When it comes to functional programming, two key functions that often come up in discussions are foldr and foldl (or foldl'). These functions are used to "fold" or combine a list of elements into a single value, but they have slightly different implications and can lead to different outcomes. In this article, we will compare and contrast the implications of using foldr vs. foldl (or foldl').
First, let's define what these functions do. Foldr, also known as "fold right," starts with the right-most element in a list and combines it with the next element to its left, and so on until it reaches the left-most element. This can be visualized as "folding" the list from right to left. On the other hand, foldl (or foldl'), also known as "fold left," starts with the left-most element and combines it with the next element to its right, and so on until it reaches the right-most element. This can be visualized as "folding" the list from left to right.
One of the main differences between these two functions is how they handle infinite lists. Foldr can work with infinite lists because it only evaluates elements as needed, starting from the right-most element. This is known as "lazy evaluation" and allows foldr to handle larger lists more efficiently. On the other hand, foldl (or foldl') cannot handle infinite lists because it evaluates every element in the list before producing a result. This is known as "strict evaluation" and can lead to performance issues when working with larger lists.
Another difference between foldr and foldl (or foldl') is the order in which they evaluate elements. As mentioned earlier, foldr starts from the right and moves left, while foldl (or foldl') starts from the left and moves right. This can have implications on the final result, especially when working with non-commutative operations. For example, if we have a list of numbers and we want to find the sum using foldr, the result will be the same as using foldl (or foldl'). However, if we have a list of strings and we want to concatenate them, the result will be different depending on which function we use. Foldr will produce the result in the same order as the original list, while foldl (or foldl') will reverse the order of the strings.
When it comes to memory usage, foldr and foldl (or foldl') also have different implications. Since foldr works with lazy evaluation, it only needs to store the current element and the result of the next operation. This means that it has a constant memory usage, making it more memory efficient. On the other hand, foldl (or foldl') needs to store every element in the list until it reaches the end, which can lead to higher memory usage when working with larger lists.
One final difference between foldr and foldl (or foldl') is the ability to use them with non-list data structures. While foldr and foldl (or foldl') are commonly used with lists, foldr can also be used with other data structures such as trees and graphs. This is because foldr only needs to know how to combine two elements, regardless of the data structure. On the other hand, foldl (or foldl') can only be used with lists, as it relies on the order of elements in the list
