What is recursion and when should I use it?

Answer 1

Any algorithm exhibits structural recursion on a datatype if basically consists of a switch-statement with a case for each case of the datatype.

for example, when you are working on a type

  tree = null 
       | leaf(value:integer) 
       | node(left: tree, right:tree)

a structural recursive algorithm would have the form

 function computeSomething(x : tree) =
   if x is null: base case
   if x is leaf: do something with x.value
   if x is node: do something with x.left,
                 do something with x.right,
                 combine the results

this is really the most obvious way to write any algorith that works on a data structure.

now, when you look at the integers (well, the natural numbers) as defined using the Peano axioms

 integer = 0 | succ(integer)

you see that a structural recursive algorithm on integers looks like this

 function computeSomething(x : integer) =
   if x is 0 : base case
   if x is succ(prev) : do something with prev

the too-well-known factorial function is about the most trivial example of this form.