HASKELL MONAD OVERVIEW

REVISED: Sunday, October 13, 2024

1. INTRODUCTION

What is a monad?

A monad is a type constructor we will refer to as M, with two operations we will refer to as return and bind.

The operation return takes a value of type a and returns a value of type M a.

The operation bind takes a value of type M a and a function of type a -> M b, and returns a value of type M b.

The return operation is used to create new monadic values, and the bind operation is used to chain together monadic computations.

2. OVERVIEW

Why use monads?

Monads are a powerful tool for structuring computations. They can represent various computational concepts, such as state, sequencing, and exceptions.

State: Monads can be used to represent computations that have side effects, such as reading or writing to a file.

Sequencing: Monads can be used to represent computations that need to be executed in a specific order.

Exceptions: Monads can be used to represent computations that can fail.

Haskell has many built-in monads, including:

Maybe: This monad represents computations that can fail.

IO: This monad represents computations that have side effects.

State: This monad represents computations that have mutable states.

3. EXAMPLE

Here is an example of how to use the Maybe monad to represent a computation that can fail:

-- mayMon.hs

import Control.Monad()

{-

The function divide x y returns a Maybe Integer, representing the result of dividing two numbers. x is the numerator, y is the denominator. 

-}

divide :: Integer -> Integer -> Maybe Integer

divide x y =

  if y == 0 then Nothing else Just (x `div` y)

{-

The function main uses the `Maybe` monad to print the result of dividing x by y.

-}

main :: IO ()

main = do

  xStr <- readLn

  yStr <- readLn

  result <- divide x y

  case result of

    Just z -> print z

    Nothing -> putStrLn "Division by zero!"

This program effectively handles division by zero using the Maybe monad, providing a Nothing value in such cases and printing an appropriate error message.

Here's a breakdown of the code:

• import Control.Monad(): Imports the Control.Monad module, which provides essential functions and type classes for working with monads, including Maybe.
• divide :: Integer -> Integer -> Maybe Integer: Defines a function named divide that takes two Integer arguments (numerator and denominator) and returns a Maybe Integer quotient result.
• if y == 0 then Nothing else Just (xdivy): Uses a conditional expression to check if the denominator (y) is zero. If it is, the function returns Nothing to indicate an error (division by zero). Otherwise, it returns Just (xdivy), where xdivy performs integer division and Just wraps the result in a Maybe value.
• main :: IO (): Defines the main function that executes the program's logic.
• x <- readLn: Reads an Integer value from the standard input and binds it to the variable x.
• y <- readLn: Reads another Integer value from the standard input and binds it to the variable y.
• result <- divide x y: Calls the divide function with the values of x and y, binds the result (either Just z or Nothing) to the variable result.
• case result of: Uses a pattern matching case expression to handle the different possible values of result.
• Just z -> print z: If result is Just z, it prints the value of z (the result of the division).
• Nothing -> putStrLn "Division by zero!": If result is Nothing, it prints the error message "Division by zero!".

This program effectively demonstrates the use of the Maybe monad for handling potential errors and providing meaningful feedback to the user.

4. CONCLUSION

Monads are a powerful tool for structuring computations in Haskell. They can be used to represent a wide variety of computational concepts, such as state, sequencing, and exceptions.

This tutorial has helped you to learn how to program using Haskell monads.

5. REFERENCES

Bird, R. (2015). Thinking Functionally with Haskell. Cambridge, England: Cambridge University Press.

Davie, A. (1992). Introduction to Functional Programming Systems Using Haskell. Cambridge, England: Cambridge University Press.

Goerzen, J. & O'Sullivan, B. &  Stewart, D. (2008). Real World Haskell. Sebastopol, CA: O'Reilly Media, Inc.

Hutton, G. (2007). Programming in Haskell. New York: Cambridge University Press.

Lipovača, M. (2011). Learn You a Haskell for Great Good!: A Beginner's Guide. San Francisco, CA: No Starch Press, Inc.

Thompson, S. (2011). The Craft of Functional Programming. Edinburgh Gate, Harlow, England: Pearson Education Limited.