How to code it? - Functional programming & problem solving heuristics

Opinions differ about the relationship of mathematics and programming. Depending on temperament, one might say that they are essentially the same as both strive for understanding in a precise formal manner. Or, it can be argued that practical engineering goals are rather different from aiming for unquestionable proofs. Functional programmers, in particular, are probably more comfortable with the connection. They tend to know that some mathematical constructs like lambda calculus, or whole theories like category theory form the basis of their favourite languages.