1.5 KiB
title |
---|
Monad |
Monad Laws
There are 3 laws which must be satisfied by a data type to be considered as monad
Left Identity
return a >>= f
must equal f a
This states that if we take a value and use return
to put it in default context,
then use >>=
to feed it into a function, it's the same as applying the
function to the original value.
Right Identity
m >>= return
must equal m
This states that if we use >>=
to feed a monadic value into return, we
get back our original monadic value.
Associativity
(m >>= f) >>= g
must equal m >>= (\x -> f x >>= g)
This allows us to chain together monadic function applications, regardless of
how they are nested.
This may seem obvious, and you may assume that it should work by default, but the associative law is required for this behavior
But what about >>=
and return
?
Simple:
>>=
, or 'bind' takes a monad and a function that takes a value and returns a
monad, and applies the function to a monad. This essentially allows us to
manipulate data within monads, which can't be accessed by non-monadic functions.
return
, on the other hand, takes a value and returns a monad containing
that value. Everything you could ever want to know about return
is right
there in the type signature:
return :: a -> m a
Maybe Monad
justHead :: Maybe Char
justHead = do
(x:xs) <- Just ""
return x
List Monad
return is same as pure of applicative
instance Monad [] where
return x = [x]
xs >>= f = concat (map f xs)
fail _ = []