In a translation of a paper on the Analytical Engine, Ada Lovelace improved upon L. F. Menambrea's work by applying rigor to the calculations that he performed. But then she took things one iteration further. In fact, she took things n iterations further. She wrote the first computer program, using the backtracking feature of the Analytical Engine to perform loops. The Lambda Calculus contains only functions. Evaluating a function is merely rewriting it to replace its parameter with its argument. How then can we represent something like numbers in a language with no primitives? We do it by writing a function that calls another function a certain number of times. The function that calls it once is the number 1. The function that calls it 100 times is the number 100. Alonzo Church demonstrated that these "Church Numerals" could be operated upon by other functions to calculate any computable number. We gain a great deal of confidence in our code if we can reason about the value of variabl
