Homework 4 (Due Monday 2/14/2011 at 10:00am)

Wiki MarkupUse the {{Intermediate Student with lambda}} language level. You can choose to use {{lambda}}, as appropriate, in any of the assigned problems. \ [For 2011: You may _not_ use {{local}} to define functions; all program functions (including helpers) must be defined at the top level.\]

Book Problems:

• 18.2.2 (10 pts)
  • In this problem, simply annotate each definition by attaching identifying subscripts (written in line such as x1 for "x sub 1" and y4 for "y sub 4") to _all_variable occurrences so that all of the uses of each defining occurrence are identified. A good way to choose a subscript value for a variable is to use the lexical nesting level of the binding occurrence. For example,

    Code Block
    (define (my-max lon) (cond [(empty? lon) (error 'my-max "applied to no arguments")] [(empty? (rest lon)) (first lon)] [else (local [(define head (first lon)) (define max-tail (my-max (rest lon)))] (if (>= head max-tail) head max-tail))]))

    becomes

    Code Block
    (define (my-max1 lon1) (cond [(empty? lon1) (error 'my-max "applied to no arguments")] [(empty? (rest lon1)) (first lon1)] [else (local [(define head2 (first lon1)) (define max-tail2 (my-max1 (rest lon1)))] (if (>= head2 max-tail2) head2 max-tail2))]))

• 20.1.1 (10 pts)
• 21.1.2 (10 pts)
• 21.2.1 (10 pts)
• 21.2.3 (10 pts)
  • "Lists of names" just means "lists of symbols."
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• 22.2.2 (10 pts) \ [For 2011: 12 pts\]
  • Name your function make-sort .
  • make-sort produces functions. Test these results by applying them to a few different arguments.
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• 23.3.9 (10 pts) \ [For 2011: 8 pts\]
  • The series represented by greg is (4, -4/3, 4/5, -4/7, ...).
• 24.0.8 (5 pts)
  • Instead of drawing arrows from the underlined occurrences, simply annotate each expression by attaching subscripts (written in line such as x1 for "x sub 1" and y4 for "y sub 4") to all variable occurrences so that all of the uses of each defining occurrence are identified. For example,

    Code Block
    (lambda (f g x) (f x (lambda (x) (g (g x)))))

    becomes

    Code Block
    (lambda (f1 g1 x1) (f1 x1 (lambda (x2) (g1 (g1 x2)))))

...