Lecture 2:
Formal
Systems
and
Languages
MU!
CS200: Computer Science
University of Virginia
Computer Science
David Evans
http://www.cs.virginia.edu/evans
Menu
• Questions from Lecture 1 Notes
• Course Expectations
• Formal Systems
– MIU-system
• Languages
– English
– Scheme
16 January 2004
CS 200 Spring 2004
2
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 2007 to compute
the same photomosaic? How long will it take in 2010?
> (/ (* (- 2007 2004) 12) 18)
2
Difference in years * 12 = number of months
Number of months / 18 = number of doublings
> (/ 60 (* 2 2))
according to Moore’s Law
15
> (/ (* (- 2010 2004) 12) 18)
60 seconds today, 2 doublings by 2007
4
15 seconds in 2007
> (/ 60 (* 2 2 2 2))
15/4
> (exact->inexact (/ 60 (* 2 2 2 2)))
3.75
60 seconds today, 4 doublings by 2010
3.75 seconds in 2010
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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 nonrecursive “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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Course
Expectations
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Course Roadmap
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CS 200 Spring 2004
Liberal Arts Illiberal Arts
(Intellectual) ($$$$)
Computer Science
1st Class
from Euclid and Ada
to
PS 1-6
Quantum Computing PS 7
and
the World Wide Web PS 8
7
What You Should Expect
• The fourth (?) coolest class at UVa
– Less cool than PHYE162, PHYE163, PHYE164
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CS 200 Spring 2004
You should expect these of
all your classes!
• This course will be consistent with
the original notion of a Liberal Arts
education
• This course will be as consistent as
possible with Mr. Jefferson’s vision
for the University
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Like Drinking from a Firehose
It may hurt a little bit, and a lot of water will
go by you, but you won’t go away thirsty!
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Help Available
• Me: David Evans (Call me “Dave” or “Coach”)
– Office Hours (Weds after class, Thurs 4-5pm)
– Always available by email, if I don’t reply in 24
hours, send again and complain
• Assistant Coaches: staffed lab hours in Small Hall
Sarah Bergkuist, Andrew Connors, Patrick Rooney,
Katie Winstanley
• Web site: http://www.cs.virginia.edu/cs200
– Everything goes on the web, you should visit it often
• Your classmates (read the course pledge
carefully!)
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What I Expect of You
1. Everything on the Course Pledge
– You should actually read it not just sign it
(you will lose points on PS1 if your
submissions reveals that you didn’t read it!)
2. You are a “Jeffersonian Student”
1. Believe knowledge is powerful
2. Interested in lots of things, ahead of your time
3. Want to use what you learn to do good things
4. Care more about what you learn than grades
and degree requirements
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Background Expected
• Language:
– Reasonable reading and writing in English
– Understanding of subject, verb and object
• Math:
– Whole numbers, add, subtract, multiply, divide
– Exponentiation, logarithms (we will review)
• Logic: and, or, not
• Computer Literacy: read email, browse web
If I ever appear to expect anything else, stop me!
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A Course for Everyone!
• CLAS, SEAS, Commerce, Arch, etc.
• 1st, 2nd, 3rd, 4th, 5th Years, Community
Scholars, Faculty
• No background expected…but challenging
even for students with lots of previous CS
courses (if you’ve already taken CS655 or
CS415 talk to me first)
• Computer Science (future-) majors…but
worthwhile even if you don’t take another CS
course Need to get course action signed by Monday!
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Survey Results
• Previous Programming: None at all (8), A little
(7), one or two courses (7), lots (5)
• Years: 1st (4), 2nd (4), 3rd (13), 4th (4)
• Majors: Art, Biology, Biomedical Business,
Engineering, Cognitive Science (7), Computer Science
(5), Electrical Engineering (2), English, Media Studies,
Psychology (2), Systems (3), Undecided (5)
• I will post a details on the web site this weekend
(including my answers to your questions)
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Three Most Important Attributes
To Do Well
• Open Mind
– Much of this course is about learning a new way of
thinking
• Persistence
– Don’t expect to understand everything the first (or
second or third) time you see it
– Don’t give up if you can’t find the answer in the book
or notes (most questions will require you to think!)
• Willingness to spend time in Small Hall
– Benefit from staffed lab hours and working with
classmates
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Any Logistics Questions?
Next: Formal Systems
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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 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.
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Languages
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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
(Charles Yang)
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
Ending a sentence with a preposition is
something up with which we will not put.
Winston Churchill
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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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How should we describe languages?
Detour:
History of Computer Programming
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ENIAC: Electronic Numerical Integrator and Computer
• Early computer (but
not the world’s first)
[1946]
• Built to calculate
bombing tables
Memory size:
twenty 10 decimal digit accumulators = 664 bits
ENIAC (1946): ½ mm
Apollo Guidance Computer (1969): 1 inch
You: 2.3 miles
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Directions for Getting 6
1. 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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CS 200 Spring 2004
Page is now missing unfortunately.
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Admiral Grace Hopper
(1906-1992)
“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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• Mathematics PhD Yale, 1934
• Entered Navy, 1943
• First to program Mark I (first
“large” computer, 51 feet long)
• Wrote first compiler (1952) –
program for programming
computers
• Co-designer of COBOL (most
widely used programming
language until a few years ago)
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USS Hopper
“Dare and Do”
Guest on David Letterman
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Code written by
humans
Compiler translates
from code in a highlevel 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.
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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
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CS 200 Spring 2004
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=1.10
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
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Backus Naur Form
non-terminal ::= replacement
We can replace non-terminal with
replacement
A ::= B means anywhere you
have an A, you can replace it
with a B.
Some replacements are terminals: a terminal
is something that never appears on the left
side of a rule.
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BNF Example
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 true.
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BNF Example
Sentence ::= NP Verb
NP ::= Noun
NP ::= Noun and NP
Noun ::= Dave
Noun ::= Scheme
Verb ::= rocks
Verb ::= sucks
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CS 200 Spring 2004
How many
different things
can we express
with this
language?
Infinitely many!
Recursion is powerful.
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Essential Scheme
Expression ::= (Expression1 Expression*)
Expression ::= (if Expression1
Expression2
Expression3 )
Expression ::= (define name Expression)
Expression ::= Primitive
Primitive ::= number
Primitive ::= + | - | * | / | < | >| =
Primitive ::= …
(many other primitives)
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Problem Set 1
• Due Wednesday (21 Jan)
• You are assigned a partner on today’s
notes
– Unless I didn’t get a registration survey from
you (come up after class)
• First staffed lab hours will be after class
today
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Charge
• Problem Set 1: Due Wednesday
– Staffed lab hours right now!
– Take advantage of them
• No class Monday: Martin Luther King Day
Use the time to learn about history of
desegregation at UVa and Dr. King’s visit to
UVa in 1963.
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CS 200 Spring 2004
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Formal Systems and Languages