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CS3 Fall 2005

CS3 Fall 2005. Lecture 9: Higher Order Functions. Administrivia. Mid-semester survey this week (Thur/Fri) you NEED to do this. Reading this week: Simply Scheme Chapters 7-9 Difference between dates, part III Two resources: http://hiroki.ucdev.org/cs3fall05 http://wla.berkeley.edu/.

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CS3 Fall 2005

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  1. CS3 Fall 2005 Lecture 9: Higher Order Functions

  2. Administrivia • Mid-semester survey this week (Thur/Fri) • you NEED to do this. • Reading this week: • Simply Scheme Chapters 7-9 • Difference between dates, part III • Two resources: • http://hiroki.ucdev.org/cs3fall05 • http://wla.berkeley.edu/

  3. When should the Midterm #2 review be? The second midterm is on Monday, Nov. 14 Do you want the review on: Sunday? (Nov. 13) Fri night? (Nov. 11) Wed night? (Nov. 9) And, what time?

  4. Quick review from last time: binary • Write binary, a procedure to generate the possible binary numbers given n bits. (binary 1)(0 1) (binary 2)(00 01 10 11) (binary 3)(000 001 010 011 100 101 110 111)

  5. What is a procedure? (or, a function).

  6. Treating functions as things • “define” associates a name with a value • The usual form associates a name with a object that is a function (define (square x) (* x x)) (define (pi) 3.1415926535) • You can define other objects, though: (define *pi* 3.1415926535) (define *month-names* ‘(january february march april may june july august september october november december))

  7. Consider two forms of “month-name”: (define (month-name1 date) (first date)) (define month-name2 first)

  8. Why have procedures as objects? Other programming languages don’t (often)

  9. Procedures can be takenas arguments… (define (apply-to-5-and-3 func) (func 5 3)) (define (math-function? func) (or (equal? func +) (equal? func -) (equal? func *) (equal? func /)))

  10. …and procedures can be returned from procedures (define (choose-func name) (cond ((equal? name ‘plus) +) ((equal? name ‘minus) -) ((equal? name ‘divide) /) (else ‘sorry))) (define (make-add-to number) (lambda (x) (+ number x))) (define add-to-5 (make-add-to 5))

  11. Higher order function (HOFs) • A HOF is a function that takes a function as an argument. • There are three main ones that work with words and sentences: • every – do something to each element • keep – return only certain elements • accumulate – combine the elements

  12. Patterns for simple recursions • Most recursive functions that operate on a sentence fall into: • Mapping: square-all EVERY • Counting: count-vowels, count-evens • Finding: member, first-even • Filtering: keep-evens KEEP • Testing: all-even? • Combining: sum-evens ACCUMULATE • Most recursive functions that operate on a sentence fall into: • Mapping: square-all • Counting: count-vowels, count-evens • Finding: member, first-even • Filtering: keep-evens • Testing: all-even? • Combining: sum-evens

  13. (define (square-all sent) (if (empty? sent) ‘() (se (square (first sent)) (square-all (bf sent)) )) (square-all ‘(1 2 3 4 5)) (every square ‘(1 2 3 4 5))

  14. Write "my-every" (my-every factorial '(1 2 3 4 5))  (1 2 6 24 120)

  15. Write "my-keep" (my-keep odd? '(1 2 3 4 5))  (1 3 5)

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