It is copyrighted bySubhashis Banerjee S. Arun-Kumar
Department of Computer Science and Engineering
Indian Institute of Technology
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CONTENTS
I Models of computation
1 Introduction
2 Mathematical preliminaries
2.0.1 Sets
2.0.2 Relations and Functions
2.0.3 Principle of Mathematical Induction
3 A functional model of computation
3.1 The primitive expressions
3.2 Substitution of functions
3.2.1 Substitution using let
3.3 De nition of functions using conditionals
3.4 Functions as inductively de ned computational processes
3.5 Recursive processes
3.6 Analysis of correctness and e ciency
3.6.1 Correctness
3.6.2 E ciency
3.6.3 E ciency, Why and How?
3.6.4 In the long run: Asymptotic analysis and Orders of growth
3.7 More examples of recursive algorithms
3.8 Scope rules
3.9 Tail-recursion and iterative processes
3.9.1 Correctness of an iterative process
3.10 More examples of iterative processes
4 The Imperative model of computation
4.1 The primitives for the imperative model
4.1.1 Variables and the assignment instruction
4.1.2 Assertions
4.1.3 The if then else instruction
4.1.4 The while do instruction
4.1.5 Functions and procedures in the imperative model
5 Step-wise re nement and Procedural Abstraction 71
5.1 Step-wise re nement
5.1.1 Executable speci cations and rapid-prototyping
5.1.2 Examples of step-wise re nement
5.2 Procedural abstraction using higher-order functions
5.2.1 Functions as input parameters
5.2.2 Polymorphic functions
5.2.3 Constructing functions using lambda ( )
5.2.4 Functions as returned values
II Data-directed programming 107
6 Abstract Data Types 109
6.1 Building the Rational data-type (pairs)
6.2 Rational data-type in ML
6.2.1 signature, datatype and module
6.3 Rational data-type in Java
6.3.1 Interfaces, Classes and Objects: Basics of Object Oriented Programming .
7 Programming with Lists
7.1 Lists
7.2 The Alpha- LIST data-type in ML
7.3 The Alpha-LIST data-type in Java
7.3.1 Sharing of lists and garbage collection
7.3.2 List programming in Java
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