Understanding Currying in Haskell: How to Convert Uncurried Functions

A comprehensive guide on currying in Haskell, including how to derive curried forms from known uncurried functions.
---

Visit these links for original content and any more details, such as alternate solutions, latest updates/developments on topic, comments, revision history etc. For example, the original title of the Question was: currying in haskell when the uncurried form is known

If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com.
---
Understanding Currying in Haskell: How to Convert Uncurried Functions

Currying is a powerful concept in Haskell that allows us to transform functions that take multiple arguments into a sequence of functions, each taking a single argument. If you're learning Haskell and are trying to write a type signature for a curried function given its uncurried form, you might find yourself a little confused. Let's clarify this process with clear explanations and examples.

The Problem: Writing a Curried Type Signature

Let's dive into the issue at hand. You might encounter a situation where you have a function defined in its uncurried form, for example, a function that takes a pair of arguments (x, y) and returns a value of type x. The challenge is to determine the correct curried type signature for this function.

For example, you might think the type signature should be:

[[See Video to Reveal this Text or Code Snippet]]

But you might wonder if this is indeed correct. Is there a better way to represent this in Haskell?

The Solution: Using GHCi

One of the best ways to determine the curried form is to utilize GHCi, the interactive GHC shell. Let’s break down the steps to help you understand how to convert from uncurried to curried functions.

Steps to Convert Using GHCi

Start by defining your uncurried function:

[[See Video to Reveal this Text or Code Snippet]]

This signifies a function f that takes a tuple of type (a, b) and returns a value of type c.

Use curry to convert it:

[[See Video to Reveal this Text or Code Snippet]]

This command will reveal the curried type of the function.
The result will be:

[[See Video to Reveal this Text or Code Snippet]]

Here, curry f indicates that it is now taking two separate arguments instead of a tuple.

Uncurry to validate the conversion:
To ensure everything is working, you can check:

[[See Video to Reveal this Text or Code Snippet]]

You’ll see:

[[See Video to Reveal this Text or Code Snippet]]

This confirms that we can revert back to the original function type.

Understanding the curry Function

The curry function has an implementation that can provide additional insight:

[[See Video to Reveal this Text or Code Snippet]]

When you pass it a function that expects a tuple, it rearranges the arguments so that they can be processed one at a time.

Example Demonstration

To illustrate this concept, let's consider a binary operator like addition:

[[See Video to Reveal this Text or Code Snippet]]

Using uncurry on addition:

[[See Video to Reveal this Text or Code Snippet]]

Using curry on the function:

[[See Video to Reveal this Text or Code Snippet]]

Additional Note: Using flip

If you're curious how to manipulate argument order, introducing flip before uncurring and currying will help. The type you suggested originally:

[[See Video to Reveal this Text or Code Snippet]]

will yield:

[[See Video to Reveal this Text or Code Snippet]]

When you apply this to a non-commutative operator, such as string concatenation:

[[See Video to Reveal this Text or Code Snippet]]

Conclusion

Understanding currying in Haskell may initially seem challenging, but by utilizing tools like GHCi and understanding the mechanics of functions, you can easily navigate between curried and uncurried forms. Remember that Haskell functions are typically fully curried, so most functions already conform to this structure. Employing tools like curry and uncurry will help you adapt functions to your needs effectively.

Feel free to experiment with these techniques and integrate them into your Haskell programming journey!