Packages' Builder

B. Standard Lists' operations

4. Recall what is the definition of reduce function on lists.
5. With the preceding function, implements the standard operators/functions:
   • (@) that catenates two lists: [1;2]@[3;4]=[1;2;3;4]
   • map f that applies f to all the values of a list: map ((+) 1) (1<>4)=2<>5
6. reduce is interesting to transforms binary operators into n-ary ones. For instance, how to:
   • sum all the values of a list by using reduce
   • join all the lists of a list
   • get the length of a list
7. With p:'t->bool, to what function corresponds the following expression ?
   join (map (fun x->if (p x) then [x] else []) xs)
8. list is an example of what is called a "monad", a mathematical concept (functor) with two operations called "return" and "bind" (:a kind of composition operator). In particular, return/bind can be defined as follow:

let ret   x    = [x];;
let (>>=) xs f = join (map f xs);;

With these definitions, give the result of the following program ?

(1<>4) >>= fun i -> 
(1<>4) >>= fun j -> 
if (i<=j) then ret (i<>j) else [];;

Can you give a sample use of such a program ?

answers