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

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

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

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

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 ½ 48 pages total (includes formal specification and examples) 23 January 2002 CS 200 Spring 2002

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 ½ 48 pages total (includes formal specification and examples) 23 January 2002 CS 200 Spring 2002

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 ½ 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

Evaluation

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

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

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

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

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

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

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

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

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

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

(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

(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

(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

(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

(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

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

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