# teaching machines

## CS 330 Lecture 31 – Maps, Filters, and Folds

April 22, 2015 by . Filed under cs330, lectures, spring 2015.

### Agenda

• what ?s
• a gallery of maps, filters, and folds
• pairs
• lambdas
• composition

### TODO

• On a 1/4 sheet, write these functions using map, filter, or fold:
•  lengths, which accepts a list of strings and yields a list of all their lengths. For example, lengths ["a", "bcd", "efghi"] yields [1, 3, 5].
•  tweens, which accepts a low, a high, and a list of numbers. It yields a list of all numbers between low and high, inclusive. For example, tweens 13 19 [5, 13, 18, 25] yields [13, 18].
• seconds, which accepts a list of pairs and returns a list of only the second elements. For example, seconds [("chris", 0), ("matt", 17), ("jacob", 10), ("caitlin", 23)] yields [0, 17, 10, 23].

### Problems

• Write a function resort that accepts a list and yields the list sorted in reverse. Use sort and reverse.
• Write a function expand that accepts a list of string-n pairs. It yields a list in which each pair has been expanded into a list comprised of n instances of its string. For example: expand [("dog", 2), ("cat", 3")] yields [["dog", "dog"], ["cat", "cat", "cat"]].
• Write a function proportionalize that accepts a list of integer weights. It returns a list of the weights, proportionalized. For example, proportionalize [1, 3, 4] yields [0.125, 0.375, 0.5].
• Write a function scalebias that accepts a scale, a bias, and a list of numbers. It yields a list where all elements have been scaled by the scale factor and offset by the bias.
• Write a function nonzeroes that accepts a list of numbers and yields a list containing only the nonzero elements. For example, nonzero [0, 1, -3, 0] yields [1, -3].
• Write a function overs that accepts an n and a list of strings and yields a list containing only those strings whose length is greater than n. For example, overs 3 ["the", "quick", "brown", "fox"] yields ["quick", "brown"].
• Write a function all that accepts a list of booleans and yields true if all elements are true.
• Write a function any that accepts a list of booleans and yields true if any element is true.
• Write a function sum that accepts a list of numbers and yields their sum.
• Write a function product that accepts a list of numbers and yields their product.
• Write a function length that accepts a list and yields its length.
• Write a function join that accepts a list of strings and yields their concatenation.
• Write a function max that accepts a list of numbers and yields their maximum.

### Code

#### Hof.hs

import Data.List

resort :: Ord a => [a] -> [a]
resort = (reverse . sort)

-- pairexpander :: (String, Int) -> [String]
-- pairexpander (s, n) = replicate n s

expand :: [(String, Int)] -> [[String]]
-- expand list = map pairexpander list
-- expand list = map (\(s, n) -> replicate n s) list
expand = map (\(s, n) -> replicate n s)

proportionalize :: [Double] -> [Double]
-- proportionalize list = map (\n -> n / total) list
-- where total = sum list
proportionalize list = map (/ total) list
where total = sum list

all' :: [Bool] -> Bool
all' [] = True
all' (first:rest) = first && all' rest

any' :: [Bool] -> Bool
any' [] = False
any' (first:rest) = first || any' rest

sum' :: [Double] -> Double
sum' [] = 0
sum' (first:rest) = first + sum' rest

foldr' mix accum [] = accum
foldr' mix accum (first:rest) = foldr' mix (mix accum first) rest

all'' = foldr' (&&) True
any'' = foldr' (||) False
sum'' = foldr' (+) 0
product'' = foldr' (*) 1
join'' = foldr' (++) ""


### Haiku

on productivity
I outsourced my job
To map and filter and fold