Class 4: Constructing Procedures

Assignments Due

• By Friday: Read Chapters 1-4 of course book, Chapters 1-3 of James Gleick’s The Information
• Monday, 5 September (11:01am): Problem Set 1 (both on-line submission and paper)
• Wednesday, 7 September (in class): Quiz 1: covers Chapters 1-4 of course book, Chapters 1-3 of The Information, Classes 1-5 (including questions)
  

  Upcoming Help Schedule (all office hours are now in Rice Hall)

• Today, 5-6:30pm (Jiamin, Rice, first floor)
• Thursday: 9:45-11am (Dave, Rice 507); 10-11:30am (Peter, Rice first floor); 1-2:30pm (Joseph, Rice first floor); 4:30-6pm (Jonathan, Rice first floor); 6-7:30pm (Jiamin, Rice first floor)

Scheme Grammar and Rules of Evaluation

(continued from Class 3)

Expression ::= ProcedureExpression

ProcedureExpression ::= (lambda (Parameters) Expression)


Parameters ::=


Parameters ::= Name Parameters

Evaluation Rule 4: A lambda expression evaluates to a procedure that takes the given parameters and has the expression as its body.

(lambda () true)

(lambda (x) (* x x))

(lambda (a)
   (lambda (b)
      (+ a b)))

Applying Constructed Procedures

((lambda () true) 1120) 

((lambda (x) (+ x 1000)) 120) 

((lambda (a) (lambda (b) (+ a b))) 5) 

(((lambda (a) (lambda (b) (+ a b))) 5) 6) 

Expression ::= IfExpression

IfExpression ::= (if Expression_Predicate Expression_Consequent Expression_Alternate)

Evaluation Rule 5: If. To evaluate an if expression, (a) evaluate the ___________________; then, (b) if the value of the predicate expression is ___________ then the value of the if expression is the value of the alternate expression; otherwise, the value of the if expression is the value of the _____________________________________.

(if false false true)

(if (> 4 3) 4 3)

((lambda (a b) (if (> a b) a b)) 5 6) 

Questions

Show how the Rules of Evaluation would evaluate:

   (define square (lambda (x) (* x x)))
   (square 4)

You will need more space for this and it will be very tedious, but it is worth doing once. Of course, you know the final value, but the important thing is to understand how following the Scheme evaluation rules steps will produce that value. You should be confident that you can determine the value of any Scheme expression just by following the evaluation rules systematically.

Evaluation Rule 3a does not say in what order the subexpressions should be evaluated in. For example, we could evaluate them left to right, or right to left, or in any other order. Does it ever matter in which order the subexpressions of an application are evaluated? (Tough question, but try to think of a Scheme expression where it would make a difference.)

Links

C++ Standard Core Language Active Issues (948 issues or problems
with C++ that the language experts can’t agree on). A new version of the C++ language was recently approved; it attempts to resolve some problems in C++, but also adds more complexity so I’m sure there will be more new issues soon…

Print PDF