How do you compare and contrast memoization with other caching techniques in functional programming?

1 What are pure functions?

A pure function is a function that always returns the same output for the same input, and does not cause any side effects in the program. Side effects are any changes to the state of the program or the environment, such as modifying global variables, printing to the console, or making network requests. Pure functions are easier to test, debug, and reuse, since they do not depend on or affect anything outside their own scope.

2 What is memoization?

Memoization is a technique that involves storing the results of expensive function calls and returning the cached result when the same inputs occur again. Memoization can speed up the execution of your code by avoiding unnecessary computations and reducing the number of function calls. Memoization is especially useful for recursive functions, dynamic programming problems, and functions that operate on large or complex data structures.

3 How to implement memoization?

There are different ways to implement memoization in functional programming languages, such as using higher-order functions, decorators, or libraries. The basic idea is to create a wrapper function that checks if the input has been seen before, and if so, returns the cached output. Otherwise, it calls the original function and stores the output in a cache. The cache can be a simple object, a map, a set, or any data structure that allows fast lookup and insertion.

4 How to use memoization effectively?

Memoization is not a one-stop solution to all performance issues. There are some trade-offs and limitations to consider before applying it to your code. Factors that influence the effectiveness of memoization include the size and complexity of the input and output, the frequency and distribution of the input, as well as the cost and purity of the function. Memoization works best for functions with a small and finite number of inputs and outputs, that are called repeatedly with similar inputs, and that are expensive to compute and pure. If the input or output is too large or complex, or if the input is random or unpredictable, memoization can consume a lot of memory and slow down the lookup process, or waste memory and computation by caching results that are never used again.

5 How does memoization compare with other caching techniques?

Memoization is a technique used in functional programming which stores and reuses data or results to improve performance or availability. There are other caching techniques such as lazy evaluation, which delays the evaluation of an expression until its value is needed, but it can also introduce memory leaks and performance issues. Eager evaluation evaluates an expression as soon as it is defined and can improve responsiveness and predictability, but it can also waste resources and cause errors. Partial application creates a new function by fixing some of the arguments of an existing function and can simplify code, create reusable functions, however, it can also increase the number of function calls and reduce readability.

6 What are the benefits and challenges of memoization in functional programming?

Memoization is a powerful technique that can enhance the performance and readability of your functional code, but it also comes with some challenges and trade-offs. It can reduce the time complexity of your code by avoiding redundant computations and function calls, and preserve the purity and referential transparency of your functions, making them easier to reason about, test, and debug. Additionally, it can leverage the immutability and equality of your data structures, resulting in more consistent and reliable code. On the other hand, memoization can also increase the space complexity and memory consumption of your code by storing the results of every function call in a cache. Furthermore, it can introduce complexity and overhead in your code by requiring you to implement or use a memoization mechanism, such as a wrapper function or a library. Lastly, it can depend on the characteristics and assumptions of your functions and inputs, which means that your code may not benefit from or even break with memoization.