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

Some Initial Thoughts, and Recap From the Church-Turing thesis all computers are equivalent to a Turing Machine and therefore are equivalent to each other. Computer manufacturers admit this; they do not say “our machine has some magic instruction which makes our computer more powerful than the competition”. Their advertising goes like this: “Our machines are faster, cheaper, easier to program and are more greener” From the Church-Turing thesis all programs can be constructed using two registers and two instructions, so all programming languages are equivalent in expressibility (power,…) 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” Why are these two instructions so fundamental? decjmpreg reg,lab inc reg

What languages do we know ?

Java Ada ALGOL 60 Assembler Basic FORTRAN Lisp Scheme Joy Haskell Clean COBOL Erlang Prolog FP F# Lua Occam Oz Pascal Python C++ SmallTalk C# C PHP Tcl

Lang Paradigm

Programming Paradigms What is a “Paradigm” ? Important Paradigms Imperative (procedural) Declarative Functional Logic Object Oriented Event Driven

OO Functional Logic Imperative

Imperative vx. Declarative 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

Generations 1stMachine – level (switches) 2ndAssembler 3rd Programmer-friendly: C++, Java, FORTRAN, COBOL 4thApplication: SQL, SPSS 5thConstraint: Prolog, OPS5 (AI)

Paradigms: Imperative Focus on dynamic aspect of computation – operational semantics Specifies step-by step what must be done

Pure Forms Godel’s purely descriptive recursive function formalism Realized by Mc.Carthy’s Lisp Turing’s Imperative formalism

Paradigms: Functional

Paradigms: Logic

Paradigms: Object Oriented

Paradigms: Event Driven

Using conditional expressions to define recursive functions Thesis: All computable functions can be defined by the recursive use of conditional expressions. if p then a else b n! = g(n,1) where g(n,s) = if n = 0 then s else g(n – 1, n x s)

Equivalence of imperative and functional programming

Flow Diagrams: Turing Von Neumann and McCarthy

Prolog Syntax SheetFacts 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.

Recursion See Recursion On page 269 of Kernighan and Richie’s book The C Programming language recursion86,139,141,182,202,269 Recursion in Language: 5 th C BC Panini Sanskrit Grammar Rules 20 th C 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

Recursion in Language begin articleadjectivenoun end ornate noun begin ornate noun relative pronoun verb end preposition fancy noun verb fancy noun fancy noun fancy noun

Recursion in Language begin articleadjectivenoun end ornate noun begin ornate noun relative pronoun verb end preposition fancy noun verb fancy noun fancy noun fancy noun

Recursion in Language begin articleadjectivenoun end begin ornate noun relative pronoun verb end preposition fancy noun verb fancy noun fancy noun

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

=expression term var num ()expression Statement Expression Term

Back to the “Timeline” Our contemporary languages have evolved (?) or have developed (?) from languages of the past. What will our future languages look like? In other words what are our future computing needs (or desires) ?

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” ?

to tree :size setpencolor [ ] if :size < 5 [stop] fd :size lt 30 tree :size*0.7 rt 60 tree :size*0.7 lt 30 bk :size end