1. David Evans http://www.cs.virginia.edu/evans CS200: Computer Science University of Virginia Computer Science Lecture 3: Rules of Evaluation

2. 22 January 2003CS 200 Spring 20032 Menu Language Elements Why don’t we just program computers using English? Evaluation Procedures Scheduled Office Hours (Olsson 236A): Wednesdays 3:30-4:30 (after class) Thursdays 4:00-5:00

3. 22 January 2003CS 200 Spring 20033 Language Elements When learning a foreign language, which elements are hardest to learn? Primitives –There are a lot of them, and learning the real meaning is hard Means of Combination –Complex, but, all natural languages have similar ones (Chomsky) SOV (45% of all languages) (Korean): Sentence ::= Subject Object Verb SVO (42%): English: Sentence ::= Subject Verb Object VSO (9%): Welsh: Sentence ::= Verb Subject Object “Lladdodd y ddraig y dyn.” (Killed the dragon the man.) OSV (<1%): Tobati (New Guinea) Schemish: Expression ::= (Verb Object) Means of Abstraction –Few of these, but tricky to learn differences across languages

4. 22 January 2003CS 200 Spring 20034 Pages in Revised 5 Report on the Algorithmic Language Scheme Primitives Means of Combination Means of Abstraction 48 pages total (includes formal specification and examples)

5. 22 January 2003CS 200 Spring 20035 Pages in Revised 5 Report on the Algorithmic Language Scheme Primitives Standard Procedures Primitive expressions Identifiers, numerals 18 2 1 Means of Combination Expressions Program structure 2222 Means of Abstraction Definitions½ 48 pages total (includes formal specification and examples)

6. 22 January 2003CS 200 Spring 20036 Pages in Revised5 Report on the Algorithmic Language Scheme Pages in C++ Language Specification (1998) Primitives Standard Procedures Primitive expressions Identifiers, numerals 18 2 1 Means of Combination Expressions Program structure 2222 Means of Abstraction Definitions½ 48 pages total (includes formal specification and examples)

7. 22 January 2003CS 200 Spring 20037 Pages in Revised 5 Report on the Algorithmic Language Scheme Pages in C++ Language Specification (1998) Primitives Standard Procedures Primitive expressions Identifiers, numerals 18 2 1 Standard Procedures Primitive expressions Identifiers, numerals 356 30 10 Means of Combination Expressions Program structure 2222 Expressions, Statements Program Structure 197 35 Means of Abstraction Definitions½Declarations, Classes173 48 pages total (includes formal specification and examples) 776 pages total (includes no formal specification or examples) Core language issues list has 389 items!

8. 22 January 2003CS 200 Spring 20038 Pages in Revised 5 Report on the Algorithmic Language SchemeEnglish Primitives Standard Procedures Primitive expressions Identifiers, numerals 18 2 1 Morphemes Words in Oxford English Dictionary ? 500,000 Means of Combination Expressions Program structure 2222 Grammar Rules English Grammar for Dummies Book 100s (?) 384 pages Means of Abstraction Definitions½Pronouns~20 48 pages total (includes formal specification and examples)

9. 22 January 2003CS 200 Spring 20039 Why don’t we just program computers using English?

10. 22 January 2003CS 200 Spring 200310 Why don’t we just program computers using English? Too hard and complex Non-native English speakers don’t need convincing. The rest of you have spent your whole life learning English (and first 5 years of your life doing little else) and still don’t know useful words like floccipoccinihilipilification! There are thoughts that even native speakers find it hard to express. By the end of today you will know enough Scheme (nearly the entire language) to express and understand every computation. By the end of the class, you will know enough to completely describe Scheme in terms of itself (try doing that in English!)

11. 22 January 2003CS 200 Spring 200311 Why don’t we just program computers using English? Not concise enough English: To find the maximum of two numbers, compare them. If the first number is greater than the second number, return the first number. Otherwise, return the second number. Scheme: (define (max a b) (if (> a b) a b))

12. 22 January 2003CS 200 Spring 200312 Why don’t we just program computers using English? Limited means of abstraction There are only a few pronouns: he, she, it, they, these, … (English doesn’t even have a gender-neutral pronoun for a person!) Only Webster and Oxford can make up new ones. define allows any programmer to make up as many pronouns as that programmer wants, and use them to represent exactly what the programmer wants.

13. 22 January 2003CS 200 Spring 200313 Why don’t we just program computers using English? Mapping between surface forms and meanings are ambiguous and imprecise The 500 words used most in the English language each have an average of 23 different meanings in the Oxford English Dictionary. http://www.vuse.vanderbilt.edu/~jgray/funny.html The exact meaning(s) of every Scheme expression is determined by simple, unambiguous rules we will learn today (and refine later in the course). I said he thought secret users only may write secret data. (From Only His Only Grammarian Can Only Say Only What Only He Only Means, Peter Neumann)

14. Evaluation

15. 22 January 2003CS 200 Spring 200315 Expressions and Values (Almost) every expression has a value –Have you seen any expressions that don’t have values? When an expression with a value is evaluated, its value is produced

16. 22 January 2003CS 200 Spring 200316 Evaluation Rule 1: Primitives If the expression is a primitive, it is self-evaluating. > 2 2 > #t #t > + #

17. 22 January 2003CS 200 Spring 200317 Evaluation Rule 2: Names If the expression is a name, it evaluates to the value associated with that name. > (define two 2) > two 2

18. 22 January 2003CS 200 Spring 200318 Evaluation Rule 3: Application 3.If the expression is an application: a)Evaluate all the subexpressions of the combination (in any order) b)Apply the value of the first subexpression to the values of all the other subexpressions. (expression 0 expression 1 expression 2 … )

19. 22 January 2003CS 200 Spring 200319 Rules for Application 1.If the procedure to apply is a primitive, just do it. 2.If the procedure is a compound procedure, evaluate the body of the procedure with each formal parameter replaced by the corresponding actual argument expression value.

20. 22 January 2003CS 200 Spring 200320 Making Procedures lambda means “make a procedure” Expression ::= (lambda (Parameters) Expression) Parameters ::= Parameters ::= Name Parameters

21. 22 January 2003CS 200 Spring 200321 Lambda Example: Tautology Function (lambda () #t) > ((lambda () #t) 200) # : expects no arguments, given 1: 200 > ((lambda () #t)) #t > ((lambda (x) x) 200) 200 make a procedure with no parameters with body #t

22. 22 January 2003CS 200 Spring 200322 You’ve Already Used Lambda! (define (closer-color? sample color1 color2) Expr) is a shortcut for: (define closer-color? (lambda (sample color1 color2) Expr))

23. 22 January 2003CS 200 Spring 200323 Eval Apply Eval and Apply are defined in terms of each other. Without Eval, there would be no Apply, Without Apply there would be no Eval!

24. 22 January 2003CS 200 Spring 200324 All of Scheme Once you understand Eval and Apply, you can understand all Scheme programs! Except: –We have special Eval rules for special forms (like if ) Evaluation Rule 4: If it is a special form, do something special.

25. 22 January 2003CS 200 Spring 200325 Evaluating Special Forms Eval 4-if. If the expression is (if Expression 0 Expression 1 Expression 2 ) evaluate Expression 0. If it evaluates to #f, the value of the if expression is the value of Expression 2. Otherwise, the value of the if expression is the value of Expression 1. Eval 4-lambda. Lambda expressions self- evaluate. (Do not do anything until it is applied.)

26. 22 January 2003CS 200 Spring 200326 More Special Forms Eval 4-define. If the expression is (define Name Expression) associate the Expression with Name. Eval 4-begin. If the expression is (begin Expression 0 Expression 1 … Expression k ) evaluate all the sub-expressions. The value of the begin expression is the value of Expression k.

27. 22 January 2003CS 200 Spring 200327 Scheme Expression ::= Primitive Eval 1: If the expression is a primitive, it is self-evaluating. Expression ::= Name Eval 2: If the expression is a name, it evaluates to the value associated with that name. Expression ::= (Expression ExpressionList) Eval 3: If the expression is an application: (a) Evaluate all the subexpressions (in any order) (b) Apply the value of the first subexpression to the values of all the other subexpressions. ExpressionList ::= ExpressionList ::= Expression ExpressionList

28. 22 January 2003CS 200 Spring 200328 Special Forms Expression ::= (lambda (Parameters) Expression) Eval 4-lambda. Lambda expressions self-evaluate. Parameters ::= Parameters ::= Name Parameters Expression ::= (define Name Expression) Eval 4-define. If the expression is (define Name Expression) associate the Expression with Name. Expression ::= (if Expression 0 Expression 1 Expression 2 ) Eval 4-if. Evaluate Expression 0. If it evaluates to #f, the value of the if expression is the value of Expression 2. Otherwise, the value of the if expression is the value of Expression 1. Expression ::= (begin ExpressionList Expression) Eval 4-begin. Evaluate all the sub-expressions. The value of the begin expression is the value of Expression.

29. 22 January 2003CS 200 Spring 200329 Now, you really know all of Scheme! (Except for 3 more special forms you will learn for PS5.)

30. 22 January 2003CS 200 Spring 200330 Example Evaluation (define square (lambda (x) (* x x))) (square 4) 16

31. 22 January 2003CS 200 Spring 200331 A Squarish Example (define square (lambda (x) (* x x))) (square 4) Its an application, use evaluation Rule 3: a)Evaluate all the subexpressions of the combination (in any order) b)Apply the value of the first subexpression to the values of all the other subexpressions.

32. 22 January 2003CS 200 Spring 200332 (define square (lambda (x) (* x x))) (square 4) Its an application, use evaluation Rule 3: a)Evaluate all the subexpressions of the combination (in any order) b)Apply the value of the first subexpression to the values of all the other subexpressions. Evaluate: square It’s a name, use evaluation Rule 2: If the expression is a name, evaluate the expression associated with that name. (lambda (x) (* x x))

33. 22 January 2003CS 200 Spring 200333 (define square (lambda (x) (* x x))) (square 4) Its an application, use evaluation Rule 3: a)Evaluate all the subexpressions of the combination (in any order) b)Apply the value of the first subexpression to the values of all the other subexpressions. Evaluate: square (lambda (x) (* x x)) Evaluate: 4 Rule 1: If the expression is a primitive, it is self- evaluating 4

34. 22 January 2003CS 200 Spring 200334 (define square (lambda (x) (* x x))) (square 4) Its an application, use evaluation Rule 3: a)Evaluate all the subexpressions of the combination (in any order) b)Apply the value of the first subexpression to the values of all the other subexpressions. Apply: square (lambda (x) (* x x)) to 4 Application Rule 2. If the procedure is a compound procedure, evaluate the body of the procedure with each formal parameter replaced by the corresponding actual argument expression value.

35. 22 January 2003CS 200 Spring 200335 Apply: square (lambda (x) (* x x) ) to 4 Application Rule 2. If the procedure is a compound procedure, evaluate the body of the procedure with each formal parameter replaced by the corresponding actual argument expression value. Body of the procedure

36. 22 January 2003CS 200 Spring 200336 Apply: square (lambda (x) (* x x) ) to 4 Application Rule 2. If the procedure is a compound procedure, evaluate the body of the procedure with each formal parameter replaced by the corresponding actual argument expression value. Body of the procedure (* 4 4)

37. 22 January 2003CS 200 Spring 200337 Evaluate: (* 4 4) Its an application, use evaluation Rule 3: a)Evaluate all the subexpressions of the combination (in any order) b)Apply the value of the first subexpression to the values of all the other subexpressions. Evaluate: * Rule 1: If the expression is a primitive, it is self- evaluating Evaluate: 4 Rule 1: If the expression is a primitive, … 4 Evaluate: 4 Rule 1: If the expression is a primitive, … 4

38. 22 January 2003CS 200 Spring 200338 Evaluate: (* 4 4) Its an application, use evaluation Rule 3: a)Evaluate all the subexpressions of the combination (in any order) b)Apply the value of the first subexpression to the values of all the other subexpressions. Apply: to 4 4 Application Rule 1: If the procedure to apply is a primitive, just do it. 16

39. 22 January 2003CS 200 Spring 200339 (square 4) Eval Rule 3a: Application square 4 Eval Rule 2: Names (lambda (x) (* x x)) Eval Rule 1: Primitive 4 Eval Rule 3b: Application Apply Rule 2: Compound Application (* 4 4 ) Eval Rule 3a: Application * 4 4 Eval Rule 1: Primitive 4 4 # Eval Rule 3b: Application Apply Rule 1: Primitive Application 16

40. 22 January 2003CS 200 Spring 200340 Charge PS2 Due Monday 3 Feb –Less code to read than PS1, but now you should understand all of it! –Lots more code to write than PS1 Reading for Friday: SICP, 1.2 Reading for Monday: GEB, Ch 5