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Javier Neira

Monads as containers - HaskellWiki - 0 views

www.haskell.org/...Monads_as_Containers

haskell monads intro as container

shared by Javier Neira on 28 Dec 09 - Cached
  • A monad is a container type together with a few methods defined on it.
  • all the elements which a monadic container holds at any one time must be the same type (it is homogeneous).
  • map (fmap), return and join,
  • ...15 more annotations...
  • map, (but called fmap in Haskell 98) actually comes from the definition of a functor
  • That is, if f is a functor, and we are given a function of type (a -> b), and a container of type (f a), we can get a new container of type (f b). This is expressed in the type of fmap: fmap :: (Functor f) => (a -> b) -> f a -> f b If you will give me a blueberry for each apple I give you (a -> b), and I have a box of apples (f a), then I can get a box of blueberries (f b). Every monad is a functor.
  • The second method, return, is specific to monads. If m is a monad, then return takes an element of type a, and gives a container of type (m a) with that element in it. So, its type in Haskell is return :: (Monad m) => a -> m a If I have an apple (a) then I can put it in a box (m a).
  • takes a container of containers m (m a), and combines them into one m a in some sensible fashion. Its Haskell type is join :: (Monad m) => m (m a) -> m a
  • If I have a box of boxes of apples (m (m a)) then I can take the apples from each, and put them in a new box (m a).
  • bind or extend, which is commonly given the symbol (>>=)
  • liftM :: (Monad m) => (a -> b) -> m a -> m b liftM f xs = xs >>= (return . f) -- take a container full of a's, to each, apply f, -- put the resulting value of type b in a new container, -- and then join all the containers together.
  • The function that does this for any monad in Haskell is called liftM -- it can be written in terms of return and bind as follows:
  • Well, in Haskell, IO is a monad.
  • Lists are most likely the simplest, most illustrative example
  • The reason that bind is so important is that it serves to chain computations on monadic containers together.
  • You might notice a similarity here between bind and function application or composition, and this is no coincidence.
  • What bind does is to take a container of type (m a) and a function of type (a -> m b). It first maps the function over the container, (which would give an m (m b)) and then applies join to the result to get a container of type (m b). Its type and definition in Haskell is the
  • xs >>= f = join (fmap f xs)
  • bind (>>=)
Javier Neira

Understanding Monads Via Python List Comprehensions « All Unkept - 0 views

lukeplant.me.uk/...via-python-list-comprehensions

haskell monads tutorial python

shared by Javier Neira on 02 Mar 10 - Cached
  • But here we have taken it to a higher level -- the Monad interface is like an abstraction of any kind of container.
  • This in turn leads to the concept that a monadic value represents a computation -- a method for computing a value, bound together with its input value.
  • Writing monads is hard, but it pays off as using them in Haskell is surprisingly easy, and allows you to do some very powerful things.
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  • One of them you have seen explicitly -- it's the 'return' method, responsible for packing things up into the monad. The other is called 'bind' or '>>=', and it does the 'unpacking' involved with the <- arrow in the do notation.
  • the 'bind' method doesn't really unpack and return the data. Instead, it is defined in such a way that it handles all unpacking 'internally', and you have to provide functions that always have to return data inside the monad.
  • It looks very much like 'unpack this data from the monad so I can use it', so it helps conceptually. In fact, together with the rest of the body of the 'do' block it forms an anonymous lambda function,
Javier Neira

A Neighborhood of Infinity: Haskell Monoids and their Uses - 0 views

blog.sigfpe.com/...ll-monoids-and-their-uses.html

monoids haskell monads examples howto

shared by Javier Neira on 30 Dec 09 - Cached
  • The Writer MonadYou can think of monoids as being accumulators. Given a running total, n, we can add in a new value a to get a new running total n' = n `mappend` a. Accumulating totals is a very common design pattern in real code so it's useful to abstract this idea. This is exactly what the Writer monad allows. We can write monadic code that accumulates values as a "side effect". The function to perform the accumulation is (somewhat confusingly) called tell. Here's an example where we're logging a trace of what we're doing.
  • This is an implementation of the factorial function that tells us what it did.
  • We use runWriter to extract the results back out. If we run> ex1 = runWriter (fact1 10)we get back both 10! and a list of what it took to compute this.
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  • and the monoid for addition is Sum
  • but there is a big advantage to using the Writer version. It has type signature f :: Integer -> Writer (Sum Integer) Integer. We can immediately read from this that our function has a side effect that involves accumulating a number in a purely additive way.
  • This is the Bool type with the disjunction operator, better known as ||.
  • "tell my caller if any value of r is ever 120"
  • One last application to mention is the Data.Foldable library. This provides a generic approach to walking through a datastructure, accumulating values as we go. The foldMap function applies a function to each element of our structure and then accumulates the return values of each of these applications. An implementation of foldMap for a tree structure might be
  • Suppose we want to accumulate two side effects at the same time. For example, maybe we want to both count instructions and leave a readable trace of our computation. We could use monad transformers to combine two writer monads. But there is a slightly easier way - we can combine two monoids into one 'product' monoid. It's defined like this:instance (Monoid a,Monoid b) => Monoid (a,b) where mempty = (mempty,mempty) mappend (u,v) (w,x) = (u `mappend` w,v `mappend` x)
Javier Neira

A Neighborhood of Infinity: The IO Monad for People who Simply Don't Care - 0 views

blog.sigfpe.com/...or-people-who-simply-dont.html

haskell io monad basics intro

shared by Javier Neira on 22 Dec 09 - No Cached
  • Many programming languages make a distinction between expressions and commands.
  • Like other languages it makes the distinction, and like other languages it has its own slightly idiosyncratic notion of what the difference is. The IO monad is just a device to help make this distinction.
  • There is no room for anything like a print command here because a print command doesn't return a value, it produces output as a side-effect
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  • It's easy to use: you just write do and then follow it by an indented list of commands. Here's a complete Haskell program:
  • Note also that commands take arguments that can be expressions. So print (2*x) is a command, but 2*x is an expression. Again, little different from a language like Python.
  • So here's an interesting feature of Haskell: commands can return values. But a command that returns a value is different from an expression with a value.
  • We have to use <- instead of let ... = ... to get a returned value out of a command. It's a pretty simple rule, the only hassle is you have to remember what's a command and what's a function.
  • get2Lines = do line1 <- getLine line2 <- getLine return (line1,line2)
  • To introduce a list of commands, use do.To return a value from a command, use return.To assign a name to an expression inside a do block use let.To assign a name to the result of a command, use <-.
  • what's a command and what's an expression? If it has any chance of doing I/O it must be a command, otherwise it's probably an expression.
  • Everything in Haskell has a type, even commands. In general, if a command returns a value of type a then the command itself is of type IO a.
  • eturn is simply a function of type a -> IO a that converts a value of type a to a command of type IO a.
  • 5. The type of a sequence of commands is the type of the last line.
  • The type of an if statement is the type of its branches. So if you want an if statement inside a do block, it needs to be a command, and so its branches need to be commands also. So it's
  • If something is of type IO a then it's a command returning an value of type a. Otherwise it's an expression. That's the rule.
  • following the rules above it's completely impossible to put an executed command inside an expression.
  • As the only way to do I/O is with commands, that means you have no way to find out what Haskell is doing inside expressions.
  • If the type isn't IO a, then you can sleep at night in the confidence that there are no side effects.
  • One last thing. Much of what I've said above is false. But what I hope I have done is describe a subset of Haskell in which you can start some I/O programming without having a clue what a monad is.
  • The idea of capturing imperative computations in a type of (immutable) values is lovely. And so is the general pattern we call "monad".
  • main = do return 1 print "Hello"
Javier Neira

Understanding Haskell Monads - 0 views

ertes.de/monads.html

haskell monads tutorial learning

shared by Javier Neira on 16 Dec 09 - Cached
  • The opposite of referentially transparent is referentially opaque. A referentially opaque function is a function that may mean different things and return different results each time, even if all arguments are the same.
  • a function that just prints a fixed text to the screen and always returns 0, is referentially opaque, because you cannot replace the function call with 0 without changing the meaning of the program.
  • n fact, a function, which doesn't take any arguments, isn't even a function in Haskell. It's simply a value. A number of simple solutions to this problem exist. One is to expect a state value as an argument and produce a new state value together with a pseudorandom number: random :: RandomState -> (Int, RandomState)
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  • A general purpose language is almost useless, if you can't develop user interfaces or read files. We would like to read keyboard input or print things to the terminal.
  • We have seen that we can solve this problem by expecting a state argument. But what's our state? The state of the terminal?
  • We seem to have found a useful solution to our problem. Just pass the state value around. But there is a problem with this approach.
  • A very special feature of Haskell is the concept of generalization. That means, instead of implementing an idea directly, you rather try to find a more general idea, which implies your idea as a special case.
  • However, the traditional programmer never had to face generalization. At most they faced abstraction,
  • they are a very abstract structure, which allows implementing functionality at an incredibly general level.
  • Haskell [1] is a purely functional programming language. Functions written in it are referentially transparent. Intuitively that means that a function called with the same arguments always gives the same result.
  • askell takes another approach. Instead of passing the world state explicitly, it employs a structure from category theory called a monad.
  • They are an abstract structure, and at first it can be difficult to understand where they are useful. The two main interpretations of monads are as containers and as computations.
  • The ⊥ value is a theoretical construct. It's the result of a function, which never returns, so you can't observe that value directly. Examples are functions, which recurse forever or which throw an exception. In both cases, there is no ordinary returning of a value.
  • Now that Nothing is a valid result, our function handles all cases.
  • You have some computation with a certain type of result and a certain structure in its result (like allowing no result, or allowing arbitrarily many results), and you want to pass that computation's result to another computation.
Javier Neira

jaspervdj - Maybe, null, and boilerplate code - 0 views

jaspervdj.be/...04-maybe-null-boilerplate.html

haskell Maybe monad example

shared by Javier Neira on 05 Jan 10 - Cached
  • A first goal they serve is as "unassigned variables". I will not cover that here, instead I will focus on another use: abnormal return values.
  • So, null is some sort of "Not found" error here. But wait - they could have used an Exception here!
  • We see a similar behavior here: when the object is found, we get a Just a, and when it is not found, we get Nothing - comparable to a null pointer.
  • ...5 more annotations...
  • So, while we can get a null back from a function, we should never give it to a function.
  • Now, if you have written a lot of Java code, you know that checking for null is a vital part of the job, and fragments like the one above are pretty common.
  • In Haskell, however, Maybe is also a monad - and monads can be used to prevent common patterns in code - in other words, they assist you in the D.R.Y.-principle2. We can therefore write the above snippet again using do-notation3.
  • getPathMonth :: Map String String -> Maybe MonthgetPathMonth m = do p <- lookup "path" m d <- parseDate p return $ getMonth d
  • he whole "check-for-null-and-short-circuit" behavior is defined by the Maybe monad -
  • Javier Neira on 05 Jan 10
     
    getPathMonth :: Map String String -> Maybe Month getPathMonth m = case M.lookup "path" m of Nothing -> Nothing (Just p) -> case parseDate p of Nothing -> Nothing (Just d) -> Just (getMonth d) getPathMonth :: Map String String -> Maybe Month getPathMonth m = do p <- parseDate p return $ getMonth d
Javier Neira

Monads in 15 minutes: Backtracking and Maybe - 0 views

www.randomhacks.net/...monads-in-15-minutes

monads haskell backtracking howto

shared by Javier Neira on 09 Nov 09 - Cached
  • type Choice a = [a] choose :: [a] -&gt; Choice a choose xs = xs
  • Because Haskell doesn’t compute answers until we ask for them, we get the actual backtracking for free!
  • The missing function is almost too trivial to mention: Given a single value of type a, we need a convenient way to construct a value of type Choice a:
  • ...5 more annotations...
  • More math trivia: return is also known as unit and η. That’s a lot of names for a very simple idea.)
  • makePairs = choose [1,2,3] &gt;&gt;= (\x -&gt; choose [4,5,6] &gt;&gt;= (\y -&gt; return (x,y)))
  • makePairs' = do x &lt;- choose [1,2,3] y &lt;- choose [4,5,6] return (x,y)
  • Every monad has three pieces: return, map and join.
  • Backtracking: The lazy way to code
Javier Neira

Learning Haskell Notes - 0 views

www.ninebynine.org/...Learning-Haskell-Notes.html

haskell learning notes

shared by Javier Neira on 09 Dec 09 - Cached
  • 8. Functors
  • A "functor" is a structured collection (or container) type with a method (fmap) that accepts a method and applies that method to the members of the collection yielding an isomorphic collection of values of a (possibly) new type. Is this right?
  • Every monad is a functor, but not the other way around; a monad is a functor PLUS functions &gt;&gt;= and return satisfying some laws
  • ...4 more annotations...
  • a functor is a type constructor PLUS a function fmap satisfying some laws.
  • I think it's better to use existentials, as they let you define multiple instances for the same type.
  • People tend to forget that the major difference between ADT's and OO-style classes is really only that with a class you can have many instances in the same program simultaneously, whereas with an ADT you can have only one; but the ADT implementation is still interchangeable.
  • sequence :: Monad m =&gt; [m a] -&gt; m [a]
Javier Neira

The best programming languages - 0 views

www.alpheccar.org/...36

smalltalk lisp haskell ruby analysis comparation

shared by Javier Neira on 11 Jan 10 - Cached
  • Haskell is not a programmable programming language (unless you look at extensions like template Haskell) but there are enough abstractions in Haskell to easily build domain specific languages with it.
  • But, the idea of time, the idea of sequencing can be built upon a purely functional system and we are led to monads
  • Monad are the recognition that the idea of sequencing operations can be formalized in a purely functional language.
  • ...2 more annotations...
  • The monad is an abstraction allowing to create new control structures and, in associations with the powerful type system of Haskell which makes possible elegant overloading of operators, it is possible to easily build new abstractions that allow to customize the programming language.
  • Unfortunately, Lisp, Smalltalk and Haskell are too different from most programming languages currently used in industry and taught in schools. They really look like alien technology to most developpers.
J.A. Alonso

A tour of the Haskell monad functions - 1 views

members.chello.nl/...tourdemonad.html

Tutorial Haskell

shared by J.A. Alonso on 24 Jan 10 - Cached
  • ap module: Control.Monad type: ap :: (Monad m) =&gt; m (a -&gt; b) -&gt; m a -&gt; m b
Javier Neira

Applicative-what? Functor-who? « wxfz :: Blog - 0 views

wxfz.wordpress.com/...applicative-what-functor-who

haskell control structures functors arrows monads intro

shared by Javier Neira on 09 Sep 10 - No Cached
  • Monads Are&nbsp;&nbsp;a kind of&nbsp;abstract data type used to represent&nbsp;computations (instead of data in the&nbsp;domain model).
J.A. Alonso

Programming with effects - 0 views

www.cs.nott.ac.uk/monads

Tutorial Haskell

shared by J.A. Alonso on 01 Feb 12 - No Cached
  • J.A. Alonso on 01 Feb 12
     
    Introducción a las mónadas en Haskell.
mesbah095

Guest Post Online - 0 views

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haskell del.icio.us imported Tutorial functional programming reference intro monads howto

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  • mesbah095 on 03 Apr 14
     
    Article Writing & Guestpost You Can Join this Site for Your Article & guest post, Just Easy way to join this site & total free Article site. This site article post to totally free Way. Guest Post & Article Post live to Life time only for Current & this time new User. http://guestpostonline.com
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