Documentation

Monads that also support choice and failure.

The join function is the conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.

guard b is return () if b is True, and mzero if b is False.

Conditional execution of monadic expressions. For example,

       when debug (putStr "Debugging\n")

will output the string Debugging\n if the Boolean value debug is True, and otherwise do nothing.

The reverse of when.

In many situations, the liftM operations can be replaced by uses of ap, which promotes function application.

       return f `ap` x1 `ap` ... `ap` xn

is equivalent to

       liftMn f x1 x2 ... xn

This generalizes the list-based concat function.

This generalizes the list-based filter function.

The mapAndUnzipM function maps its first argument over a list, returning the result as a pair of lists. This function is mainly used with complicated data structures or a state-transforming monad.

The zipWithM function generalizes zipWith to arbitrary monads.

zipWithM_ is the extension of zipWithM which ignores the final result.

The foldM function is analogous to foldl, except that its result is encapsulated in a monad. Note that foldM works from left-to-right over the list arguments. This could be an issue where (>>) and the `folded function' are not commutative.

       foldM f a1 [x1, x2, ..., xm]

==

       do
         a2 <- f a1 x1
         a3 <- f a2 x2
         ...
         f am xm

If right-to-left evaluation is required, the input list should be reversed.

Promote a function to a monad.

Promote a function to a monad, scanning the monadic arguments from left to right. For example,

    liftM2 (+) [0,1] [0,2] = [0,2,1,3]
    liftM2 (+) (Just 1) Nothing = Nothing

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Minimal complete definition: >>= and return.

Instances of Monad should satisfy the following laws:

 return a >>= k  ==  k a
 m >>= return  ==  m
 m >>= (\x -> k x >>= h)  ==  (m >>= k) >>= h

Instances of both Monad and Functor should additionally satisfy the law:

 fmap f xs  ==  xs >>= return . f

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws:

 fmap id  ==  id
 fmap (f . g)  ==  fmap f . fmap g

The instances of Functor for lists, Maybe and IO satisfy these laws.

mapM f is equivalent to sequence . map f.

mapM_ f is equivalent to sequence_ . map f.

Evaluate each action in the sequence from left to right, and collect the results.

Evaluate each action in the sequence from left to right, and ignore the results.

Same as >>=, but with the arguments interchanged.