A flashback and analogy

You've probably heard about how the notion of sum types (e.g. Algol 68 unions, Rust enums, Haskell types) and product types (e.g. tuples or structs) generalizes, e.g. [a] can be thought of as ${a^0} + {a^1} + {a^2} + {a^3} + ...$ where the exponent corresponds to the length of the list.

This morning I had a flashback from that to my days in introductory numerical analysis and Taylor series, Chebyshev polynomials, and other infinite bases for function spaces. Just as evaluating, e.g., exp(x) can be done by evaluating the first N terms of the corresponding Taylor series where N may vary depending on x but is nonetheless finite, in Haskell, as long as you only evaluate finitely many elements of an "infinite" list, you can do what you need to do.