From this excellent post by Mike Vanier,
One of the key concepts in Haskell
that sets it apart from other
programming languages is the concept
of a "monad". People seem to find this
difficult to learn (I did as well),
and as a result there are loads of
monad tutorials on the web, some of
which are very good (I particularly
like All About Monads by Jeff
Newbern). It's even been said that
writing a monad tutorial is a rite of
passage for new Haskell programmers.
However, one big problem with many
monad tutorials is that they try to
explain what monads are in reference
to existing concepts that the reader
already understands (I've even seen
this in presentations by Simon
Peyton-Jones, the main author of the
GHC compiler and general Haskell grand
poobah). This is a mistake, and I'm
going to tell you why.
It's natural, when trying to explain
what something is, to explain it by
reference to things the other person
already knows about. This works well
when the new thing is similar in some
ways to things the other person is
familiar with. It breaks down utterly
when the new thing is completely out
of the experience of the person
learning it. For instance, if you were
trying to explain what fire is to a
caveman who had never seen a fire,
what would you say? "It's kind of like
a cross between air and water, but
hot..." Not very effective. Similarly,
explaining what an atom is in terms of
quantum mechanics is problematic,
because we know that the electron
doesn't really orbit around the
nucleus like a planet around a star,
and the notion of a "delocalized
electron cloud" doesn't really mean
much. Feynman once said that nobody
really understood quantum mechanics,
and on an intuitive level that's true.
But on a mathematical level, quantum
mechanics is well-understood; we just
don't have a good intuition for what
the math really means.
How does this relate to monads? Time
and again, in tutorials, blog posts
and on the Haskell mailing lists, I've
seen monads explained in one of two
supposedly-intuitive ways: a monad is
"kind of like an action" or "kind of
like a container". How can something
be both an action and a container?
Aren't these separate concepts? Is a
monad some kind of weird "active
container"? No, but the point is that
claiming that a monad is a kind of
action or a kind of container is
incorrect. So what is a monad, anyway?
Here's the answer: A monad is a
purely abstract concept, with no
fundamental relationship to anything
you've probably ever heard of
before. The notion of a monad comes
from category theory, which is the
most abstract branch of mathematics I
know of. In fact, the whole point of
category theory is to abstract out all
of the structure of mathematics to
expose the similarities and analogies
between seemingly disparate areas (for
instance, between algebra and
topology), so as to condense
mathematics into its fundamental
concepts, and thus reduce redundancy.
(I could go on about this for quite a
while, but I'd rather get back to the
point I'm trying to make.) Since I'm
guessing that most programmers
learning Haskell don't know much about
category theory, monads are not going
to mean anything to them. That doesn't
mean that they need to learn all about
category theory to use monads in
Haskell (fortunately), but it does
mean that they need to get comfortable
thinking about things in a more
abstract way than they are probably
used to.
Please go to the link at the top of the post to read the full article.
