Difference between revisions of "The Other Prelude"

-- module: TheOtherPrelude
import Prelude ()    -- hide everything


-- the idea is to remove 'fmap'.
-- both map :: (a -> b) -> [a] -> [b] ('fmap' for the monad []) 
-- and (.) :: (a -> b) -> (e -> a) -> (e -> b) ('fmap' for the (->) e monad)
-- are good names, and are intuitively prefix and infix respectively.
class Functor f where
  -- 'fmap' is guilty of nothing but a bad name
  map, (.) :: (a -> b) -> f a -> f b

  -- implementing either is enough
  map = (.)
  (.) = map


-- the following has been shamelessly copied,
-- from the Functor hierarchy proposal[1] wiki page.
class Functor f => Applicative f where
  -- lifting a value
  return :: a -> f a

  -- should this be named 'ap'? is 'ap' a good name?
  -- can you come up with a better name?
  -- can it refactor the liftM* type gymnastics?
  (<*>) :: f (a -> b) -> f a -> f b   
  
  -- when the second is independent of the first
  (>>) :: m a -> m b -> m b

  -- is there a better definition?
  fa >> fb = (map (const id) fa) <*> fb


-- this leaves little left for the actual Monad class
class Applicative m => Monad m where
  -- the binding operation, gist of a monad 
  (>>=) :: m a -> (a -> m b) -> m b

  -- throwing out the outer monad
  join :: m (m a) -> m a

  -- intuitive definitions
  x >>= f = join (map f x)
  join x = x >>= id


-- we shamelessly copy from the MonadPlus reform proposal[2] now.

-- zero will be used when pattern matching against refutable patterns in
-- do-notation as well as to provide support for monad comprehensions.

-- should satisfy 'left zero': zero >>= f = zero
class Monad m => MonadZero m where
  zero :: m a


-- should satisfy 'monoid' 
-- zero ++ b = b, b ++ zero = b, (a ++ b) ++ c = a ++ (b ++ c)
-- and 'left distribution'
-- (a ++ b) >>= f = (a >>= f) ++ (b >>= f)
class MonadZero m => MonadPlus m where
  (++) :: m a -> m a -> m a


-- should satisfy 'monoid' 
-- zero `orElse` b = b, b `orElse` zero = b
-- (a `orElse` b) `orElse` c = a `orElse` (b `orElse` c)
-- and 'left catch'
-- (return a) `orElse` b = a
class MonadZero m => MonadOr m where
  orElse :: m a -> m a -> m a

-- module: TheOtherPrelude.Utilities

import Prelude () -- hide everything

-- this is the if-then-else proposal
-- the name has been chosen to reflect the magic of Church booleans!
boolean True  x _ = x
boolean False _ y = y

-- ''The Other Prelude'' is an alternative, not a replacement.
-- So we need to hide everything from the Prelude
import Prelude ()                                

-- This is just an example assuming there is nothing to hide
import TheOtherPrelude                               

-- Hopefully, this module will contain lift,...
-- Standard convention is to use M.lift (instead of liftM)
import qualified TheOtherPrelude.Monad.Kleisli as M