A funny thing happened on the way to the formula
Patricia Johann · 1999
The concept of a function is arguably one of the most fundamental in computer science. It is frequently also one of the most problematic. In particular, students often have difficulty inferring, in a mathematically well-supported manner, equality of functions from equality of function values. That is, the transitions they make from demonstrations of equality of values of functions to demonstrations of equality of those functions themselves are often not well reasoned. In this complementary paper to [GK97] we describe one line of reasoning which we have found helps elucidate the mathematical principles according to which such inferences can correctly be made.