CS3 Fall 2005 Lecture 10: More on higher order functions

Oct 24Higher order procedures Oct 31More HOF – "tic-tac-toe" program: SS chapter 10! – "Change Making" case study, in the reader Nov 7Miniproject #3: Election-processing – Friday is a holiday – Thursday a catch-up day – MP#3 due Thur/Fri: plan ahead! Review Session: Wednesday Nov 14Midterm #2 Lists Nov 21Start on the project: check-off #1 Nov 28Work on the project: checks #2 Dec 5Checkoff #3, finish the project Dec 17Final Exam (midterm #3)

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 the Mid Semester Survey

Tic Tac Toe

X | | O | O | X | | "X _ _" "O O X" "_ _ _" "X _ _ O O X _ _ _" The board

X | | O | O | X | | "X _ _ O O X _ _ _" Triples (another representation to help the search for possible moves ) ()x23oox789xo72o83x9xo93o7

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

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

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

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))

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))

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) '( ))  ( )

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

When do you NEED lambda? 1.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) 2.When you need to make a function on the fly

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