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David Evans http://www.cs.virginia.edu/evans

Lecture 2: Formal Systems and Languages. MU!. David Evans http://www.cs.virginia.edu/evans. CS200: Computer Science University of Virginia Computer Science. Menu. Questions from Lecture 1 Notes Course Expectations Formal Systems MIU -system Languages English Scheme.

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David Evans http://www.cs.virginia.edu/evans

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

  2. Menu • Questions from Lecture 1 Notes • Course Expectations • Formal Systems • MIU-system • Languages • English • Scheme CS 200 Spring 2004

  3. Difference in years * 12 = number of months Number of months / 18 = number of doublings according to Moore’s Law 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 > (/ 60 (* 2 2)) 15 > (/ (* (- 2010 2004) 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 2007 15 seconds in 2007 60 seconds today, 4 doublings by 2010 3.75 seconds in 2010 CS 200 Spring 2004

  4. 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. CS 200 Spring 2004

  5. 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! CS 200 Spring 2004

  6. Course Expectations CS 200 Spring 2004

  7. Course Roadmap Computer Science from Euclid and Ada to Quantum Computing and the World Wide Web 1st Class Liberal Arts (Intellectual) PS 1-6 PS 7 Illiberal Arts ($$$$) PS 8 CS 200 Spring 2004

  8. What You Should Expect • The fourth (?) coolest class at UVa • Less cool than PHYE162, PHYE163, PHYE164 • 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 You should expect these of all your classes! CS 200 Spring 2004

  9. 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! CS 200 Spring 2004

  10. 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!) CS 200 Spring 2004

  11. What I Expect of You • 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!) • You are a “Jeffersonian Student” • Believe knowledge is powerful • Interested in lots of things, ahead of your time • Want to use what you learn to do good things • Care more about what you learn than grades and degree requirements CS 200 Spring 2004

  12. 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! CS 200 Spring 2004

  13. 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! CS 200 Spring 2004

  14. 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) CS 200 Spring 2004

  15. 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 CS 200 Spring 2004

  16. Any Logistics Questions?Next: Formal Systems CS 200 Spring 2004

  17. 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 CS 200 Spring 2004

  18. 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 IIIoccurs in one of the strings in your collection you may make a new string with U in place of III. • Rule IV: If UUoccurs inside one of your strings, you can drop it. CS 200 Spring 2004

  19. 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 IIIoccurs in one of the strings in your collection you may make a new string with U in place of III. • Rule IV: If UUoccurs inside one of your strings, you can drop it. CS 200 Spring 2004

  20. Languages CS 200 Spring 2004

  21. 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. CS 200 Spring 2004

  22. 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. CS 200 Spring 2004

  23. Languages and Formal Systems What is the difference between a formal system and a language? With a language, the surface forms have meaning. CS 200 Spring 2004

  24. 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 CS 200 Spring 2004

  25. 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 ::= SubjectVerbObject • 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 CS 200 Spring 2004

  26. 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. CS 200 Spring 2004

  27. Detour: History of Computer Programming How should we describe languages? CS 200 Spring 2004

  28. 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 Apollo Guidance Computer (1969): 1 inch You: 2.3 miles ENIAC (1946): ½ mm CS 200 Spring 2004

  29. 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. http://www.seas.upenn.edu/~museum/qman/node6.html Page is now missing unfortunately. CS 200 Spring 2004

  30. Admiral Grace Hopper (1906-1992) • 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) • “Nobody believed that I had a running compiler and nobody would touch it. They told me computers could only do arithmetic.” CS 200 Spring 2004

  31. USS Hopper Guest on David Letterman “Dare and Do” CS 200 Spring 2004

  32. Code written by humans 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. CS 200 Spring 2004

  33. 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. CS 200 Spring 2004

  34. IBM 704 Fortran manual, 1956 “I think there is a world market for maybe five computers.” Thomas Watson, Chairman of IBM, 1943 CS 200 Spring 2004

  35. 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 CS 200 Spring 2004

  36. Backus Naur Form non-terminal ::= replacement We can replace non-terminal with replacement Some replacements are terminals: a terminal is something that never appears on the left side of a rule. A ::= B means anywhere you have an A, you can replace it with a B. CS 200 Spring 2004

  37. 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. CS 200 Spring 2004

  38. BNF Example 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. CS 200 Spring 2004

  39. Essential Scheme Expression ::= (Expression1Expression*) Expression ::=(ifExpression1 Expression2 Expression3 ) Expression ::= (definenameExpression) Expression ::=Primitive Primitive ::= number Primitive ::= + | - | * | / | < | >| = Primitive ::= … (many other primitives) CS 200 Spring 2004

  40. 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 CS 200 Spring 2004

  41. 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. CS 200 Spring 2004

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