comp3104 2010-11 programming languages proposal 1 all humans possess a common logical structure...

Comp3104 2010-11 Programming Languages

Proposal 1 All humans possess a common logical structure which operates independently of language

Proposal 2 Language determines what the individual perceives in the world and how he thinks about it.

“A language that doesn’t affect the way you think about programming, is not worth knowing”

The Whorfian Hypothesis

• All computers are equivalent to a Turing Machine and therefore are equivalent to each other.

• Computer manufacturers do not say “our machine has some magic instruction which makes our computer more powerful than the competition”. They say “Our machines are faster, cheaper, and are more greener”

• All programs can be constructed using two registers and two instructions, so all programming languages are equivalent

• Language developers admit this; they do not say “our language has some magic feature which allows our language to do more than in any other language”. Instead, their advertising goes like this. “Our language is more user-friendly, our compilers are faster and they produce smaller executable files, and are more greener”

What languages do we know ?

Java

Ada

ALGOL 60

Assembler

Basic

FORTRANLisp

Scheme

Joy

Haskell

Clean

COBOL

Erlang

Prolog

FP

F#Lua

Occam

Oz

Pascal

Python

C++

SmallTalk

C#

C

PHP

Tcl

Criteria for ComparisonCriteria

C Java

asm

Schem

e

Prolog

LangLang

LangLang

Lang

Lang

Lang

Lang

Lang

LangLang

Lang

Paradigm

Paradigm

Paradigm

Paradigm

Programming Paradigms

What is a “Paradigm” ?

Important Paradigms

• Imperative (procedural)

• Declarative

• Functional

• Logic

• Object Oriented

• Event Driven

Imperative vs. Declarative (Functional)

float x;

float function square(float a) {

float b;

b = a x a;

return b;

}

x = square(3);

(define (square a) (x a a))

(square 3)

Matlab

Lisp

C

Java

C++

Event Driven

ActionScript

Prolog

Functional

Object Oriented

Logic

Imperative

Assembler

Timeline

Scheme : Definitions and Expressions

Scheme : Functions

(define (seven x) (* x 7))

Scheme : Functions

(define (sum x y) (+ x y))

Scheme : Conditionals (1)

(define (test x) (cond ( (> x 0)1) ( (= x 0)0) ( (< x 0)-1)))

Scheme : Conditionals (2)

(define (test2 x) (if (< x 0)(- x) x))

RecursionRecursion See Recursion

On page 269 in the index of Kernighan and Richie’s book The C Programming language

recursion 86,139,141,182,202,269

Recursion in Language: 5thC BC Panini Sanskrit Grammar Rules

20thC Chomsky theorizes that unlimited extension of English is possible through the use of recursion.

… try Googling “Recursion”

There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we now know we don’t know. But there are also unknown unknowns. These are things we do not know we don’t know

US Defense Secretary Donald Rumsfeld on February 12, 2002

Little harmonic Labyrinth

Scheme : Recursion : The Factorial Function (1)

How many ways can you get n people to sit in n chairs ?

n = 3. (A,B,C)

n = 4. (A,B,C,D)

Scheme : Recursion

(define (sum n) (if (= n 1)1 (+ n (sum(- n 1)))))

sum the numbers 1 to N(e,g, 1 to 4)

4 + 3 + 2 + 1= 4 + (3 + 2 + 1)= 4 + 3 + (2+1)= 4 + 3 + 2 + (1)

(sum 4) = 4 + (sum 3) =

Scheme : Recursion (2) The Factorial Function

(define (fact n) (if (= n 1)1 (* n (fact (- n 1)))))

Functional Recursion // Imperative Iteration

(define (fact n) (if (= n 1)1 (* n (fact (- n 1)))))

I lost the number of my new mobile phone

How can I find the number ? Get my girlfriend to phone every single mobile number. (OK I’ll cook supper!)

Approximate solution: Say a mobile number has 10 digits (actually 11) and each digit can be 0 – 9 (10 possibilitities). So the solution is 10! How long will this take? Calculatore!

Fundamental Principles of Recursion

A recursive function must call a simplified version of itself. This is guaranteed to “bottom out” (to halt). Any call to itself would produce an infinite regress.

Don’t run this … ah go on then ..

(define (fact n) (if (= n 1)1 (* n (fact n))))

... and wait for the error message ... or worse

Recursion in Language

begin article adjective noun end

ornate noun

beginornatenoun

relativepronoun

verb

end

preposition

fancynoun

verb

fancynoun

fancynoun

fancy noun

Recursion in Language

begin article adjective noun end

ornate noun

beginornatenoun

relativepronoun

verb

end

preposition

fancynoun

verb

fancynoun

fancynoun

fancy noun

Recursion in Language

begin article adjective noun end

beginornatenoun

relativepronoun

verb

end

preposition

fancynoun

verb

fancynoun

fancynoun

Recursion is not Self-Reference

A recursive function makes reference to a simplified version of itself: (I am) better than what (I was)

I’m the humblest person I know

I never make misteaks

“I never make predictions. I never have and I never will”

This sentence contains five words

This sentence no verb

( )A

A +

var

A

Compilers - Parsing

( )

+

var

A

var = expression

term

+

-

term

+

-

var

num

( )expression

Statement

Expression

Term

Prolog Syntax Sheet Facts and Rules

parent(abraham, isaac).

Fact. Lower case for names.

parent(isaac, esau).

Fact. Lower case for names.

grandfather(X,Y) :- parent(X,A),parent(A,Y).

Rule. If X is the grandfather of Y then X is the parent of A and A is the

parent of Y. For example, if george “X” is the parent of colin “A” and colin “A” is the

parent of tristan “Y” then george “X” is the grandparent of Tristan “Y”.

Queries

?- parent(abraham,X).

The capital X designates an “output” variable which will be all sons of

Abraham.

?- grandfather(abraham,X).

The capital X designates an “output” variable which will be all grandchildren

of Abraham.

lectures(colin,3063).

lectures(colin,3079).

lectures(pete,3078).

lectures(richard,3062).

lectures(richard,3040).

studies(tom,3063).

studies(tom,3062).

studies(kate,3063).

studies(kate,3040).

studies(kate,3062).

?- lectures(colin,Mo),studies(kate,Mo).

?- lectures(colin,Mo),studies(X,Mo).

Monty Python Holy Grail

witch(X) :- burns(X),female(X).burns(X) :- wooden(X).wooden(X) :- floats(X).

wooden(woodBridge).stone(stoneBridge).

floats(bread).floats(apple).floats(cherry).

floats(X) :- sameweight(duck, X).female(girl).sameweight(duck,girl).

?- witch(girl)

Monty Python Holy Grail

Yes[trace] 12 ?- witch(girl). Call: (7) witch(girl) ? creep Call: (8) burns(girl) ? creep Call: (9) wooden(girl) ? creep Call: (10) floats(girl) ? creep Call: (11) sameweight(duck, girl) ? creep Exit: (11) sameweight(duck, girl) ? creep Exit: (10) floats(girl) ? creep Exit: (9) wooden(girl) ? creep Exit: (8) burns(girl) ? creep Call: (8) female(girl) ? creep Exit: (8) female(girl) ? creep Exit: (7) witch(girl) ? creep

Yes

Coda

It is easier to write an incorrect program than to read a correct one.

There are two ways to write error-free programs, only the third one works.

It is easier to change the specification to fit the program than vice-versa

Why did the Roman Empire collapse? What is the Latin for “office automation” ?