So actually it looks like I need to understand type theory to understand this.
Thanks, Mohan On Sep 7, 7:04 pm, Nicolas Oury <nicolas.o...@gmail.com> wrote: > > ...and report your findings here or blog somewhere if you don't mind > > :) I've been reading a lot about monads lately and can't get my head > > around it yet so any help appreciated (I'm coming from Java and > > Clojure is my first real functional language - that's why it causes > > headaches, I believe). > > I have no blog so I will try an explanation here. > I think monad are quite difficult to grasp, so the more different > explanations you read, the better. > Monads are made to represent computations in an abstract way. > Sometimes the basic computation laws are not those you want > and then you want to introduce other computation laws. > Monad is one way to do so (among other like applicative functors or > Kieisli arrows) > Monad corresponds to the computations that are best described as an > imperative program. > > So a monad is a type transformer: M<A> for all A , in Java words. > Something of type M<A> is a computation in the world of computation M > that returns values of type A. > > (M for example can be > IO: the computations that do input/outputs to find their results, > State: the computations that use a and update an internal state > List: more surprisingly, the non-deterministic computations: each > computation yeilds a list of possible results) > > There are a few operators you need for a monad: > - return : A -> M<A> . It says that any computation model must be able > to handle the lack of computation. "Do nothing and return this value" > - bind : M<A> -> (A -> M<B>) -> M<B> > "If I give you a computation that gives back values in A and for each > values in A I tell you how to compute a value in B, > then you can compute a value in B. " > That's a strong assumption, because it allows to use the whole power > of Clojure to construct a computation from the result of the first > computation. > Some model of computations are more restrictive than monad on that. > > From this two operators you can define two others: > - map : (A -> B) -> M<A> -> M<B> > "If I give you a function from A to B, then you can transform a > computation that returns value in A in computation that returns values > in B." > (map f compA = (bind compA (fn [x] (return (f x))))) > > - join : M<M<A>> -> M<A> > "I can run a subprogram" This is again something quite specific to > monad as computation devices. (Bind can be constructed from join and > map) > They are dynamic programs that can compute a program and run it. > join compMA = (bind compMA identity) > > bind compA f = (join (map f compA)) > > All these operators must respect some laws, that are quite natural. > Like returning a value and starting a computation is the same as starting a > computation directly from the value: > > - (bind (return a) f) = (f a) > > .... > > To work out an example, the state monad is a computation that can use > and modify a state, so: M<A> = S -> [S, A] . I need a state and return > a new state and a value A. > return a = (fn [s] -> [s a]) > bind compA f = > (fn [s1] -> > ; we give the state to the first comutation > (let [[s2 a] (compA s1) > ; we compute the next computation > compB (f a)] > ; we give the state to the second computation > (compB s2))) > > Hope that helps. > > Nicolas. -- You received this message because you are subscribed to the Google Groups "Clojure" group. To post to this group, send email to clojure@googlegroups.com Note that posts from new members are moderated - please be patient with your first post. To unsubscribe from this group, send email to clojure+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/clojure?hl=en
