Introduction to Computational Linguistics

6. Sets and Functors 17
write it down twice since the set is written out linearly. In the same way, OCaML
stores sets in a particular way, here in form of a binary branching tree. Next,
OCaML demands from you that you order the elements linearly, in advance. You
can order them in any way you please, but given two distinct elements a and b,
either a < b or b < a must hold. This is needed to access the set, to define set
union, and so on. The best way to think of a set as being a list of objects ordered
in a strictly ascending sequence. If you want to access an element, you can say:
take the least of the elements. This picks out an element. And it picks out exactly
one. The latter is important because OCaML operates deterministically. Every
operation you define must be total and deterministic.
If elements must always be ordered—how can we arrange the ordering? Here
is how.
(45)
module OPStrings =
struct
type t = string * string
let compare x y =
if x = y then 0
else if fst x > fst y || (fst x = fst y
&& snd x > snd y) then 1
else -1
end;;
(The indentation is just for aesthetic purposes and not necessary.) This is what
OCaML answers:
(46)
module OPStrings :
sig type t = string * string val compare :
’a * ’b −> ’a * ’b −> int end
It says that there is now a module called OPString with the following signature:
there is a type t and a function compare, and their types inside the signature are
given. A signature, by the way, is a set of functions together with their types. The
signature is given inside sig· · · end.
Now what is this program doing for us? It defines a module, which is a complete
unit that has its own name. We have given it the name OPStrings. The