Lecture 01

01.00 Introduction

Overview

1. What does a computer do?
2. What are a computer's fundamental operations?
3. Fundamental operations and imperative knowledge
4. Algorithms
5. How to use programming languages to implement algorithms

01.01 Basics of Computation

Goals in this couse

1. Learn to program
2. Learn to think computationally, algorithmically

What does a computer do?

1. Performs calculations
   • Built-in primitives
   • User-defined methods
2. Remembers results

Analogies with everyday examples

• Computing time (lamp 1 ft, ball 1m)
• Computing storage

Insufficiency of basic operations

• 5.2 days to search the Web
• 10¹²³ different possible chess games

Moral: Computers are fast, but we still need efficient algorithms!

Computing limitations:

1. Size of problem
   • Useful in encryption
2. Fundamentally impossible to compute
   • E.g., Turing's halting problem

01.02 Types of Knowledge

What is knowledge?

Two types of knowledge:

1. Declarative knowledge: facts; check truth
2. Imperative knowledge: how to; find truth

Example: finding square root (Heron of Alexandria)

• Diagramming this imperative knowledge as flow of command

Algorithms are recipes

• Example: custard

01.03 Basic Machine Architecture

Two general types of computers:

1. Fixed-program computer: executes a specific set of commands
2. Stored-program computer: machines that stores and manipulates instructions
   • Program, i.e. sequence of instructions, stored in computer
   • Interpreter executes instructions in program

Basic machine architecture

1. Memory
2. Control unit (houses program counter)
3. Arithmetic logic unit (ALU)

Basic mechanics:

• Program counter in control unit advances through program in memory
• Memory sends input to ALU, stores output from ALU
• Tests within ALU can effect change on the program counter in control unit

Flow diagram

Basic primitives

• Six primitives are sufficient to compute anything that is computable
• Computers with these six primitives are called Turing complete

"a serious pain in some parts of the anatomy"

01.04 Programming Language Characteristics

Creating recipes

Each programming language provides

1. a set of primitive operations
2. mechanisms for combining these primitive operations
3. mechanisms for assigning values to computation or expression

Aspects of a computer language

1. Primitive constructs (analogous to words)
2. Syntax -- how to put words together to form "well-formed" expression
3. Semantics -- meaning
   1. Static semantics -- which syntactically valid strings have meaning
   2. Formal semantics -- the meaning associated with syntactically valid string free of static semantic errors

In computer science, there is always exactly one formal semantic meaning for any syntactically valid string free of static semantic errors

When things go wrong

1. Syntactic errors
2. Static semantic errors
   • Compiled versus interpreted languages
3. No such thing as (formal) semantic error, but program may produce result programmer did not intend