Monads


Prerequisites



  • Some kind of idea of Haskell syntax
  • Haskell Platform installed
    • Platform requires Xcode on Mac
  • Clone: git@github.com:paasar/Haskell-intro.git

Solution to a problem that was not


1990 - A committee formed by Simon Peyton-Jones, Paul Hudak, Philip Wadler, Ashton Kutcher, and People for the Ethical Treatment of Animals creates Haskell, a pure, non-strict, functional language. Haskell gets some resistance due to the complexity of using monads to control side effects. Wadler tries to appease critics by explaining that "a monad is a monoid in the category of endofunctors, what's the problem?"

  • Monads were and are a solution to a problem that didn't exist before pure code was introduced.
  • With monads you can manage unpure operations like IO in otherwise pure code.
  • However, monads are useful in other things and also outside functional programming.

You may have used monads already

       Java (QueryDSL)
List result = query.from(customer) //customer: Domain object
    .where(customer.lastName.like("A%"), customer.active.eq(true)) //BooleanExpression x2
    .orderBy(customer.lastName.asc(), customer.firstName.desc()) //OrderSpecifier x2
    .list(customer);

JPAQuery qFrom = query.from(nn);
JPAQuery qFromWhere = qFrom.where(mm);
JPAQuery qFromWhereOrder = qFromWhere.orderBy(oo);
List result = qFromWhereOrder.list(customer);

       JavaScript (jQuery)
$("span").fadeIn("slow").text("Alert!");

Monad is...

  • Context
  • Wrapper
  • A way to chain functions in a context
  • Very abstract
    • State
    • Maybe
    • Future
    • IO
    • you name it

Monadic laws




1.
The first monadic law is that a monad is a wrapper around another type. In Haskell, one has the IO String type, which is returned from functions that read from files, console input, or system calls – IO is a monad that wraps the String data type.



2.
The second monadic law is just as simple: all monads must have a function to wrap themselves around other data types.

Haskell refers to this as a type constructor – a function that takes some data and wraps that data inside a new type. (jQuery’s type constructor is its parentheses.)


3.
The third monadic law, and the only one that’s even remotely complicated, is that all monads must be able to feed the value or values that they wrap into another function, as long as that function eventually returns a monad.

fadeIn(), text(), and all the other chainable functions are examples of this – they take the elements given inside the jQuery object, perform their function on them, then rewraps them back into the jQuery object and returns them.

Haskell syntax

module Main where
 
main :: IO ()
main = putStrLn "Hello, World!"

-- Type annotation (optional)
factorial :: Integer -> Integer
-- Using recursion
factorial 0 = 1
factorial n | n > 0 = n * factorial (n - 1)            | otherwise = error "No negs plz."

-- Using fold (implements product)
factorial' n = foldl1 (*) [1..n]


data TrafficLight = Red | Yellow | Green
type Name = Stringdata Person = Person
               {
                 firstName :: Name
               , lastName :: Name
               , age :: Int
               } deriving Show

More Haskell syntax

-- class is kind of like interface in Javaclass YesNo a where  yesno :: a -> Bool
-- instances are the implementing part for some typeinstance YesNo Int where  yesno 0 = False  yesno _ = True
instance YesNo [a] where  yesno [] = False  yesno _  = True

Monad in Haskell code

class Monad m where
    -- chain, bind
    (>>=)  :: m a -> (a -> m b) -> m b
    -- inject, wrapper, pure
    return :: a -> m a
foo :: (Monad m) => Int -> m Intbar :: (Monad m) => Int -> m Bool

return 1 >>= foo >>= bar

continued

-- With 'concrete' State monad
foo' :: Int -> MyState Intfoo' x = do  put x  return x + x
bar' :: Int -> MyState Bool
bar' y = do  xFromState <- get  return y * xFromState > 10

stuff :: MyState Boolstuff = return 1 >>= foo' >>= bar'
doStuff :: MyState BooldoStuff = do  x <- foo' 1  z <- bar' x  return z-- foo' 1 --> MyState 2 (1) --> bar' 2 --> MyState False (1)

References & links

  • http://learnyouahaskell.com/
  • http://importantshock.wordpress.com/2009/01/18/jquery-is-a-monad/
  • http://strongtyped.blogspot.fi/2010/01/monad-non-tutorial.html
  • Crockford on Monads (~1 h)
    http://www.youtube.com/watch?v=dkZFtimgAcM
  • http://www.querydsl.com
  • http://james-iry.blogspot.co.uk/2009/05/brief-incomplete-and-mostly-wrong.html

Monads

By Ari Paasonen

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Monads

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