How do you combine and compose different combinators in Haskell?

2 How to combine combinators?

One way to combine combinators is to use them as arguments to other combinators. For example, you can use the composition combinator to combine the identity combinator and another function, such as the square function. This will create a new function that squares its argument and then returns it unchanged. In Haskell, you can write this as (\f g x -> f (g x)) (\x -> x) (\x -> x * x), or more simply, as (\x -> x) . (\x -> x * x), using the . operator for composition. You can also use parentheses to group combinators and apply them to values, such as ((\x -> x) . (\x -> x * x)) 2, which will return 4.

3 How to compose combinators?

Another way to combine combinators is to use them to create new combinators. For example, you can use the identity combinator and the composition combinator to create the flip combinator, which is a function that swaps the order of the arguments of another function. This will allow you to apply a function that expects two arguments in reverse order, such as the subtraction function. In Haskell, you can write the flip combinator as (\f x y -> f y x) . (\f g x -> f (g x)), or more simply, as flip = (.) . flip. You can then use the flip combinator to apply the subtraction function in reverse order, such as flip (-) 2 3, which will return 1.

4 Why use combinators?

Combinators are useful for several reasons. First, they allow you to reuse existing functions and create new ones without having to write them from scratch. This can save you time and effort, and make your code more concise and elegant. Second, they allow you to abstract over common patterns and behaviors, and express them in a general and flexible way. This can make your code more readable and maintainable, and easier to reason about and test. Third, they allow you to exploit the power of higher-order functions, which are functions that can take other functions as arguments or return them as results. This can enable you to write more expressive and modular code, and leverage the features of functional programming.

5 How to learn more combinators?

There are many more combinators than the ones we have seen so far, and each one has its own name and purpose. Some of the most common ones are map, filter, fold, zip, curry, uncurry, and many more. You can learn more about them by reading books, tutorials, and blogs on functional programming and Haskell, or by exploring the documentation and libraries of Haskell. You can also practice writing your own combinators, or finding new ways to combine and compose existing ones. The more you use combinators, the more you will appreciate their power and beauty.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?