Functions are Values

The functions of section~#secsimilarities#27605> stretch our understanding of evaluation. It is easy to understand how functions consume numbers and symbols; structures and lists are a bit more complicated, but still within our grasp; but functions consuming functions is a strange idea. As a matter of fact, the functions of section~#secsimilarities#27606> violate the Scheme grammar of section~#secsynsem#27607>. In this section, we discuss how to adjust Scheme's grammar and evaluation rules so that they cover these functions. Without a good understanding of these ideas, we cannot hope to abstract functions. Once we understand these ideas, we can turn to the problem of writing contracts for such functions. Finally, the last part of the section introduces functions that produce functions, another powerful abstraction technique.