Most of what you do in programming all day is combining some functions together to build bigger functions from them. Usually you have not only functions in your toolbox but also other things like operators, variable assignments and the like, but generally your program combines together lots of "computations" to bigger computations that will be combined together further.
A monad is some way to do this "combining of computations".
Usually your most basic "operator" to combine two computations together is ;:
a; b
When you say this you mean "first do a, then do b". The result a; b is basically again a computation that can be combined together with more stuff.
This is a simple monad, it is a way of combing small computations to bigger ones. The ; says "do the thing on the left, then do the thing on the right".
Another thing that can be seen as a monad in object oriented languages is the .. Often you find things like this:
a.b().c().d()
The . basically means "evaluate the computation on the left, and then call the method on the right on the result of that". It is another way to combine functions/computations together, a little more complicated than ;. And the concept of chaining things together with . is a monad, since it's a way of combining two computations together to a new computation.
Another fairly common monad, that has no special syntax, is this pattern:
rv = socket.bind(address, port);
if (rv == -1)
return -1;
rv = socket.connect(...);
if (rv == -1)
return -1;
rv = socket.send(...);
if (rv == -1)
return -1;
A return value of -1 indicates failure, but there is no real way to abstract out this error checking, even if you have lots of API-calls that you need to combine in this fashion. This is basically just another monad that combines the function calls by the rule "if the function on the left returned -1, do return -1 ourselves, otherwise call the function on the right". If we had an operator >>= that did this thing we could simply write:
socket.bind(...) >>= socket.connect(...) >>= socket.send(...)
It would make things more readable and help to abstract out our special way of combining functions, so that we don't need to repeat ourselves over and over again.
And there are many more ways to combine functions/computations that are useful as a general pattern and can be abstracted in a monad, enabling the user of the monad to write much more concise and clear code, since all the book-keeping and management of the used functions is done in the monad.
For example the above >>= could be extended to "do the error checking and then call the right side on the socket that we got as input", so that we don't need to explicitly specify socket lots of times:
new socket() >>= bind(...) >>= connect(...) >>= send(...);
The formal definition is a bit more complicated since you have to worry about how to get the result of one function as an input to the next one, if that function needs that input and since you want to make sure that the functions you combine fit into the way you try to combine them in your monad. But the basic concept is just that you formalize different ways to combine functions together.
