Higher-Order Functions

Higher-Order Function

: Functions are first-class, meaning they can be manipulated as values

A higher-order function is

1. A function that a function as an argument

2. A function that returns a functionas a return value

Describing Function

: A function's domain is the set of all inputs it might possibly take as arguments

: A function's range is the set of output values it might possibly return

: A pure function's behavior is the relationship it creates between input and output

A guide to Designing Function

Give each function exactly one job, but make it apply to many related situations

 

Generalization

Generalizing patterns with arguements

: Regular geometric shapes relate length and area

 

Higher-Order Functions

Generalizing Over Computational Process

: The common structure among functions may be a computational process, rather than a number

 

Functions as Return values

Locally Defined Functions

: Functions defined within other function bodies are bound to names in a local frame

Call Expressions as Operator Expressions

: An expression that evaluates to a function / An expression that evaluates to its argument

 

Self Reference

Returning a Function using its own name

python codes ex

def print_sums(n) :

   print(n)

   def next_sum(k) :

      return print_sums(n + k)

   return next_sum

print_sums(1)(3)(5)

answer. 1 / 4 / 9 / Function

 

Summary

-   Higher-order function : any function that either accepts a function as an argument and / or returns a function

-   Why are these useful ?

: Generalize over different form of computation

: Helps remove repetitive segments of code

-   One use case: summation

: We generalized over the computation of each term

-   We saw nested functions can access variables in outer function (area) as well as the outer function itself (print_sums)