Parse and evaluate expressions written as nested function calls, such as add of one and the product of two and three.

How to answer

The happy path is a few lines of recursion, so the grade comes from structure and from what you do with bad input. Customers send malformed config and filter strings every day, and the error message is part of the product.

1. Write the grammar down first. The prompt is spoken, so write the example as you understand it, add(1, mul(2, 3)), and confirm it isn’t (add 1 (mul 2 3)) before writing the grammar. It fits on one line of the board: expr := number | name "(" [expr ("," expr)*] ")". Then ask the questions the grammar raises: negative and decimal numbers, whitespace, case in names, which functions exist and how many arguments each takes, and whether an error is an exception or a message.
2. Split into three stages. A tokenizer turns characters into tokens with positions. A parser turns tokens into a tree. An evaluator walks the tree. Say why: each stage can be tested alone, syntax errors stay apart from math errors, and the tree can be checked before anything runs.
3. Keep a position on every node. The tokenizer records offsets and the tree keeps them, so a later stage (an arity check, a division by zero) can still point at the source.
4. List malformed inputs before you code. Missing and extra parentheses, an empty argument, trailing input, an unknown function, the wrong number of arguments, division by zero, an empty string. Each error names what was expected, what was found and where. Where more than one token is valid, name them all: after an argument, a comma is as valid as a closing parenthesis.
5. Guard the depth. Deep enough nesting raises Python’s RecursionError. Cap the depth and raise your own error, and mention the explicit-stack alternative.
6. Choose the number type. Floats make add(0.1, 0.2) wrong in the last digit. Use Fraction if the answer must be exact; Decimal keeps decimal inputs exact but still rounds div(1, 3).

The trap is eval(): it runs arbitrary code, and when it fails you can’t say where.