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Slide 2 Administrivia Mid-semester survey this week (Thur/Fri) –you NEED to do this. Interviews should be starting in a few weeks. I apologize for not getting the midterm solutions and last week's lecture on-line: check tomorrow.

Slide 3 March 7Tree recursion, etc. Number-spelling Miniproject (#2) March 14Higher order procedures March 21Spring Break March 28More HOF, tic-tac-toe Elections Miniproject (#3) April 4Case Study: Making Change (tree- recursion) April 11Midterm #2 (during lecture) Extending sentences, words to lists (in lab) April 18Advanced list processing (recursion) Start on the big project

Slide 4 > (find-evens '( ))  (se 2 (se 4 (se 6 ())  (2 4 6) (se 2 (se 4 (se 6 () sent = ( ) sent = ( ) sent = ( ) sent = ( 5 6 ) sent = ( 6 ) sent = ( )

Slide 5 Find all the even numbers (define (find-evens sent) (cond ((empty? sent) ;base case '() ) ((odd? (first sent)) ;rec case 1 (find-evens (bf sent)) ) (else ;rec case 2: even (se (first sent) (find-evens (bf sent))) ) ))

Slide 6 (define (pascal C R) (cond ((= C 0) 1) ;base case ((= C R) 1) ;base case (else ;tree recurse (+ (pascal C (- R 1)) (pascal (- C 1) (- R 1)) )))

Slide 7 > (pascal 2 5) (+ (pascal 2 5) (pascal 2 4) (pascal 1 4) (+ (pascal 2 3) (pascal 1 3) (pascal 0 3) (+ (pascal 2 2) (pascal 1 2) (pascal 0 2)  1 (pascal 1 2) (pascal 0 2)  1 (+ (pascal 1 1) (pascal 0 1)  1 (+ (pascal 1 1)  1 (pascal 0 1)  1 (+ (pascal 1 1)  1 (pascal 0 1)  1

Slide 8 What is a procedure? (or, a function).

Slide 9 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) ) –You can define other objects, though: (define *pi* ) (define *month-names* ‘(january february march april may june july august september october november december))

Slide 10 Consider two forms of “month-name”: (define (month-name1 date) (first date)) (define month-name2 first)

Slide 11 Why have procedures as objects? Other programming languages don’t (often)

Slide 12 Procedures can be taken as arguments… (define (apply-to-5-and-3 func) (func 5 3)) (define (math-function? func) (or (equal? func +) (equal? func -) (equal? func *) (equal? func /)))

Slide 13 …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))

Slide 14 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

Slide 15 Patterns for simple recursions 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

Slide 16 (define (square-all sent) (if (empty? sent) ‘() (se (square (first sent)) (square-all (bf sent)) )) (square-all ‘( )) (every square ‘( ))