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David Evans cs.virginia/~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. Pictures – passing around now, write your name and draw an arrow to your face Unresolved Questions from Lecture 1

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David Evans cs.virginia/~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 • 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 CS 200 Spring 2002

  3. 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 CS 200 Spring 2002

  4. 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 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 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? > (/ (* (- 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 2005 15 seconds in 2005 60 seconds today, 4 doublings by 2008 3.75 seconds in 2008 CS 200 Spring 2002

  6. 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 2002

  7. 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 2002

  8. 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.) 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 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 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. CS 200 Spring 2002

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

  13. 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 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 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 2002

  15. 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 2002

  16. Languages 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. 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. 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. 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 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 ::= SubjectVerbObject • Precise rules, but not the ones you learned in grammar school 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. CS 200 Spring 2002

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

  24. 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 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. http://www.seas.upenn.edu/~museum/qman/node6.html 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.” CS 200 Spring 2002

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

  28. 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 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. CS 200 Spring 2002

  30. 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 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 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. CS 200 Spring 2002

  33. 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 useful. CS 200 Spring 2002

  34. 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 2002

  35. Scheme CS 200 Spring 2002

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

  37. 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). CS 200 Spring 2002

  38. 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.” CS 200 Spring 2002

  39. Means of Combination • Special Forms (ifExpression1 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… CS 200 Spring 2002

  40. Essential Scheme Expression ::= (Expression1Expression*) Expression ::= (ifExpression1 Expression2 Expression3 ) Expression ::=Primitive Primitive ::= numeral Primitive ::= + Primitive ::= … (other primitives) CS 200 Spring 2002

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

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