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Contents
I Models of computation
1 Introduction
2 Mathematical preliminaries
201 Sets                                    
202 Relations and Functions                         
203 Principle of Mathematical Induction                  
3 A functional model of computation
31 The primitive expressions                            
32 Substitution of functions                             
321 Substitution using let                          
33 Definition of functions using conditionals                    
34 Functions as inductively defined computational processes          
35 Recursive processes                               
36 Analysis of correctness and e±ciency                      
361 Correctness                                
362 E±ciency                                 
363 E±ciency, Why and How?                        
364 In the long run: Asymptotic analysis and Orders of growth     
37 More examples of recursive algorithms                     
38 Scope rules                                    
39 Tail-recursion and iterative processes                      
391 Correctness of an iterative process                   
310 More examples of iterative processes                      
4 The Imperative model of computation
41 The primitives for the imperative model                    
411 Variables and the assignment instruction               
412 Assertions                                 
413 The if then else instruction                       
414 The while do instruction                         
4 CONTENTS
415 Functions and procedures in the imperative model          
5 Step-wise refinement and Procedural Abstraction
51 Step-wise refinement                               
511 Executable specifications and rapid-prototyping            
512 Examples of step-wise refinement                    
52 Procedural abstraction using higher-order functions              
521 Functions as input parameters                     
522 Polymorphic functions                          
523 Constructing functions using lambda (¸)                
524 Functions as returned values                      
II Data-directed programming
6 Abstract Data Types
61 Building the Rational data-type (pairs)                     
62 Rational data-type in ML                            
621 signature, datatype and module                   
63 Rational data-type in Java                           
631 Interfaces, Classes and Objects: Basics of Object Oriented Programming

7 Programming with Lists
71 Lists                                        
72 The ®¡LIST data-type in ML                         
73 The ®¡LIST data-type in Java                        
731 Sharing of lists and garbage collection                 
732 List programming in Java

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