1. David Evans http://www.cs.virginia.edu/~evans
Lecture 2: Formal Systems
and
Languages
MU!
CS200: Computer Science
University of Virginia
Computer Science
David Evans

2. Menu
Pictures – passing around now, write your name and draw an arrow to your face
Unresolved Questions from Lecture 1
Formal Systems
MIU-system
Languages
English
Scheme
18 January 2002
CS 200 Spring 2002

3. Conundrums What is the real name of the College? My theory:
Web site: “College of Arts and Sciences”
Then what does “CLAS” stand for?
Col-Lege of Arts and Sciences?
Why does it have Government, Math and Foreign Languages Departments?
My theory:
The “Liberal” is Silent
18 January 2002
CS 200 Spring 2002

4. If it takes 60 seconds to compute a photomosaic for Problem Set 1 today on a typical PC, estimate how long it will take CS200 students in 2005 to compute the same photomosaic? How long will it take in 2008?
> (/ (* ( ) 12) 18)) 2
> (/ 60 (* 2 2)) 15
> (/ (* ( ) 12) 18) 4
> (/ 60 (* ))
15/4
> (exact->inexact (/ 60 (* )))
3.75
Difference in years * 12 = number of months
Number of months / 18 = number of doublings
according to Moore’s Law
18 January 2002
CS 200 Spring 2002

5. If it takes 60 seconds to compute a photomosaic for Problem Set 1 today on a typical PC, estimate how long it will take CS200 students in 2005 to compute the same photomosaic? How long will it take in 2008?
> (/ (* ( ) 12) 18)) 2
> (/ 60 (* 2 2)) 15
> (/ (* ( ) 12) 18) 4
> (/ 60 (* ))
15/4
> (exact->inexact (/ 60 (* )))
3.75
60 seconds today, 2 doublings by 2005
15 seconds in 2005
60 seconds today, 4 doublings by 2008
3.75 seconds in 2008
18 January 2002
CS 200 Spring 2002

6. They would run out of original things to say.
Are there any non-recursive natural languages? What would happen to a society that spoke one?
Not for humans at least.
They would run out of original things to say.
Chimps and Dolphins are able to learn non-recursive “languages” (some linguists argue they are not really “languages”), but only humans can learn recursive languages.
18 January 2002
CS 200 Spring 2002

7. “Its all been said before.”
Running out of Ideas
“Its all been said before.”
Eventually true for a non-recursive language.
Never true for a recursive language.
There is always something original left to say!
18 January 2002
CS 200 Spring 2002

8. Survey Results
Everyone who is in the course should have received an with the PS1 groups in it. (Sent out at 6:30pm yesterday.)
18 January 2002
CS 200 Spring 2002

9. C(L)AS Class Majors Years Undecided: 5½ Cognitive Science: 4
Media Studies: 2
Econ (1½), Math (1½), East Asian Studies, English, Pre-Commerce
Years
First: 6, Second: 8, Third: 1, Fourth: 2
18 January 2002
CS 200 Spring 2002

10. Wrote a Program No: 6 Yes: 11
Some experience with C++, BASIC, Pascal, Java
It won’t make much difference in this class after the first problem set
18 January 2002
CS 200 Spring 2002

11. Other Questions Found Class: COD (7), People (6), other (4)
Exams: take home (12), in class (3), don’t care (2)
Exam 1 will be take home, no promises on Exam 2
Prefer partners (6), some of each (3), no preference (2), alone (6)
Most accomplishments in CS were done by groups
Most of the assignments you will work with partners, some you will have choices
If you prefer to work alone, you need to convince me you can work well with a team first, and then maybe I will let you.
18 January 2002
CS 200 Spring 2002

12. Summary of your answers to the other questions and my answers to the survey questions are on the course web site.
Formal Systems
18 January 2002
CS 200 Spring 2002

13. Formal Systems Set of symbols Set of rules for manipulating symbols
Starting Points
Primitives
Set of rules for manipulating symbols
Hofstadter: Rules of Production, Rules of Inference
Also: Rules of Combination
18 January 2002
CS 200 Spring 2002

14. The MIU System Symbols: M, I, U Rules of Production:
Rule I: If you have a string ending in I, you can add a U at the end.
Rule II: Suppose you have Mx. Then you may add Mxx to your collection.
Rule III: If III occurs in one of the strings in your collection you may make a new string with U in place of III.
Rule IV: If UU occurs inside one of your strings, you can drop it.
18 January 2002
CS 200 Spring 2002

15. Start with MUI, produce MIU
MIU System Example
Start with MUI, produce MIU
Rules of Production:
Rule I: If you have a string ending in I, you can add a U at the end.
Rule II: Suppose you have Mx. Then you may add Mxx to your collection.
Rule III: If III occurs in one of the strings in your collection you may make a new string with U in place of III.
Rule IV: If UU occurs inside one of your strings, you can drop it.
18 January 2002
CS 200 Spring 2002

16. Languages
18 January 2002
CS 200 Spring 2002

17. What is a language? Webster:
A systematic means of communicating ideas or feelings by the use of conventionalized signs, sounds, gestures, or marks having understood meanings.
18 January 2002
CS 200 Spring 2002

18. Linguist’s Definition
A description of pairs (S, M), where S stands for sound, or any kind of surface forms, and M stands for meaning.
A theory of language must specify the properties of S and M, and how they are related.
18 January 2002
CS 200 Spring 2002

19. Languages and Formal Systems
What is the difference between a formal system and a language?
With a language, the surface forms have meaning.
18 January 2002
CS 200 Spring 2002

20. What are languages made of?
Primitives (almost all languages have these)
The simplest surface forms with meaning
Means of Combination (all languages have these)
Like Rules of Production for Formal Systems
Ways to make new surface forms from ones you already have
Means of Abstraction (all powerful languages have these)
Ways to use simple surface forms to represent complicated ones
18 January 2002
CS 200 Spring 2002

21. Does English have these?
Primitives
Words (?)
e.g., “antifloccipoccinihilipilification” – not a primitive
Morphemes – smallest units of meaning
e.g., anti- (“opposite”)
Means of combination
e.g., Sentence ::= Subject Verb Object
Precise rules, but not the ones you learned in grammar school
18 January 2002
CS 200 Spring 2002

22. Does English have these?
Means of abstraction
Pronouns: she, he, it, they, which, etc.
Confusing since they don’t always mean the same thing, it depends on where they is used.
The “these” in the slide title is an abstraction for the three elements of language introduced 2 slides ago.
The “they” in the confusing sentence is an abstraction for pronouns.
18 January 2002
CS 200 Spring 2002

23. Detour: History of Computer Programming
How should we describe languages?
Detour: History of Computer Programming
18 January 2002
CS 200 Spring 2002

24. ENIAC Electronic Numerical Integrator and Computer
First American computer (but not the World’s first) [1946]
Presper Eckert and John Mauchly
Build to calculate bombing tables for Army
Programmed by flipping switches and connecting cables
18 January 2002
CS 200 Spring 2002

25. Directions for Getting 6
Choose any regular accumulator (ie. Accumulator #9).
Direct the Initiating Pulse to terminal 5i.
The initiating pulse is produced by the initiating unit's Io terminal each time the Eniac is started. This terminal is usually, by default, plugged into Program Line 1-1 (described later). Simply connect a program cable from Program Line 1-1 to terminal 5i on this Accumulator.
Set the Repeat Switch for Program Control 5 to 6.
Set the Operation Switch for Program Control 5 to  .
Set the Clear-Correct switch to C.
Turn on and clear the Eniac.
Normally, when the Eniac is first started, a clearing process is begun. If the Eniac had been previously started, or if there are random neons illuminated in the accumulators, the ``Initial Clear'' button of the Initiating device can be pressed.
Press the ``Initiating Pulse Switch'' that is located on the Initiating device.
Stand back.
18 January 2002
CS 200 Spring 2002

26. Admiral Grace Hopper (1906-1992)
Entered Naval Reserves in 1943
Programmed Mark I (first “large” computer)
Wrote first compiler (1952) – program for programming computers
“Nobody believed that I had a running compiler and nobody would touch it. They told me computers could only do arithmetic.”
18 January 2002
CS 200 Spring 2002

27. USS Hopper “Dare and Do” Guest on David Letterman 18 January 2002
CS 200 Spring 2002

28. Code written by humans Compiler Code machine can run
Compiler translates
from code in a high-level language to machine code
Compiler
Code machine can run
DrScheme uses an interpreter. An interpreter is like a compiler, except it runs quickly and quietly on small bits of code at a time.
18 January 2002
CS 200 Spring 2002

29. John Backus Chemistry major at UVA (entered 1943)
Flunked out after second semester
Joined IBM as programmer in 1950
Developed Fortran, first commercially successful programming language and compiler
I flunked out every year. I never studied. I hated studying. I was just goofing around. It had the delightful consequence that every year I went to summer school in New Hampshire where I spent the summer sailing and having a nice time.
18 January 2002
CS 200 Spring 2002

30. “I think there is a world market for maybe five computers.”
IBM 704 Fortran manual, 1956
“I think there is a world market for maybe five computers.”
Thomas Watson, Chairman of IBM, 1943
18 January 2002
CS 200 Spring 2002

31. Backus Naur Form Fortran language was described using English
Imprecise
Verbose, lots to read
Ad hoc
DO 10 I=1.10
Assigns 1.10 to the variable DO10I
DO 10 I=1,10
Loops for I = 1 to 10
Often blamed for loss of Mariner-I, but probably not true.
Wanted a more precise way of describing a language
18 January 2002
CS 200 Spring 2002

32. Backus Naur Form non-terminal ::= replacement
We can replace non-terminal with replacement
Some replacements are terminals: something that does not appear on the left side of a rule.
A ::= B means anywhere you have an A, you can replace it with a B.
18 January 2002
CS 200 Spring 2002

33. BNF Example NP ::= Noun Noun ::= Dave Noun ::= Scheme Verb ::= rocks
Sentence ::= NP Verb
NP ::= Noun
Noun ::= Dave
Noun ::= Scheme
Verb ::= rocks
Verb ::= sucks
What are the terminals?
Dave, Scheme, rocks, sucks
How many different things can we express with this language?
4, but only 2 are useful.
18 January 2002
CS 200 Spring 2002

34. BNF Example NP ::= Noun NP ::= Noun and NP Noun ::= Dave
Sentence ::= NP Verb
NP ::= Noun
NP ::= Noun and NP
Noun ::= Dave
Noun ::= Scheme
Verb ::= rocks
Verb ::= sucks
How many different things can we express with this language?
Infinitely many!
Recursion is powerful.
18 January 2002
CS 200 Spring 2002

35. Scheme
18 January 2002
CS 200 Spring 2002

36. Scheme Primitives Means of Combination Means of Abstraction
Like all powerful languages, Scheme has:
Primitives
Means of Combination
Means of Abstraction
18 January 2002
CS 200 Spring 2002

37. Scheme Primitives Numerals 0 655 3.52 -58 Functions + - round
Examples
Numerals
Functions + - round
Constants #f #t
(false) (true)
The primitives probably mean what you think they do (but expressing precisely what they mean is hard).
18 January 2002
CS 200 Spring 2002

38. Means of Combination Application Expression ::= (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.”
18 January 2002
CS 200 Spring 2002

39. Means of Combination Special Forms A few others we’ll see later…
(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 we’ll see later…
18 January 2002
CS 200 Spring 2002

40. Essential Scheme Expression ::= (Expression1 Expression*)
Expression ::= (if Expression1
Expression2
Expression3 )
Expression ::= Primitive
Primitive ::= numeral
Primitive ::= +
Primitive ::= … (other primitives)
18 January 2002
CS 200 Spring 2002

41. Means of Abstraction > (define two 2) > (define plus +)
Expression ::= (define name Expression)
> (define two 2)
> (define plus +)
> (plus two two) 4
> (define five 4)
> (= (plus two two) five) #t
Note that defines don’t evaluate to anything.
18 January 2002
CS 200 Spring 2002

42. Charge Start PS1 this weekend A lot to read and understand
Not a lot of code to write
Take advantage of staffed Lab hours Sunday 7-11 in Olsson 001 (knock loudly if it is locked)
The first bug: Admiral Hopper’s Notebook, Sept 1945
Moth found in UNIVAC relay
18 January 2002
CS 200 Spring 2002