Introduction to Computational Linguistics

5. Modules 15
let length l = length_aux 0 l
First, the function is defined via an auxiliary function. You expect therefore to
be able to use a function List.length_aux. But you cannot. The answer to
the puzzle is provided by the file list.mli. Apart form the commentary (which
OCaML ignores anyway) it only provides a list of functions and their types. This
is the type interface. It tells OCaML which of the functions defined in list.ml
are public. By default all functions are public (for example, if you did not make
a type interface file). If a type interface exists, only the listed functions can be
used outside of the module. The second surprise is the definition of the function
length_aux. It uses only one argument, but at one occasion uses two! The
answer is that a function definition of the form let f x = specifies that x is
the first argument of f , but the resulting type of the function may be a function
and so take further arguments. Thus, unless you have to, you need not mention
all arguments. However, dropping arguments must proceed from the rightmost
boundary. For example, suppose we have defined the function exp x y, which
calculates x y . The following function will yield [5; 25; 125] for the list [1;2;3]:
(39) let lexp l = List.map (exp 5) l
You may even define this function as follows:
(40) let lexp = List.map (exp 5)
However, if you want to define a function that raises every member of the list to
the fifth power, this requires more thought. For then we must abstract from the
innermost argument position. Here is a solution:
(41) let rexp = List.map (fun y -> exp y 5)
A more abstract version is this:
(42)
let switch f x y = f y x;;
let lexp = List.map ((switch exp) 5)
The function switch switches the order of the function (in fact any function). The
so defined reversal can be applied in the same way as the original, with arguments
now in reverse order.