Lecture 01 | Introduction to 6.00

Programming: The most fun you can have with your clothes on.

Declarative and Imperative Knowledge.

Declarative Knowledge

Declarative knowledge is composed of statement of facts.

example:-

• y is the square root of x if and only if y * y = x.

The above point is a fact, declarative knowledge does not tell you how to find the SQUARE ROOT, interestingly it tells you how to test the square root.

Imperative Knowledge

Imperative knowledge is about how to accomplish something. Declarative knowledge is about testing the validity of the knowledge and Imperative about finding how to generate the knowledge.

Consider the steps to find a square root of a number, The Declarative knowledge tells us.

• y is the square root of x if and only if y * y = x.

Imperative knowledge tells us how to find the square root, consider the below steps:-

2. if `g * g` is close enough to `x`, then `g` is a good approximation of the square root of `x`.
3. Otherwise, create a new guess by averaging `g` and `x/g`, i.e `g(new) = (g(old) + x/g(old))/2`
4. Using this new guess, go back to Step 2.

**Example:- **
If we have to find square root of 25, which is 5,

Iteration 1:

1. Start withÂ  `g = 3`.
2. `3 * 3 = 9`, which is not close to `25`.
3. Calculate new guess, `g(new) = (3 + 25/3)/2 = 5.666666666666667`.
4. Restart at Step 2.

Iteration 2:

1. Start with `g = 5.666666666666667`
2. `5.666666666666667 * 5.666666666666667 = 32.11111111111111`, which is not close to `25.`
3. Calculate new guess, `g(new) = (5.666666666666667 + 25/5.666666666666667)/2 = 5.03921568627451`.
4. Restart at step 2.

Iteration 3:

1. Start with `g = 5.03921568627451`
2. `5.03921568627451 * 5.03921568627451 = 25.39369473279508`, which is close to `25`, so stop.

So from the above steps we can deduce that.

Algorithms

An algorithm is a description on how to perform a computation. We say that the algorithm have CONVERGED, which is fancy way to saying that it has halted.

An algorithm consists of these terms:-

• Instructions:- Set of step to perform the computation, so in the above algorithm we have 4 sets of instructions
• Flow of control:- How the instruction are supposed to execute i.e. the sequence of execution, which in the above algorithms is Step 1,2,3,4 and then repeat from step 2
• Termination condition:- The particular condition on which the execution of instruction will be halted/ converged, in the above algorithm it is if `g * g` is close enough to `x`. In the absence of a termination condition the algorithm will repeat till infinity.

Fixed program and stored program computers

We have defined the algorithm to find the square root, now this is a theoretical set of instruction, which needs to be converted to a mechanical process for it to be possible to do automatic computation using computers.

One way will be to design a machine which specifically computes square roots, meaning to design a circuit to implement this algorithm. This is used to be the way all computers worked and they were called:-

Fixed Program Computers

• Fixed Program Computers:- They were designed to do very specific things, ex, The very first computer designed was supposed to compute the trajectory of artillery, and then Alan Turing designed a computer to break the enigma code, and thats all these computers were capable of nothing else.

Thee type of computer are not very efficient and cost effective, so then came Stored Program Computers.

Stored Program Computer

A stored program computer looks like this. It has the following main components.

• Memory
• Control Unit: A control unit basically tells Memory what to do, like fetch some data, put some data,
• Arithmetic Logic Unit: This is the brains of the computer,
• Accumulator: Its stores the result.
• Input
• Output

Typically a computers have a very minimal instruction sets, based on which we can create great programs based on the different combination of these instructions.
Alan Turing in fact said that a primitive computer does not need more than 6 Instructions.

Programming Language

A programming language provide as discussed in the section Algorithms.

• the set of primitive instruction to work on a computers.
• a set of primitive control structures.

One programming language differ from another in these two points along with how the instructions are clubbed together to perform complex actions.

These together defines a programming language.

Syntax

• Syntax: Tells us which sequence of character and symbols constitute a well formed string, but it may not have a meaning
• ex: x = 3 + 4, is syntacticly correct
• but, x = 3 4 is not

Static semantics

• Static Semantic: Tells us which well formed strings have meaning.
• ex: 3/”abc”, is syntacticly correct, but does not have a meaning

Semantics

• Semantics : Looks only at those strings which are syntacticly correct, and static semantically correct and assigns a real meaning to it. So like in natural language can have ambiguity, a programming language cannot have any ambiguity.

Types of errors

There are times programs does not give output which we desired, in place of that it might give these:-

• Program can Crash
• In a properly designed computing system, the crash, should be local, that means it should not destroy the whole system.
• Program can go never stop, i.e. Infinite Loop.
• Program which runs to completion but produces wrong output.

The problems mentioned above is in ascending order of erroneousness, i.e., crash is much more acceptable than an infinite loop which is acceptable than a wrong output, because a wrong output can result in very life threatening results, and you may not be aware of any errors in the program, but the other two are errors in the programs.

Compiled Vs Interpreted Language

In terms of error handling, Python is somewhere in the middle, it is not as robust as Java, but better than C at weeding out meaning less things.

A programming language should have a strong Static Semantics, so that it behaves as expected.

In terms of debugging a Interpreted language is much better than a compiled language, because the error thrown by Interpreted languages are close to the language of the code whereas in case of compiled languages, it is close to the object code it is compiled into.

References

Problem Sets

Problem Set 0 (Assigned)
Problem set 0 is assigned in this session. This is an ungraded problem set. The instructions can be found on the session page where it is due, Lecture 2 Core Elements of a Program.

Check Yourself

What is the difference between declarative and imperative knowledge?

Declarative knowledge is a statement of fact, it shows how to test a program.

Imperative knowledge is like a recipe/algorithms which tells how to implements a knowledge.

What is the advantage of a stored-program computer?

The same computer can do multiple work, like compute the bank balance and also tells the trajectory of a missile, whereas a Fixed program computer will do just one task.

What are the syntax, static semantics, and semantics of a language?

Syntax tells how to make a well formed statement.
Static Semantic tells if a statements have meaning.
Semantics tells that if a statement is Static Semantically correct it should have only one well formed meaning.

What sorts of errors can occur in a program?

There are 3 possible errors in a program.
1. Crash
2. Infinite Loop
3. Wrong Output.