Programming Languages: Concepts and Implementation

8.4 Putting It All Together: Higher-Order Functions

Curried functions and partial function application open up new possibilities in programming, especially with respect to higher-order functions (HOFs). Recall that a higher-order function, such as map in Scheme, is a function that either accepts functions as arguments or returns a function as a value, or both. Such functions capture common, typically recursive, programming patterns as functions. They provide the glue that enables us to combine simple functions to make more complex functions. The use of curried HOFs lifts us to the third layer of functional programming: More Efficient and Abstract Functional Programming (Figure 5.10).

Most HOFs are curried, which makes them powerful and flexible. ...