Worksheet

A13.5 Map, filter and fold

Functional programming · A level · AQA 7517 4.12.2.1, Eduqas A500QS 1.4 · about 25 min

What this lesson is about

The three higher-order functions, foldl and foldr, and a pipeline over a log of sensor readings.

• The log
• map: change every item
• filter: keep some items
• fold: combine everything into one value
• Putting them together
• On the robot

Questions 6 marks in all

1. [1 mark]What does this program print?

   cms = [12, 45, 30, 61]
   print(list(map(lambda cm: cm * 10, filter(lambda cm: cm > 25, cms))))

2. [1 mark]What does filter do?

   1. AProduces a new list containing exactly the items of the original that match a given condition
   2. BApplies a function to every item and returns the list of results
   3. CReduces a list to a single value with a combining function
   4. DRemoves the first item of a list

3. [1 mark]What is the value of foldl (-) 10 [1,2,3]?

4. [1 mark]What is the value of foldr (-) 0 [5,3,1]?

5. [1 mark]What does this program print?

   from functools import reduce
   
   log = [(0, 40), (90, 15), (180, 62), (270, 33)]
   far = reduce(lambda a, b: a if a[1] >= b[1] else b, log)
   print(far[0])

6. [1 mark]What is the result of the Haskell expression map (*2) [1,2,3]? Write it as a Haskell list.

The task: analyse the sweep

Analyse sweep.csv (above) with map, filter and fold. There must be no for or while anywhere in the program (so no comprehensions either), and no min, max or sum: use map, filter and reduce instead. - parse(line) takes one line of the file, such as "2.4,60,24.5", and returns a tuple (time, heading, cm) with time a float, heading an int and cm a float. - Read the file, skip the header line, and map parse over the rest. - Keep only the valid readings, those under 400 cm, and print valid: <how many>. - Of the valid readings, print the headings of those over 40 cm, in the order they are in the file, as clear: 0 30 ... separated by spaces. - Fold the valid readings to find the nearest, and print nearest: <cm> cm at <heading>. - Fold the valid readings to their total, and print mean: <mean cm> rounded to one decimal place. The robot does not move.

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()
from functools import reduce

f = open("sweep.csv", "r")
lines = f.read().splitlines()
f.close()

for line in lines[1:]:
    print(line)

Plan your program here, then type it in and press Run.

Do it on the robot
www.bugbotlab.com/learn/a13-5-map-filter-and-fold/
The simulator checks it and tells you when it passes. Nothing to install, no account.

Challenges

1. Write foldr (-) 0 [5,3,1] and foldl (-) 0 [5,3,1] with brackets, work out both, then check the left one with reduce.
2. Use one fold, and no len, to count how many valid readings are under 20 cm.
3. Write your own my_map(f, xs) and my_filter(p, xs) using recursion and no loops.