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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

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]
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

The Haskell 98 Library Report: Arrays - 0 views

www.haskell.org/...array.html

haskell library Array reference

shared by Javier Neira on 10 Nov 09 - Cached
  • 16.2  Incremental Array Updates The operator (//) takes an array and a list of pairs and returns an array identical to the left argument except that it has been updated by the associations in the right argument. (As with the array function, the indices in the association list must be unique for the updated elements to be defined.) For example, if m is a 1-origin, n by n matrix, then m//[((i,i), 0) | i <- [1..n]] is the same matrix, except with the diagonal zeroed.
  • -- A rectangular subarray subArray :: (Ix a) => (a,a) -> Array a b -> Array a b subArray bnds = ixmap bnds (\i->i) -- A row of a matrix row :: (Ix a, Ix b) => a -> Array (a,b) c -> Array b c row i x = ixmap (l',u') (\j->(i,j)) x where ((_,l'),(_,u')) = bounds x -- Diagonal of a matrix (assumed to be square) diag :: (Ix a) => Array (a,a) b -> Array a b diag x = ixmap (l,u) (\i->(i,i)) x        where           ((l,_),(u,_)) = bounds x -- Projection of first components of an array of pairs firstArray :: (Ix a) => Array a (b,c) -> Array a b firstArray = fmap (\(x,y)->x)
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