Streams and Monad Laws. Warning: The proof that this definition of >>= satisfies the monad laws is actually bogus, since it uses induction rather than coinduction. Thanks to Jeremy Gibbons for pointing this out. I hope to post another article that spells out the details at some point. When I first encountered the definition of monadic binding for streams, I wondered if there might be alternative definitions. This article is about how the two unfair versions of monadic bind do not satisfy the monadic laws, and how the fair definition does. For convenience, streams are represented as lists in this article, since this provides us with all the list operators on our type: type Stream = List For those of you who don’t know this off the top of your head, here’s the definition of the monad (ignoring the fact that we can’t write a class instance of a type synonym): instance Monad Stream where return x = repeat xs >>= f = diag (map f xs) Here repeat and diag have the following definitions: repeat x = x : repeat x Monad Laws.
The Trivial Monad. Update: I've added some solutions to exercises below. Haskell monads form a type class. And Haskell type classes are essentially interfaces shared by some types. So the Monad type class is a common API for talking to a bunch of different types. So the question is this: what's so special about this API? One way to grasp an API is to see concrete examples. APIs often capture design patterns, and the design pattern here is a one-way wrapper. Without further ado, here's a wrapper type: data W a = W a deriving Show (The Show bit is just so we can play with these things interactively.)
Note how it doesn't add anything except some wrapping. Return :: a -> W areturn x = W x (We could have just used W instead of return. And now we need one more thing - a way to manipulate wrapped data leaving it wrapped. Fmap :: (a -> b) -> (W a -> W b)fmap f (W x) = W (f x) It seems that we've finished. A = W 1b = fmap (+1) a But here's something we can't do. F :: Int -> W Intf x = W (x+1) And that's it. G x y = ... Control.Monad.Writer. A tour of the Haskell monad functions. Home This reference guide describes monad and functor functions in the modules Prelude and Control.Monad. It describes functions of The Haskell 98 Library Report only; example code is limited to Haskell 2010. The lines in the "Usage" sections, starting with "> " are commands/expressions typed in a Hugs 98 shell.
For most of the examples, it is necessary to give the command :l Control.Monad first; in some cases, source code must be entered in a file and the file must be loaded. If you have any suggestions for improvement, send me an e-mail (remove "REMOVE-THIS. " from the address.) Acknowledgements: For this reference manual, "A tour of the Haskell Prelude", by Bernie Pope and Arjan van IJzendoorn was used as an example. The example at fail, summing lists of two elements, was written by Yitzchak Gale. Copyright 2005 - 2013, Henk-Jan van Tuyl No part of this text may be sold, either seperately or as part of a product.
Home. Understanding Monads Via Python List Comprehensions « All Unkept. An attempt to explain monads and their usefulness in Haskell, assuming only some simple knowledge of Python. List comprehensions are a great Python feature that have been borrowed from Haskell/ML, and ultimately from set theory. As you probably know, they provide a convenient syntax for building lists from other lists or sequences: >>> lst = [1, 2, 3] >>> [x*2 for x in lst] [2, 4, 6] The alternative to the list comprehension is something like this: >>> newlist = [] >>> for x in lst: ... newlist.append(x*2) List comprehensions remove this annoying bit of boilerplate, helping to give Python the conciseness we love. While learning Haskell, I found list comprehensions a reassuring plateau of familiarity amidst the otherwise rather treacherous, alien landscape, but they also provide a way in to the impenetrable forest of 'Monads'.
Prelude> let lst = [1,2,3] Prelude> [ x*2 | x <- lst ] [2,4,6] Haskell has another way of implementing the same thing, though -- using its 'do' notation: Woah! Magic! Mike's World-O-Programming. The If Works - Translation from Haskell to JavaScript of selected portions of the best introduction to monads I’ve ever read. (With apologies to John Gruber and A Neighborhood of Infinity.) I know, I know, the world does not need yet another introduction to monads (or yet another article complaining that world does not need yet another introduction to monads). So you’ll be glad to know this isn’t one of those, in the sense that it’s not new.
I thought I’d write it because, first, monads are worth knowing about, and second, because I want to get into how they relate to asynchronous programming and I want a baseline in JavaScript to help explain things I might write later. It’s also a valuable exercise in thinking in terms of types. First up, a little back story. Let’s consider an example. Var sine = function(x) { return Math.sin(x) }; And you have another function for taking the cube of a number: var cube = function(x) { return x * x * x }; These functions take one number as input and return one number as output, making them composable: you can use the output of one as the input to the next: So what is a monad?
You Could Have Invented Monads! (And Maybe You Already Have.) If you hadn't guessed, this is about monads as they appear in pure functional programming languages like Haskell. They are closely related to the monads of category theory, but are not exactly the same because Haskell doesn't enforce the identities satisfied by categorical monads. Writing introductions to monads seems to have developed into an industry.
There's a gentle Introduction, a Haskell Programmer's introduction with the advice "Don't Panic", an introduction for the "Working Haskell Programmer" and countless others that introduce monads as everything from a type of functor to a type of space suit. But all of these introduce monads as something esoteric in need of explanation. But what I want to argue is that they aren't esoteric at all. Many of the problems that monads try to solve are related to the issue of side effects. Side Effects: Debugging Pure Functions In an imperative programming language such as C++, functions behave nothing like the functions of mathematics.
Solution and. A Gentle Introduction to Haskell: About Monads. A Gentle Introduction to Haskell, Version 98back next top Many newcomers to Haskell are puzzled by the concept of monads. Monads are frequently encountered in Haskell: the IO system is constructed using a monad, a special syntax for monads has been provided (do expressions), and the standard libraries contain an entire module dedicated to monads. In this section we explore monadic programming in more detail. This section is perhaps less "gentle" than the others.
Here we address not only the language features that involve monads but also try to reveal the bigger picture: why monads are such an important tool and how they are used. There is no single way of explaining monads that works for everyone; more explanations can be found at haskell.org. 9.1 Monadic Classes The Prelude contains a number of classes defining monads are they are used in Haskell. A monad is constructed on top of a polymorphic type such as IO. The Monad class defines two basic operators: >>= (bind) and return. Understanding Haskell Monads. Copyright © 2011 Ertugrul Söylemez Version 1.04 (2011-04-20) Haskell is a modern purely functional programming language, which is easy to learn, has a beautiful syntax and is very productive. However, one of the greatest barriers for learning it are monads. Although they are quite simple, they can be very confusing for a beginner.
As I have deep interest in extending Haskell's deployment in the real world, I'm writing this introduction for you. 1. I have written this tutorial for Haskell newcomers, who have some basic understanding of the language and probably attempted to understand one of the key concepts of it before, namely monads . Haskell is a functional programming language. However, the traditional programmer never had to face generalization. Some of you may have read Brent Yorgey's Abstraction, intuition, and the "monad tutorial fallacy" [ 5 ], which explains very evidently why writing yet another interpretation of monads is useless for a newcomer. 2. What about input/output? 3. Online Tutorial: What the hell are Monads? Noel Winstanley, 1999 Introduction This is a basic introduction to monads, monadic programming and IO, motivated by a number of people who've asked me to explain this topic, and also by similar queries I've seen on mailing lists.
This introduction is presented by means of examples rather than theory, and assumes a little knowledge of Haskell. Maybe Once upon a time, people wrote their Haskell programs by sequencing together operations in an ad-hoc way. The Maybe type, defined in the prelude as: > data Maybe a = Just a | Nothing can be used to model failure. > f :: a -> Maybe b takes an a and may produce a result b (wrapped in the Just constructor) or it may fail to produce a value, and return Nothing. Example In a database application, the query operation may have the following form > doQuery :: Query -> DB -> Maybe Record That is, doing a Query over the database DB may return a Record or it may fail and return Nothing. Using the thenMB combinator, the above code can be rewritten as below.
State.