Scheme Continued

1
Scheme Continued

• Based on notes by John E. Savage
• I suggest that you have DrScheme open to try out
  the examples that are discussed.

2
Recursion

• Finish writing and testing functions in Class03
  Scheme and Recursion.doc. These were started in
  class03.scm.
• In the process of doing the above, introduce
  tracing and local variables.

3
Tracing

• (display identifier) (newline)
• (display (list s1 s2 s3)) (newline)
• places blank between s-expressions
• surrounds with ( )
• (display s1) (display s2) (display s3) (newline)
• places no blank between s-expressions
• s-expression could be a string such as "junk "

4
Local Variables

• (let ltbindingsgt ltbodygt)
• ltbindingsgt of form ((ltvar1gt ltinit1gt) )
• ltinitigt evaluated in external environment
• value of last expression in ltbodygt is returned
• gt (let ((x 2) (y 3)) ( x y))
• 6
• gt (let ((x 2) (y 3))
• (let ((x 7) (z ( x y))) z evaluated with
  x2, y3
• ( z x)))
• 35
• (letrec ltbindingsgt ltbodygt)
• same as let except ltinitigt evaluated with local
  values of ltvarigt if possible

5
More on Local Variables

• (letrec
• ((even?
• (lambda (n)
• (if (zero? n) t (odd? (sub1 n)))))
• (odd?
• (lambda (n)
• (if (zero? n) f (even? (sub1 n))))))
• (even? 88)
• t
• even? defined in terms of odd? which is defined
  in terms of even?
• even? and odd? are local to the scope of letrec

6
Questions Answered

• Can Scheme handle nondecimal numbers?
• Numbers are input and displayed in base 10.
  However, it is possible to convert between
  decimal and bases 2, 8, or 16 as shown
• gt (string-gtnumber AF36 16)
• 44854
• gt (number-gtstring 44854 16)
• "af36
• Why do I get parentheses and periods in my
  output?
• You may be consing two atoms togethergt (cons a
  b)(a . b)
• Rather than consing an atom to a listgt (cons a
  (b))(a b)

7
Questions Answered

• Is Scheme polymorphic?
• No
• gt (define fun (lambda (x) ( x x)))
• gt (define fun (lambda (x y) ( x y)))
• gt (fun 4)
• procedure fun expects 2 arguments, given 1 4
• Then how can Scheme handle functions with an
  indeterminate number of arguments?
• In the lambda statement, use a single argument
  without surrounding parentheses. This formal
  parameter is bound to a list of arguments
  passed.gt (define fun (lambda x x))gt (fun 2 3
  4)(2 3 4)

8
caadar and Helper Functions

• The value function
• gt (value '(3 (4 5)))
• 23
• gt (value '(((1 - 7) / 3) (4 5)))
• 18
• Helper Functions
• (define 1st-sub-exp (lambda (aexp) (car aexp)))
• (define operator (lambda (aexp) (cadr aexp)))
• (define 2nd-sub-exp (lambda (aexp) (caddr aexp)))
• Implementation
• (define value
• (lambda (aexp)
• (cond
• ((atom? aexp) aexp)
• ((eq? (operator aexp) ')
• ( (value (1st-sub-exp aexp)) (value
  (2nd-sub-exp aexp))))
• ((eq? (operator aexp) '-)
• (- (value (1st-sub-exp aexp)) (value
  (2nd-sub-exp aexp))))
• ((eq? (operator aexp) ')

9
If there is time . . .

• Note thelittleschemer.scm resource.
• Implement some set theory functions for sets of
  atoms or for sets that may include sets as
  elements.