Administrivia
• Make sure you have completed the
Mid Semester Survey
– Scheduled the week before Spring Break
– this will be worth some points
• Reading is important for this week:
– Tic-tac-toe, chapter 10 in SS
– Case study: change-making
March 14
Higher order procedures
March 21
Spring Break
March 28
Tic-Tac-Toe – read SS chapter 10!
Case Study: Making Change (tree-recursion)
– in the reader!
Elections mini-project (#3)
April 4
April 11
April 18
April 25
May 2
May 9
Midterm #2 (during lecture)
Extending sentences, words to lists (in lab)
Advanced list processing (recursion)
Start on the big project
Work on the big project (check-off 1, 2)
Big project (check-off 3)
Big Project due!
Tic Tac Toe
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
(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))
Write "my-keep"
(my-keep odd? '(1 2 3 4 5))
 (1 3 5)
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? '(1 2 3 4 5))  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))  (1 2 3 3)
5)
squares-greater-than-100
(s-g-t-100 '(2 9 13 16 9 45)  (169 256 2025)
6)
sum-of-squares
(sos '(1 2 3 4 5 6 7)  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 '())
– (every square "")
– (every square "12345")
• What about (keep
odd? '())
– (keep odd? "")
• How about (accumulate
–
–
–
–
–
–
(accumulate
(accumulate
(accumulate
(accumulate
(accumulate
(accumulate
+
'())
+ "")
* '())
word '(a))
+ '(a)
word '(a b))
+ '(a b))
return?
lambda
• "lambda" is a special form that lets you
make 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)
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
(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
Ha!
• Make a procedure that returns a
procedure that takes a number X and
returns a procedure that takes a number
and adds X to it.
– Whew!