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CS3 Fall 2005

CS3 Fall 2005. Lecture 10: More on higher order functions. Administrivia. Reading is important for this week: Tic-tac-toe, chapter 10 in Simply Scheme (Tuesday) Difference between dates part III case-study in the reader (Tuesday) Change-making case-study in the reader (Thursday)

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CS3 Fall 2005

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  1. CS3 Fall 2005 Lecture 10: More on higher order functions

  2. Administrivia • Reading is important for this week: • Tic-tac-toe, chapter 10 in Simply Scheme (Tuesday) • Difference between dates part III case-study in the reader (Tuesday) • Change-making case-study in the reader (Thursday) • Note: there is a limit to the number of quizzes you can take outside of lab: 4 quizzes • Make sure you have completed theMid Semester Survey

  3. Tic Tac Toe

  4. The board X | | ---+---+--- O | O | X ---+---+--- | | "X _ _" "O O X" "_ _ _" "X _ _ O O X _ _ _"

  5. (another representation to help the search for possible moves) Triples X | | ---+---+--- O | O | X ---+---+--- | | "X _ _ O O X _ _ _" ( x23 oox 789 xo7 2o8 3x9 xo9 3o7 )

  6. Higher order function (HOFs) • A HOF is a procedure that takes a procedure 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

  7. A definition of every (define (my-every proc ws) (if (empty? ws) '() (se (proc (first ws)) (my-every (bf ws)) ))) • Every does a lot of work for you: • Checking the conditional • Returning the proper base case • Combing the various recursive steps • Invoking itself recursively on a smaller problem

  8. Which HOFs would you use to write these? • capitalize-proper-names (c-p-n '(mr. smith goes to washington)) (mr. Smith goes to Washington) • count-if (count-if odd? '(1 2 3 4 5))  3 • longest-word (longest-word '(I had fun on spring break))  spring • count-vowels-in-each (c-e-l '(I have forgotten everything))  (1 2 3 3) • squares-greater-than-100 (s-g-t-100 '(2 9 13 16 9 45)  (169 256 2025) • sum-of-squares (sos '(1 2 3 4 5 6 7)  30 • successive-concatenation (sc '(a b c d e)  (a ab abc abcd abcde)

  9. Write successive-concatenation (sc '(a b c d e))  (a ab abc abcd abcde) (sc '(the big red barn))  (the thebig thebigred thebigredbarn) (define (sc sent) (accumulate (lambda ?? ) sent))

  10. HOF: Base cases can be confusing • What does (every square '()) return? • (every square"") • (every square "12345") • What about (keep odd? '()) • (keep odd? "") • How about (accumulate + '()) • (accumulate + "") • (accumulate * '()) • (accumulate word '(a)) • (accumulate + '(a) • (accumulate word '(a b)) • (accumulate + '(a b))

  11. lambda • "lambda" is a special form that returns a function: (lambda (param1 param2 …)statement1 statement2 ) (lambda (x) (* x x)  [a function] (every (lambda (x) (* x x) '(1 2 3 4)) (1 4 9 16)

  12. Can a function defined by a lambda be recursive? (lambda (sent) (if (empty? sent) '() (se (square (first sent)) (????(bf sent)))))

  13. When do you NEED lambda? • When you need the context (inside a two-parameter procedure) (add-suffix '-is-great '(nate sam mary)) (nate-is-great sam-is-great mary-is-great) • When you need to make a function on the fly

  14. Procedures that make procedures • Generally, name procedures that create procedures "make-XXX" (make-bookends 'o)  #[closure arglist=(inner-wd) d7d0e0] ((make-bookends 'o) 'hi)  ohio ((make-bookends 'to) 'ron)  toronto (define tom-bookend (make-bookends 'tom)) (tom-bookends "")  tomtom

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