David Evans cs.virginia/~evans

David Evanshttp://www.cs.virginia.edu/~evans

CS200: Computer ScienceUniversity of VirginiaComputer Science

Lecture 2: Formal SystemsandLanguages

MU!

18 January 2002 CS 200 Spring 2002 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

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Conundrums

• What is the real name of the College?– 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

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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? > (/ (* (- 2005 2002) 12) 18))2> (/ 60 (* 2 2))15> (/ (* (- 2008 2002) 12) 18)4> (/ 60 (* 2 2 2 2))15/4> (exact->inexact (/ 60 (* 2 2 2 2)))3.75

Difference in years * 12 = number of monthsNumber of months / 18 = number of doublings according to Moore’s Law

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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? > (/ (* (- 2005 2002) 12) 18))2> (/ 60 (* 2 2))15> (/ (* (- 2008 2002) 12) 18)4> (/ 60 (* 2 2 2 2))15/4> (exact->inexact (/ 60 (* 2 2 2 2)))3.75

60 seconds today, 2 doublings by 200515 seconds in 2005

60 seconds today, 4 doublings by 20083.75 seconds in 2008

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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.

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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!

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Survey Results

Everyone who is in the course should have received an email 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

– 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

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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

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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.

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Formal Systems

Summary of your answers to the other questions and my answers to the survey questions are on the course web site.

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Formal Systems

• Set of symbols– Starting Points– Primitives

• Set of rules for manipulating symbols– Hofstadter: Rules of Production, Rules of

Inference– Also: Rules of Combination

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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.

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MIU System ExampleStart 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.

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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.

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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.

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Languages and Formal Systems

What is the difference between a formal system and a language?

With a language, the surface forms have meaning.

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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

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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

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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.

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Detour:

History of Computer Programming

How should we describe languages?

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ENIACElectronic 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

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Directions for Getting 61. Choose any regular accumulator (ie. Accumulator #9). 2. Direct the Initiating Pulse to terminal 5i. 3. 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.

4. Set the Repeat Switch for Program Control 5 to 6. 5. Set the Operation Switch for Program Control 5 to  . 6. Set the Clear-Correct switch to C. 7. Turn on and clear the Eniac. 8. 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.

9. Press the ``Initiating Pulse Switch'' that is located on the Initiating device. 10.Stand back.

http://www.seas.upenn.edu/~museum/qman/node6.html

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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.”

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USS Hopper

Guest on David Letterman

“Dare and Do”

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Code written by humans

Compiler

Code machine can run

Compiler translatesfrom code in a high-level language to machine code

DrScheme uses an interpreter. An interpreter is like a compiler, except it runs quickly and quietly on small bits of code at a time.

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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.

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IBM 704 Fortran manual, 1956

“I think there is a world market for maybe five computers.”Thomas Watson, Chairman of IBM, 1943

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Backus Naur Form• Fortran language was described using English

– Imprecise– Verbose, lots to read– Ad hoc

DO 10 I=1.10Assigns 1.10 to the variable DO10I

DO 10 I=1,10Loops 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

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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.

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BNF Example

Sentence ::= NP VerbNP ::= NounNoun ::= Dave

Noun ::= SchemeVerb ::= rocks

Verb ::= sucks

How many different things can we express with this language?

What are the terminals?

Dave, Scheme, rocks, sucks

4, but only 2 are useful.

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BNF Example

Sentence ::= NP VerbNP ::= NounNP ::= Noun and NPNoun ::= Dave

Noun ::= SchemeVerb ::= rocks

Verb ::= sucks

How many different things can we express with this language?

Infinitely many!Recursion is powerful.

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Scheme

18 January 2002 CS 200 Spring 2002 36

Scheme

Like all powerful languages, Scheme has:– Primitives

– Means of Combination

– Means of Abstraction

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Scheme Primitives Examples

• Numerals 0 655 3.52 -58

• Functions + - round

• Constants #f #t (false) (true)

The primitives probably mean what you think they do (but expressing precisely what they mean is hard).

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Means of Combination• Application

Expression ::= (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.”

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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 we’ll see later…

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Essential Scheme

Expression ::= (Expression1 Expression*)

Expression ::= (if Expression1

Expression2

Expression3 )Expression ::= PrimitivePrimitive ::= numeral Primitive ::= +Primitive ::= … (other primitives)

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Means of AbstractionExpression ::= (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 42The first bug: Admiral Hopper’s Notebook, Sept 1945Moth found in UNIVAC relay

ChargeStart 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)