What is a program? A testable input-to-output contract

Concept and intended result

A program is a set of steps the computer executes using explicit input and rules. For a simple shop receipt, the inputs are a price in integer cents and an item quantity. The output is the total in cents. Decide the allowed domain before writing code: prices cannot be negative, and the quantity is a whole number from zero through 100. A syntactically valid multiplication can still be a wrong program if it quietly accepts negative amounts.

Runnable Python 3 exercise

Save as 01_What_is_a_program.py and run with Python 3. Predict the output before executing; every example has assertions and uses only local synthetic values.

def total_cents(price_cents, count):
    if type(price_cents) is not int or price_cents < 0:
        raise ValueError("price must be nonnegative integer cents")
    if type(count) is not int or not 0 <= count <= 100:
        raise ValueError("invalid quantity")
    return price_cents * count
assert total_cents(125, 3) == 375
assert total_cents(125, 0) == 0
for inputs in ((-1,2),(100,-1),(100,101),(True,2)):
    try: total_cents(*inputs)
    except ValueError: pass
    else: raise AssertionError("invalid inputs accepted")
print("PASS input -> checked rule -> output")

Why this works

The function isolates one calculation and returns a result rather than printing inside the logic. Its caller can display euros later, but the core keeps integer cents to avoid decimal rounding problems. The type(...) is int check intentionally rejects Boolean input, even though Python considers bool a subtype of int. Separate invalid input from a legitimate total of zero. Assertions express the expected behavior in a form a machine can check.

Guided learner lab

Draw a three-box diagram for input, validation and output. Change the unit price to 149 cents and quantity to four; calculate 596 cents on paper before running. Predict outputs for quantity zero and the rejected cases. Add a maximum-price check and write one test on each side of its boundary. Keep the same result for the same input so the helper stays deterministic.

Diagnosing mistakes

If the output seems incorrect, print or inspect the two inputs before multiplication and identify whether their units are cents or euros. If a program fails while another example runs, capture its exact input and traceback. A passing example is evidence for those cases, not proof of every possible input.