Lab: Functional Programming#

Goals for this lab:

Use map, filter, and reduce to process data without explicit loops.
Write and use a closure.
Refactor a side-effecting program into a pure core and an imperative shell.
Test the pure core with both doctest and a property-based test.

1. Transform and Filter#

Given prices = [19.99, 5.0, 42.5, 8.75, 100.0]:

Use map to produce a new list with 8% sales tax added to each price.
Use filter to keep only the prices above 10.0.
Use functools.reduce to compute the total of all prices, then check your answer against the built-in sum.

For each part, also write the list-comprehension equivalent and decide which reads more clearly.

2. A Closure#

Write a function make_between(low, high) that returns a predicate — a function of one argument that returns True when its argument is in the range [low, high]. Then use it with filter:

>>> in_range = make_between(10, 50)
>>> list(filter(in_range, [5, 12, 40, 99, 50]))
[12, 40, 50]

3. Pure Core, Imperative Shell#

Here is a program that does everything at once — reading, computing, and printing all tangled together:

def report(path):
    total = 0
    count = 0
    for line in open(path):
        total += float(line)
        count += 1
    print(f"average = {total / count}")

Identify every side effect in report.
Refactor it into a pure core — one or more pure functions that do the computing — and a thin imperative shell that does only the file reading and printing.
Add a docstring with a doctest to each pure function, and run python -m doctest on your file.

4. A Property-Based Test#

Install hypothesis (pip install hypothesis) and write a property-based test for your average function from exercise 3:

State the invariant that the average of a non-empty list of integers lies between its smallest and largest element, and test it with @given.
Run it with pytest. Then change average to divide by len(scores) + 1 and run the test again — confirm that hypothesis finds a counterexample and reports the smallest one it can.

5. Challenge: Functional Newton#

Using the iterate and converged_value helpers from the Worked Examples section, write a sqrt(c) function that finds the square root of c as a fixed point of the step x -> (x + c / x) / 2 (the Babylonian method). Test it with an oracle property against math.sqrt.

Lab: Functional Programming

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