|20-CS-4003-001||Organization of Programming Languages||Fall 2018|
class Monad m where return :: a -> m a (>>=) :: m a -> (a -> m b) -> m b (>>) :: m a -> m b -> m b x >> y = x >>= \_ -> y fail :: String -> m a fail msg = error msg
Monads are a type class consisting of at least four operators
return, >>=, >>, and
fail as shown to the left. These and others will be described
in detail later. For now we mention 1) the >>= operator
(called bind) either returns "Nothing" if it is passed "Nothing" as it's
1st argument; or if it's 1st argument is a "Just ..." it
strips off the Just, and passes the contents into the function supplied
as it's 2nd argument; 2) the return operator takes a value
from a plain type and puts it into a monadic container (that is, does
the opposite of >>; 3) the >> operator
is essentially the same as >>=, but does not pass the
contents of the monad to the function specified as 2nd argument; 4)
the fail operator is used when a condition is not satisfied.
The operator filerM filters out all elements of 2nd argument
xs that do not fulfill the 1st argument predicate p,
where p is a function that returns a value of type
The operator foldM is the monadic version of foldl:
that is, it takes a function of type
The operator guard returns () if its argument is True, otherwise it returns mzero. The value of v13 is Just 3 and the value of v14 is Nothing.
The operator liftM lets a non-monadic function (1st argument)
operate on the contents of a monad (2nd argument). To the left,
v15 has value Just 23 and v16 has value
Just [24,25]. The type of liftM is
The operator mapM applies a monadic function (1st argument)
The operator mzero is the zero of the MonadPlus class.
To the left, the value of v17 is  and the value of
v18 is Nothing. Its type is
The operator mplus is the plus of the MonadPlus class. To the left, v19 has value "ab", v20 has value Just "a", v21 has value Just 10, v22 has value Just 10, v23 has value Just 10.
The operator sequence evaluates all monadic values in the
input list from left to right and returns a list of the "contents" of
these monads, placing this list in a monad of the same type.
Evaluating can be interpreted as "performing an action", for example
in the case of print. To the left v27 displays
The operator unless executes a monadic expression (2nd
argument) when the first argument evaluates to False.
Looking at v29 shows "OK". The type of
The operator when executes a monadic expression (2nd argument)
when the first argument evaluates to True.
Looking at v30 shows "OK". The type of when is
Monads are useful in any situation where the programmer wants to carry out a purely functional computation while a related computation is carried out on the side. In imperative programming the side effects are embedded in the semantics of the programming language; with monads, they are made explicit in the monad definition, thus avoiding errors by action at a distance.