kinds • Specifications • Procedural abstractions 13

Specification • Contract between client and implementer – Client will rely on behavior in specification – Implementer only needs to provide this behavior – Implementer is free to change implementation • Tells the client of an abstraction what the procedure is expected to do • Tells the implementer of an abstraction what implementation must do to satisfy the client 14

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) • May have different meanings depending on the reader (or the programmer) • Can be understood only by humans (for the most part) • Manual effort needed to check code against specs For now we will write informal specifications, but will 15 attempt to make them as precise as possible

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 Chefs association 16

Recipe: History and Trivia • Earliest recipe -> stone tablet in Babylonia (1600 BC). Recipes popular in Roman & Greek times • Gained popularity with invention of printing press • Early recipes often imprecise -> served more as a reminder to someone who knew how to prepare the dish e. g. , “Do it till it is done” • Modern recipe format invented around 1816 by Dr. William Kitchener: “The cook’s oracle” – Used precise terms such as “add 1 quart of vinegar” – Listed ingredients and name of dish at beginning – Specified processes such as boil, steam, fry in detail Recipe Book: circa 1507 17

Recommendations for recipe writing • The following is what the chef’s association recommends for recipe writers today – Use a straightforward descriptive name for the dish, rather than a name that is fun or creative – Indicate preparation and cooking times at the beginning – List ingredients separately at the top of the recipe. – List the main ingredient (such as meat) first 18

How to write procedural specifications ? • Choose a name for the procedure that is descriptive and (preferably) pronounceable • 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 19

Procedural Specifications - 1 • Factorial: Fact(n) = 1 * 2 *3 …. * n * (n- 1) static int Fact(int n) { // EFFECTS: Returns the factorial of n // where fact(n) = 1 * 2 * … * n // REQUIRES: n >= 0 // MODIFIES: None (this can be dropped) … } 20

Procedural Specifications – 2 (Multiple Implementations) Using Iteration Using recursion public static int fact(int N ) { int result = 1; public static int fact(int N) { int result; for (int i =1; i<=N; i++) { result = result * i; } } if (N==0) result = 1; else result = N * fact(N – 1); return result; } return result; Both implementations (should) have the same behavior. Can you see any difference ? 21

Group Activity • Write the specification for a sorting routine. You should not constrain the sorting to a specific algorithm or implementation. However, you should take care that the sorting does what you would “expect”. • Trade the specification with another group and have them write an implementation for it 23

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 (or maybe not) – No need to say that array elements are non-null (implied by first clause)

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 }

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

EFFECTS Clause • Specifies what the EFFECT of the procedure is – Include both return value and heap objects – Include any exceptions thrown by the procedure – Must say how the modifications are made 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)

Implementation: Bubble sort public static void sort( int[] a ) { // REQUIRES: Array a not be Null // MODIFIES: Array a // EFFECTS: Array a is sorted in ascending order int i, j; for (i= 0; i<a. length; i++) for (j=i+1; j<a. length; j++) if (a[i] > a[j]) { // Swap a[i] and a[j] } }

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:

Solution: Group Activity • The array may contain null objects – Need to put this in the REQUIRES clause 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. compare. To for determining order 30

Procedural Specifications: Example 1 public class Vectors { //OVERVIEW: Provides useful standalone procedures // for manipulating vectors public static void remove. Duplicates ( 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. … } } 31

Procedural Specifications: Example 2 } if (v== null) return; // v may be NULL as per REQUIRES for (int i = 0; i < v. size(); ++i) { Object x = v. get(i); int j = i + 1; while ( j < v. size() ) { if ( ! x. equals( v. get(j) ) ) j++; else { v. set(j, v. last. Element() ); v. remove( j ); } } Does the above implementation satisfy the specification ? Why or why not ? 32

Procedural Specification: Example 3 • Does the following implementation satisfy the specification ? public static void remove. Duplicates ( 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(); } 33

Procedural Specifications: Example 4 public class Vectors { //OVERVIEW: Provides useful standalone procedures // for manipulating vectors } public static void remove. Duplicates ( 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 } 34

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

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 down in writing ! 36

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 37

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 ? 1. What if there is more than one element equal to x ? 2. What if there is no element equal to x ? How will you fix these issues ? 38

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 39

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 40

Group Activity 1. Specify minimum procedure in Java that returns the index of the element in an array of integers that has minimum value. For example, if it’s given an array {1, 2, 1}, it would return the index ‘ 2’. Aim at writing specification that is sufficiently restrictive, general, and clear. 2. Use the procedure in another one to find the kth smallest element in an array. Write the spec and the implementation. 41

Summary • Abstraction: Needed for doing modular decomposition productively – By parameterization: Standard for programming – By specification: Focus of this class • Provides locality and modifiability • Specifies contract between implementer & user • Allows implementation to vary independent of client – Good specifications are sufficiently restrictive, general and as clear as possible – Specifications should ensure that they do not permit incorrect implementations 42

To do before next class • Read Chapters 1, 3 and 9 in the textbook • Try exercises 3. 1 to 3. 4 and 3. 7 • Attempt Assignment 1 on class webpage – Need to choose a partner for the assignments – Learn Java NOW if you haven’t started yet ! – If you did badly in Quiz 1, rethink taking the class 43

Under-determined Behavior Vs. Non. Deterministic Implementation • Procedure specification can specify underdetermined behaviour • Procedure implementation can have non-deterministic implementation 44

Under-determined behaviour • A procedure is underdetermined if for certain inputs its specification allows more than one possible result. For example, • public static Integer find. Max(Integer x, Integer y, Integer z) // REQUIRES: x, y, and z are not null // EFFECTS: returns the largest number out of the 3 input integers, // e. g. , if x = 10, y = 3, z = -7, then return x • public static int search (int[] a, int x) throws Not. Found. Exception, Null. Pointer. Exception // EFFECTS: If a is null throws Null. Pointer. Exception, else // returns i such that a[ i ] = x; // If no such element is found, it returns -1 45

A deterministic implementation • An implementation of a procedure is deterministic if, for the same inputs, it always produces the same result. – Most procedures will be in this category • Examples of procedures that require nondeterministic implementations int random (int min, int max) // REQUIRES: max > min + 1 // EFFECTS: returns a random integer result such that min < result < max 46