Lecture 3: Rules of Evaluation
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This document discusses rules of evaluation in Scheme. It begins with a menu that outlines describing languages, questions from notes, and Scheme grammar and rules of evaluation. The document then provides more details on Backus-Naur form for precisely describing programming languages and how it works with nonterminals and terminals. It concludes by noting that Scheme uses an interpreter to run code.
Lecture 3: Rules of Evaluation
- 1. Class 3: Rules of Evaluation David Evans cs1120 Fall 2011
- 2. Menu Describing Languages Questions from Notes Computing photomosaics, non-recursive languages, hardest language elements to learn Scheme: Grammar and Rules of Evaluation 2
- 3. Code written by humans Compiler translates from code in a high- Compiler/Interpreter level language to machine code. Code machine can run Scheme uses an interpreter. An interpreter is like a compiler, except it runs quickly and quietly on small bits of code at a time.
- 4. 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 John Backus, 1924 – 2007
- 5. IBM 704 Fortran manual, 1956
- 6. Describing Languages 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 incorrectly blamed for loss of Mariner-I) Backus wanted a precise way of describing a language
- 7. Backus Naur Form symbol ::= replacement We can replace symbol with replacement A ::= B means anywhere you have an A, you can replace it with a B. nonterminal – symbol that appears on left side of rule terminals – symbol that never appears on the left side of a rule Note: this is named for John Backus for being the first person to advocate using it for describing programming languages, but linguists were using similar techniques much earlier. 7
- 8. Recap: Zero, One, Infinity word ::= anti-word This rule can make 0 words. word ::= hippopotomonstrosesquipedaliophobia This rule can make 1 word. word ::= anti-word word ::= hippopotomonstrosesquipedaliophobia These two rules can make infinitely many words, enough to express all ideas in the universe! 8
- 9. Simple BNF Grammar s ::= 0s s ::= 0 9
- 10. Rapid Exponential Growth Question from Class 1: What other things have changed as much as (or more that!) computing power in your lifetime? Communication (global IP traffic, PB/month) (Alex) Energy Consumption (world energy use, TW) (Filip) Human (number of cells) (Ouamdwipwaw) Knowledge (Tyson’s measure) (Deirdre Regan) National Debt (Michael) TV (number of pixels) (gtc5sn) Wealth (world GDP) (Chris Smith) 10
- 12. 1991 value 2011 value Growth Doubling time Energy Consumption (world 102,300 142,300 (2008) 1.39 38 years energy use, TW) (Filip) Communication (global IP traffic, PB/month) (Alex) Wealth (world GDP) (Chris $21T $60T (2008) 2.67 12 years Smith)Energy Consumption (world energy use, TW) (Filip) Human (number of cells) (Ouamdwipwaw) Knowledge (Tyson’s measure) 15 years (Deirdre Regan) (Tyson’s measure) (Deirdre Regan) Knowledge National Debt Debt (Michael) National (Michael) $3.2T (56% $14.7T (93% of 4.6 9 years of GDP) GDP) TV (number of pixels) (gtc5sn) TV (number of pixels) (gtc5sn) 486x243, 3 1920×1080, 500 2926 1.73 years Wealth (world GDP) (Chris Smith) channels = channels = 354292 1036800000 Computing Power/Dollar 18 months (Moore’s Law) Communication (global IP 0.001 20,197 20M 9.9 months traffic, PB/month) (Alex) Human (number of cells) 1 50 Trillion 50 5.3 months (Ouamdwipwaw) Trillion 12
- 13. Genome Sequencing 1990: Human Genome Project starts, estimate $3B to sequence one genome ($0.50/base) 2000: Human Genome Project declared complete, cost ~$300M Whitehead Institute, MIT 13
- 14. $100,000,000 Cost to sequence human genome Moore’s Law prediction (halve every 18 months) $10,000,000 $1,000,000 $100,000 $10,000 Jun 2010 Jun 2005 Sep 2001 Feb 2002 Sep 2006 Feb 2007 May 2003 Apr 2006 Aug 2004 May 2008 Aug 2009 Mar 2004 Jan 2005 Nov 2005 Mar 2009 Jan 2010 Dec 2002 Dec 2007 Jul 2002 Jul 2007 Oct 2003 Oct 2008 14 Data from National Human Genome Research Institute: http://www.genome.gov/sequencingcosts
- 15. $100,000,000 Cost to sequence human genome Moore’s Law prediction (halve every 18 months) $10,000,000 $1,000,000 $100,000 $10,000 Ion torrent Personal Genome Machine Sep 2001 Feb 2002 Sep 2006 Feb 2007 May 2003 Aug 2004 Nov 2005 Apr 2006 May 2008 Aug 2009 Mar 2004 Jan 2005 Mar 2009 Dec 2002 Jun 2005 Jan 2010 Jun 2010 Dec 2007 Jul 2002 Oct 2003 Jul 2007 Oct 2008 15 Data from National Human Genome Research Institute: http://www.genome.gov/sequencingcosts
- 16. Doubling time: 38000 in 2 years = 48 days Human Genome Sequencing Using Unchained Base Reads on Self-Assembling DNA Nanoarrays. Radoje Drmanac, Andrew B. Sparks, Matthew J. Callow, Aaron L. Halpern, Norman L. Burns, Bahram G. Kermani, Paolo Carnevali, Igor Nazarenko, Geoffrey B. Nilsen, George Yeung, Fredrik Dahl, Andres Fernandez, Bryan Staker, Krishna P. Pant, Jonathan Baccash, Adam P. Borcherding, Anushka Brownley, Ryan Cedeno, Linsu Chen, Dan Chernikoff, Alex Cheung, Razvan Chirita, Benjamin Curson, Jessica C. Ebert, Coleen R. Hacker, Robert Hartlage, Brian Hauser, Steve Huang,Church (Personal Genome Project)Calvin Kong, Tom Landers, Catherine Le, George Yuan Jiang, Vitali Karpinchyk, Mark Koenig, Jia Liu, Celeste E. McBride, Matt Morenzoni, Robert E. Morey, Karl Mutch, Helena Perazich, Kimberly Perry, Brock A. Peters, Joe Peterson, Charit L. Pethiyagoda, Kaliprasad Pothuraju, Claudia Richter, Abraham M. Rosenbaum, Shaunak Roy, Jay Shafto, Uladzislau Sharanhovich, Karen W. Shannon, Conrad G. Sheppy, Michel Sun, Joseph V. Thakuria, Anne Tran, Dylan Vu, Alexander Wait Zaranek, Xiaodi Wu, Snezana Drmanac, Arnold R. Oliphant, William C. Banyai, Bruce Martin, Dennis G. Ballinger, George M. Church, Clifford A. Reid. Science, January 2010.
- 18. Scheme Grammar Program ::= ε | ProgramElement Program ProgramElement ::= Expression | Definition Definition ::= (define Name Expression) Expression ::= PrimitiveExpression | NameExpression | ApplicationExpression | ProcedureExpression | IfExpression PrimitiveExpression ::= Number | true | false | PrimitiveProcedure NameExpression ::= Name ApplicationExpression ::= (Expression MoreExpressions) MoreExpressions ::= ε | Expression MoreExpressions ProcedureExpression ::= (lambda (Parameters) Expression) Parameters ::= ε | Name Parameters IfExpression ::= (if ExpressionPred ExpressionConsequent ExpressionAlt) 18
- 19. Assigning Meanings Program ::= ε | ProgramElement Program ProgramElement ::= Expression | Definition Definition ::= (define Name Expression) Expression ::= PrimitiveExpression | NameExpression | ApplicationExpression | ProcedureExpression | IfExpression PrimitiveExpression ::= Number | true | false| PrimitiveProcedure NameExpression ::= Name ApplicationExpression ::= (Expression MoreExpressions) MoreExpressions ::= ε | Expression MoreExpressions ProcedureExpression ::= (lambda (Parameters) Expression) Parameters ::= ε | Name Parameters IfExpression ::= (if ExpressionPred ExpressionConsequent ExpressionAlt) This grammar generates (nearly) all surface forms in the Scheme language. What do we need to do to know the meaning of every Scheme program? 19
- 20. Expressions and Values Expression ::= PrimitiveExpression | NameExpression | ApplicationExpression | ProcedureExpression | IfExpression When an expression with a value is evaluated, a value is produced Our goal is to define a meaning function, Eval, that defines the value of every Scheme expression: Eval(Expression) Value Today we do this informally with rules in English. (In PS7 we will do it with a program.) 20
- 21. Primitive Expressions PrimitiveExpression ::= Number | true | false | PrimitiveProcedure 21
- 22. Evaluation Rule 1: Primitives If the expression is a primitive, it evaluates to its pre-defined value. >2 Primitives are the 2 smallest units of > true meaning: they can’t #t be broken down >+ further, you need to #<primitive:+> know what they mean. 22
- 23. Name Expressions Expression ::= NameExpression NameExpression ::= Name 23
- 24. Evaluation Rule 2: Names A name evaluates to the value associated with that name. > (define two 2) > two 2 Caveat: this simple rule only works if the value associated with a name never changes (until PS5). 24
- 25. Application Expressions Expression ::= Application Expression ApplicationExpression ::= (Expression MoreExpressions) MoreExpressions ::= ε MoreExpressions ::= Expression MoreExpressions 25
- 26. Evaluation Rule 3: Application 3. To evaluation an application expression: a) Evaluate all the subexpressions (in any order) b) Apply the value of the first subexpression to the values of all the other subexpressions. (Expression0 Expression1 Expression2 … )
- 27. Rules for Application 1. Primitives. If the procedure to apply is a primitive procedure, just do it. 2. Constructed Procedures. If the procedure is a constructed procedure, evaluate the body of the procedure with each parameter name bound to the corresponding input expression value. 27
- 28. Eval and Apply are defined recursively. Eval Without Eval, there would be no Apply Apply, without Apply there would be no Eval! 28
- 29. Language Elements When learning a foreign language, which elements are hardest to learn? 29
- 30. Charge We will cover the rest of the rules Wednesday, then you will know enough to describe every possible computation! Reading: should be finished with Chapter 3 now, Chapter 4, Gleick Ch 1-3 by Friday PS1 is Due Monday: Find your assigned partner Get started earlier and take advantage of scheduled help hours 30