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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

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
  • ...18 more annotations...
  • 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

Existential type - HaskellWiki - 0 views

www.haskell.org/...Existential_type

ghc type existential

shared by Javier Neira on 21 Dec 09 - Cached
  • First of all, it is now impossible for a function to demand a Worker having a specific type of buffer. Second, the type of foo can now be derived automatically without needing an explicit type signature. (No monomorphism restriction.) Thirdly, since code now has no idea what type the buffer function returns, you are more limited in what you can do to it.
  • This illustrates creating a heterogeneous list, all of whose members implement "Show", and progressing through that list to show these items: data Obj = forall a. (Show a) => Obj a   xs :: [Obj] xs = [Obj 1, Obj "foo", Obj 'c']   doShow :: [Obj] -> String doShow [] = "" doShow ((Obj x):xs) = show x ++ doShow xs With output: doShow xs ==> "1\"foo\"'c'"
  • Existential types in conjunction with type classes can be used to emulate the dynamic dispatch mechanism of object oriented programming languages. To illustrate this concept I show how a classic example from object oriented programming can be encoded in Haskell.
Javier Neira

Smart constructors - HaskellWiki - 0 views

www.haskell.org/...Smart_constructors

type haskell constructor restriction

shared by Javier Neira on 24 Jan 10 - Cached
  • The most interesting are probably the static checks that can be done with Type arithmetic, that enforce the number of bands at compile time, rather than runtime, by lifting the band count into the type level.
  • typecheck perform the check statically, using phantom types and Peano numbers.
  • So encode a type-level version of the bounds check. Only resistors with bands >= 4 and <= 8 are valid:
  • ...1 more annotation...
  • Further checks can be obtained by separating the metal and ceramic values on the type level, so no function that takes a metal resistor can be accidentally passed a ceramic one. A newtype is useful for this:
Javier Neira

Learn You a Haskell for Great Good! - Types and Typeclasses - 0 views

learnyouahaskell.com/types-and-typeclasses

type classes haskell tutorial intro

shared by Javier Neira on 22 Dec 09 - Cached
  • That's why we can use explicit type annotations. Type annotations are a way of explicitly saying what the type of an expression should be. We do that by adding :: at the end of the expression and then specifying a type.
Xiaobin Huang

'Cannot justify constraints in explicitly typed binding ', Hugs complained. - 10 views

Now I know, it should be 'permutation :: Eq a => [a]->[[a]]'. Xiaobin Huang wrote: > hi all, > > I'm new to Haskell. > > I wrote a permutation prog. > > permutation [] = [[]] > p...

started by Xiaobin Huang on 14 Nov 08 1 follow-up, last by Xiaobin Huang on 16 Nov 08
J.A. Alonso

Programming errors in traversal programs over structured data - 0 views

userpages.uni-koblenz.de/...syb42

artículo Haskell

shared by J.A. Alonso on 30 Jan 12 - No Cached
  • J.A. Alonso on 30 Jan 12
     
    Traversal strategies `a la Stratego (also `a la Strafunski and 'Scrap Your Boilerplate') provide an exceptionally versatile and uniform means of querying and transforming deeply nested and heterogeneously structured data including terms in functional programming and rewriting, objects in OO programming, and XML documents in XML programming. However, the resulting traversal programs are prone to programming errors. We are specifically concerned with errors that go beyond conservative type errors; examples we examine include divergent traversals, prematurely terminated traversals, and traversals with dead code. Based on an inventory of possible programming errors we explore options of static typing and static analysis so that some categories of errors can be avoided. This exploration generates suggestions for improvements to strategy libraries as well as their underlyingq programming languages. Haskell is used for illustrations and specifications with sufficient explanations to make the presentation comprehensible to the non-specialist. The overall ideas are language-agnostic and they are summarized accordingly.
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 >>= 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 => [m a] -> m [a]
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] -> 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] >>= (\x -> choose [4,5,6] >>= (\y -> return (x,y)))
  • makePairs' = do x <- choose [1,2,3] y <- choose [4,5,6] return (x,y)
  • Every monad has three pieces: return, map and join.
  • Backtracking: The lazy way to code
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.
  • ...6 more annotations...
  • 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

Hoogle - 0 views

haskell.org/hoogle

haskell search api hoogle programming

shared by Javier Neira on 26 Jan 10 - Cached
  • Javier Neira on 26 Jan 10
     
    Hoogle is a Haskell API search engine, which allows you to search many standard Haskell libraries by either function name, or by approximate type signature.
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) => m (a -> b) -> m a -> m b
J.A. Alonso

Foundations of Functional Programming - bu Robin Cockett - 0 views

pages.cpsc.ucalgary.ca/...webnotes.html

curso haskell i1m

shared by J.A. Alonso on 06 Oct 11 - No Cached
  • J.A. Alonso on 06 Oct 11
     
    The purpose of the course is to explore various aspects of functional programming using Haskell. In particular, the course provides an introduction to the lambda calculus, types in programming, and the role of these in the implementation of functional programming.
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  a kind of abstract data type used to represent computations (instead of data in the domain model).
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)
  • ...12 more annotations...
  • 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.
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