Lecture 2: Schreme David Evans Available within the network will be functions and services to which you subscribe on a regular basis and others that you call for when you need them. In the former group will be investment guidance, tax counseling, selective dissemination of information in your field of specialization, announcement of cultural, sport, and entertainment events that fit your interests, etc. In the latter group will be dictionaries, encyclopedias, indexes, catalogues, editing programs, teaching programs, testing programs, programming systems, data bases, and – most important – communication, display, and modeling programs. All these will be – at some late date in the history of networking - systematized and coherent; you will be able to get along in one basic language up to the point at which you choose a specialized language for its power or terseness. Background just got here last week finished degree at MIT week before Philosophy of advising students don’t come to grad school to implement someone else’s idea can get paid more to do that in industry learn to be a researcher important part of that is deciding what problems and ideas are worth spending time on grad students should have their own project looking for students who can come up with their own ideas for research will take good students interested in things I’m interested in – systems, programming languages & compilers, security rest of talk – give you a flavor of the kinds of things I am interested in meant to give you ideas (hopefully even inspiration!) but not meant to suggest what you should work on J. C. R. Licklider and Robert W. Taylor, The Computer as a Communication Device, April 1968 CS655: Programming Languages University of Virginia Computer Science David Evans http://www.cs.virginia.edu/~evans

Menu Registration Survey Results Universal Languages My Answers Universal Languages Stuff Languages are Made Of Scheme Infinitely many different functions 23 Jan 2001 CS 655: Lecture 2

Favorite Programming Languages C 41/3 C++ 21/3 Java 21/3 Perl 1 My answer: For getting work done: C (with LCLint) For reading other people’s code: CLU For fun: FL, Scheme 23 Jan 2001 CS 655: Lecture 2

Most Hated PL COBOL 2 Perl 2 (also favorite) Java 1 Lisp 1 None 4 My answer: For asthetics, readability: APL For teaching intro CS courses: C++ For writing big systems: Lisp 23 Jan 2001 CS 655: Lecture 2

Experience of Students in this Class C++ (38 years), C (36), BASIC (29), Pascal (21), various assemblies (12), Java (9), Perl (5), FORTRAN (4), Python (2½), Ada (2), Lisp dialects (1½), COBOL (1), Smalltalk (½) Algol60 direct successors = 106 Pre-Algol languages = 46 Completely object-oriented languages = ½ But O-O doesn’t really mean anything Pure functional languages = 0 Python is close (but has globals and state) 23 Jan 2001 CS 655: Lecture 2

Partner Preference Assigned Randomly 4 Choose Your Own 4 No Clear Preference 2 23 Jan 2001 CS 655: Lecture 2

Can class go over time? No problem 10 Problem 0 One said, “but if I am bored and you keep me there I will be really annoyed and glare at you”. 23 Jan 2001 CS 655: Lecture 2

Technical Questions Used higher-order procedures: No: 4 A little: 3 Yes: 3 Wrote function that returned infinitely many possible different functions No: 10 (some used tables of function pointers) Fixed points: find x where f(x) = x Gets really interesting when x is a function! 23 Jan 2001 CS 655: Lecture 2

Why taking this class? 23 Jan 2001 CS 655: Lecture 2

Next: Computability and Universal Programming Languages 23 Jan 2001 CS 655: Lecture 2

Computability A programming language is universal if it can express all computable functions. A function is “computable” if there exists an algorithm that computes it. An algorithm is a computational procedure that takes a finite number of steps. What’s a computational procedure? 23 Jan 2001 CS 655: Lecture 2

Turing Machine Tape head can: Read symbol from tape Write symbol on tape Move tape left or right one square Change its own state (finite state machine)   Infinitely long tape 23 Jan 2001 CS 655: Lecture 2

Universal Turing Machine Universal Turing Machine is a Turing machine that can simulate any other Turing machine Input (start state on tape) contains both a description of a Turing Machine (i.e., a program) and its input Yes, there really are such things Hopefully you will see it in CS660 23 Jan 2001 CS 655: Lecture 2

Computability A computational procedure is something that can be described by a Turing Machine A language is universal if it can express: all algorithms = all finite computational procedures = all Turing machines = one Universal Turing Machine 23 Jan 2001 CS 655: Lecture 2

Not everything is computable Halting Problem – will a Turing Machine halt? Suppose we could compute it: (define (halts? P) ...) returns true if P halts, false otherwise. 23 Jan 2001 CS 655: Lecture 2

(define contradicts-halts (if (halts? contradict-halts) (loop-forever) Based on Duane Boning, http://sicp.ai.mit.edu/Fall-1999/lectures/lec25/6001-12-9-99-computability.ppt (define contradicts-halts (if (halts? contradict-halts) (loop-forever) #t)) If contradict-halts halts, it loops forever; If contradict-halts doesn’t halt, value is true. Yikes! halts? must not exisit! Note: this is not a proof. (proof in 650) Perhaps it is if that doesn’t exist. 23 Jan 2001 CS 655: Lecture 2

Is a language universal? How can we prove a language is universal? Produce a program that implements a Universal Turing Machine in the language (usually this is pretty easy) How can we prove a language is not universal? Prove that it cannot express the function of some Turing Machine 23 Jan 2001 CS 655: Lecture 2

Elements of Language 23 Jan 2001 CS 655: Lecture 2

Elements of Language (Almost?) All Languages have: English: Primitives Means of combination English: Primitives = words (?) e.g., “Floccipoccinihilipilification” (the act of rendering useless) e.g., Sentence = Subject Verb Object 23 Jan 2001 CS 655: Lecture 2

Means of Combination Allow us to say infinitely many things with a finite number of primitives In English, words aren’t really primitives (linguists call the primitives morphemes – smallest units of meaning) Means of Combination work on word parts: Antifloccipoccinihilipilification (the act of not rendering useless) Antifloccipoccinihilipilificationator (one who does the act of not rendering useless) 23 Jan 2001 CS 655: Lecture 2

Describing Means of Combination BNF (Backus Naur Form) <non-terminal> ::= <replacement> Terminals are primitives in the language (don’t appear on left-hand side.) Alternatives <non-terminal> ::= <replacement1> | <replacement2> short for: <non-terminal> ::= <replacement2> 23 Jan 2001 CS 655: Lecture 2

BNF John Backus Normal  Peter Naur (Donald Knuth’s suggestion) FORTRAN (manual described syntax using verbose English, not a formal notation) Member of Algol60 committee, introduced formal notation for syntax Influential in development of functional languages: FP, FL, Turing Lecture Normal  Peter Naur (Donald Knuth’s suggestion) Chair of Algol60 committee 23 Jan 2001 CS 655: Lecture 2

BNF Example NP ::= Noun VP ::= Verb Noun ::= Dave | Scheme Sentence ::= NP VP NP ::= Noun VP ::= Verb Noun ::= Dave | Scheme Verb ::= rocks | sucks Could this language be a universal programming language? 23 Jan 2001 CS 655: Lecture 2

BNF Example NP ::= Noun VP ::= Verb | Noun and NP Sentence ::= NP VP NP ::= Noun VP ::= Verb Noun ::= Dave | Scheme Verb ::= rocks | sucks | Noun and NP We can express infinitely many things with a tiny language! With the right meaning function, this could be a universal programming language. 23 Jan 2001 CS 655: Lecture 2

Scheme 23 Jan 2001 CS 655: Lecture 2

Scheme Like all (?) languages, Scheme has: Primitives Means of Combination Also, like all (?) reasonable programming languages it has: Means of Abstraction 23 Jan 2001 CS 655: Lecture 2

Mini-Scheme Primitives Examples Numerals 0 655 3.52 -58 Functions + Constants #f #t You know what the primitives mean. Numeral  Number 655  655 Function  Function +  math addition 23 Jan 2001 CS 655: Lecture 2

Means of Combination Application Expression ::= (Expression) Expression ::= (Expression Expression) Expression ::= (Expression Expression Expression) ... Expression ::= (Expression*) (+ 655 58) (* (+ 0 (+ 2 2)) 6) “Evaluate all the expressions, then apply the first expression (a procedure) to all the other values.” 23 Jan 2001 CS 655: Lecture 2

Means of Combination Special Forms (if Expression1 Expression2 Expression3 ) If the value of Expression1 is #f, the value of the if is the value of Expression3. Otherwise, it is the value of Expression2 . A few others, but they are not necessary (note: neither is if!) 23 Jan 2001 CS 655: Lecture 2

Means of Combination Make Procedure Expression ::= (lambda (Variable) Expression) “A procedure that when applied to value, evaluates to Expression with all instances of Variable substituted for by value.” Note: “substitution” is complicated. 23 Jan 2001 CS 655: Lecture 2

Mini-Scheme Expression ::= (Expression*) | (lambda (Variable) Expression) | (if Expression1 Expression2 Expression3 ) | numeral | #f | #t | + Variable ::= identifier Is mini-scheme a Universal Programming Language? (Left as challenge problem.) 23 Jan 2001 CS 655: Lecture 2

Means of Abstraction (define Variable Expression) Substitute Expression for Variable. (define two 2) 2 (+ two two) 4 23 Jan 2001 CS 655: Lecture 2

Abstracting Procedures (define square (lambda (x) (* x x)) proc (square two) 4 (define (Variable1 Variable2) Expression) is just an abbreviation for: (define Variable1 (lambda (Variable2) Expression) 23 Jan 2001 CS 655: Lecture 2

Multiple Arguments (define (Variable1 Variable2 Variable3) Expression) is just an abbreviation for: (define Variable1 (lambda (Variable2) (lambda (Variable3) Expression))) This is called “currying”. 23 Jan 2001 CS 655: Lecture 2

Currying (define add (lambda (x) (lambda (y) (+ x y)))) (add 5) proc 7 23 Jan 2001 CS 655: Lecture 2

add add is a procedure that returns infinitely many different procedures! (define add (lambda (x) (lambda (y) (+ x y)))) 23 Jan 2001 CS 655: Lecture 2

triadd (define triadd (lambda (x) (lambda (y) (lambda (z) (+ x y z))))) triadd is a procedure that returns infinitely many different procedures, each of which is a procedure that returns infinitely many different procedures! So, after today your answer to survey question: “Yes, infinitely many!” 23 Jan 2001 CS 655: Lecture 2

Charge Problem Set 1 out today Its not long but may be hard, start it soon Question 0 think about: Do we really need define? What scheme expressions do not have values? Next time: Higher-Order Functions, Intro to Metacircular Evaluators 23 Jan 2001 CS 655: Lecture 2