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

2. Menu Unresolved Questions from Lecture 2 Evaluation Procedures
Origami Programming
23 January 2002
CS 200 Spring 2002

3. Language Elements
When learning a foreign language, which of primitives, means of combination or means of abstraction is hardest to learn?
Primitives
There are a lot of them
Learning the real meaning is hard
Means of Combination
They are complex
But, all languages have similar ones!
Chomsky Universal Grammar
Means of Abstraction
Few of these, but tricky to learn differences across languages
23 January 2002
CS 200 Spring 2002

4. Primitives Means of Combination Means of Abstraction
Pages in Revised5 Report on the Algorithmic Language Scheme
Primitives
Means of Combination
Means of Abstraction
48 pages total (includes formal specification and examples)
23 January 2002
CS 200 Spring 2002

5. Primitives Means of Combination Means of Abstraction
Pages in Revised5 Report on the Algorithmic Language Scheme
Primitives
Standard Procedures
Primitive expressions
Identifiers, numerals 18 2 1
Means of Combination
Expressions
Program structure
Means of Abstraction
Definitions
48 pages total (includes formal specification and examples)
23 January 2002
CS 200 Spring 2002

6. Primitives Means of Combination Means of Abstraction
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
Means of Abstraction
Definitions
48 pages total (includes formal specification and examples)
23 January 2002
CS 200 Spring 2002

7. Primitives Means of Combination Means of Abstraction
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
356 30 10
Means of Combination
Expressions
Program structure
Expressions, Statements
Program Structure
197 35
Means of Abstraction
Definitions
Declarations, Classes
173
48 pages total (includes formal specification and examples)
776 pages total (includes no formal specification or examples)
Core language issues list has 313 items!
23 January 2002
CS 200 Spring 2002

8. Evaluation

9. 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
23 January 2002
CS 200 Spring 2002

10. DrScheme
When you press “Execute”, DrScheme will evaluate all the expressions in the Definitions window
When you type return in the Interactions Window, DrScheme evaluates the expression at the last prompt, and prints its value in blue.
23 January 2002
CS 200 Spring 2002

11. Evaluation Rule 1: Primitives
If the expression is a primitive, it is self-evaluating.
> 2 2
> #t #t
> +
#<primitive:+>
23 January 2002
CS 200 Spring 2002

12. Evaluation Rule 2: Names
If the expression is a name, it evaluates to the value associated with that name.
> (define two 2)
> two 2
23 January 2002
CS 200 Spring 2002

13. Evaluation Rule 3: Application
If the expression is an application:
Evaluate all the subexpressions of the combination (in any order)
Apply the value of the first subexpression to the values of all the other subexpressions.
(expression0 expression1 expression2 … )
23 January 2002
CS 200 Spring 2002

14. Rules for Application
If the procedure to apply is a primitive, just do it.
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.
23 January 2002
CS 200 Spring 2002

15. Making Procedures lambda means “make a procedure” Expression ::=
(lambda (Parameters) Expression)
Parameters ::=
Parameters ::= Name Parameters
23 January 2002
CS 200 Spring 2002

16. Lambda Example: Tautology Function
make a procedure
with no parameters
with body #t
(lambda ()
#t)
> ((lambda () #t) 200)
#<procedure>: expects no arguments, given 1: 200
> ((lambda () #t)) #t
> ((lambda (x) x) 200)
200
23 January 2002
CS 200 Spring 2002

17. 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 January 2002
CS 200 Spring 2002

18. A Squarish Example (define square (lambda (x) (* x x))) (square 4)
Its an application, use evaluation Rule 3:
Evaluate all the subexpressions of the combination (in any order)
Apply the value of the first subexpression to the values of all the other subexpressions.
23 January 2002
CS 200 Spring 2002

19. (lambda (x) (* x x)) (define square (lambda (x) (* x x))) (square 4)
Its an application, use evaluation Rule 3:
Evaluate all the subexpressions of the combination (in any order)
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))
23 January 2002
CS 200 Spring 2002

20. (lambda (x) (* x x)) 4 (define square (lambda (x) (* x x))) (square 4)
Its an application, use evaluation Rule 3:
Evaluate all the subexpressions of the combination (in any order)
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
23 January 2002
CS 200 Spring 2002

21. (lambda (x) (* x x)) (define square (lambda (x) (* x x))) (square 4)
Its an application, use evaluation Rule 3:
Evaluate all the subexpressions of the combination (in any order)
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.
23 January 2002
CS 200 Spring 2002

22. (lambda (x) (* x x) ) Apply: square to 4
Body of the procedure
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.
23 January 2002
CS 200 Spring 2002

23. (lambda (x) (* x x) ) (* 4 4) Apply: square to 4
Body of the procedure
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.
(* 4 4)
23 January 2002
CS 200 Spring 2002

24. (* 4 4) To be continued… Next time… evaluating 23 January 2002
CS 200 Spring 2002

25. Charge PS1 Due Friday Staffed Lab Hours Tonight Reading for next week:
5-9 in Cocke
6-9 in Small Hall
Reading for next week:
GEB Chapter 5
SICP Section 1.2
23 January 2002
CS 200 Spring 2002