Haskell

1
Haskell

• Chapter 4

2
Recursion

• Like other languages
• Base case
• Recursive call
• Author programs a number of built-in functions as
  examples
• Quick
• maximum 3,5,4 gt 5 Whats the base case?
• replicate 4 3 gt 3,3,3,3 Whats the base case?
• take 3 1..10 gt 1,2,3 Whats the base case?
• take 5 1..3 gt 1,2,3 Whats the base case?

3
Maximum

• maximum' (Ord a) gt a -gt a
• maximum' error "can't take maximum of empty
  list
• -- base case, if only one item, return it
• maximum' x x
• -- else return max of first element or recursive
  call
• maximum' (xxs) max x (maximum' xs)

4
Replicate

• replicate' Int -gt a -gt a
• replicate' n x
• -- base case returns empty list
• n lt 0
• -- else cons element to result of recursive call
• otherwise x replicate' (n-1) x
• Used guards because boolean condition, not a
  pattern
• replicate' 3 5
• 5 replicate 2 5 gt 5,5,5
• 5 replicate 1 5 gt 5, 5
• 5 replicate 0 5 gt 5
• n 0, gt

5
Take

• Two base cases (n0, or empty list)
• Guard without otherwise will fall through to
  patterns
• take' (Num i, Ord i) gt i -gt a -gt a
• take' n _
• n lt 0
• take' _
• take' n (xxs) x take' (n-1) xs

Quick trace (turn in) take' 20 1..10 take' 3
1..10
6
Reverse

• Note rather than because both are lists
• works at front of list, not back
• reverse' a -gt a
• reverse'
• reverse' (xxs) reverse' xs x

7
Repeat

• Haskell supports infinite lists
• repeat' a -gt a
• repeat' x xrepeat' x
• repeat 3
• 3 repeat 3
• 3 repeat 3
• etc,

8
Think it through dont look ahead!

• Preludegt zip 1,2,3 4,5,6
• (1,4),(2,5),(3,6)
• How would you write zip?
• How many base cases?
• Whats the recursive call?
• Patterns or guards?
• give patterns a try!

Add to your class participation
9
Zip

• zip' a -gt b -gt (a,b)
• zip' _
• zip' _
• zip' (xxs) (yys) (x,y)zip' xs ys

10
Quick Exercise

• With a partner, trace this code with this list of
  numbers
• 5,2,6,7,1,3,9,4
• quicksort (Ord a) gt a -gt a
• quicksort
• quicksort (xxs)
• let
• smallerOrEqual a a lt- xs, a lt x
• larger a a lt- xs, a gt x
• in quicksort smallerOrEqual x quicksort
  larger

Turn in for class participation credit
11
Play and Share?

• No, lets start on the homework.