1. 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

2. 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

3. Favorite Programming Languages
C /3
C /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
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CS 655: Lecture 2

4. 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
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CS 655: Lecture 2

5. 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)
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CS 655: Lecture 2

6. Partner Preference Assigned Randomly 4 Choose Your Own 4
No Clear Preference 2
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7. 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”.
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CS 655: Lecture 2

8. 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!
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CS 655: Lecture 2

9. Why taking this class?
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CS 655: Lecture 2

10. Next: Computability and Universal Programming Languages
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CS 655: Lecture 2

11. 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?
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CS 655: Lecture 2

12. 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
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CS 655: Lecture 2

13. 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

14. 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
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CS 655: Lecture 2

15. 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.
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CS 655: Lecture 2

16. (define contradicts-halts (if (halts? contradict-halts) (loop-forever)
Based on Duane Boning,
(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.
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CS 655: Lecture 2

17. 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
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CS 655: Lecture 2

18. Elements of Language
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CS 655: Lecture 2

19. 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
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CS 655: Lecture 2

20. 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)
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CS 655: Lecture 2

21. 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>
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CS 655: Lecture 2

22. 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
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23. 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?
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CS 655: Lecture 2

24. 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.
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CS 655: Lecture 2

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

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

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

29. 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!)
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CS 655: Lecture 2

30. 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.
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CS 655: Lecture 2

31. 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.)
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CS 655: Lecture 2

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

33. 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)
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CS 655: Lecture 2

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

35. Currying (define add (lambda (x) (lambda (y) (+ x y)))) (add 5) proc7
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CS 655: Lecture 2

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

37. 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!”
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CS 655: Lecture 2

38. 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