Lecture 2: Formal Systems and Languages MU! CS200: Computer Science University of Virginia Computer Science David Evans http://www.cs.virginia.edu/~evans 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 2 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 18 January 2002 CS 200 Spring 2002 3 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 Difference in years * 12 = number of months Number of months / 18 = number of doublings > (/ 60 (* 2 2)) according to Moore’s Law 15 > (/ (* (- 2008 2002) 12) 18) 4 > (/ 60 (* 2 2 2 2)) 15/4 > (exact->inexact (/ 60 (* 2 2 2 2))) 3.75 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? > (/ (* (- 2005 2002) 12) 18)) 2 60 seconds today, 2 doublings by 2005 > (/ 60 (* 2 2)) 15 seconds in 2005 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, 4 doublings by 2008 3.75 seconds in 2008 18 January 2002 CS 200 Spring 2002 5 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. 18 January 2002 CS 200 Spring 2002 6 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 7 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 8 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 18 January 2002 CS 200 Spring 2002 9 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 10 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 11 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 12 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 18 January 2002 CS 200 Spring 2002 13 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 14 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 15 Languages 18 January 2002 CS 200 Spring 2002 16 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 17 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 18 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 19 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 20 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 21 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 22 How should we describe languages? Detour: History of Computer Programming 18 January 2002 CS 200 Spring 2002 23 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 24 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 18 January 2002 CS 200 Spring 2002 25 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 26 USS Hopper “Dare and Do” Guest on David Letterman 18 January 2002 CS 200 Spring 2002 27 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. 18 January 2002 CS 200 Spring 2002 28 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 18 January 2002 CS 200 Spring 2002 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. 29 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 30 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 31 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: something that does not appear on the left side of a rule. 18 January 2002 CS 200 Spring 2002 32 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. 18 January 2002 CS 200 Spring 2002 33 BNF Example Sentence ::= NP Verb NP ::= Noun NP ::= Noun and NP Noun ::= Dave Noun ::= Scheme Verb ::= rocks Verb ::= sucks 18 January 2002 CS 200 Spring 2002 How many different things can we express with this language? Infinitely many! Recursion is powerful. 34 Scheme 18 January 2002 CS 200 Spring 2002 35 Scheme Like all powerful languages, Scheme has: – Primitives – Means of Combination – Means of Abstraction 18 January 2002 CS 200 Spring 2002 36 Scheme Primitives • Numerals • Functions • Constants 0 + #f Examples 655 3.52 -58 round #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 37 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.” 18 January 2002 CS 200 Spring 2002 38 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… 18 January 2002 CS 200 Spring 2002 39 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 40 Means of Abstraction Expression ::= (define name Expression) > (define two 2) Note that defines don’t evaluate to anything. > (define plus +) > (plus two two) 4 > (define five 4) > (= (plus two two) five) #t 18 January 2002 CS 200 Spring 2002 41 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) 18 January 2002 The first bug: Admiral Hopper’s Notebook, Sept 1945 200 Spring 2002 Moth found inCSUNIVAC relay 42