Concepts of Programming Languages

706 Chapter 15 Functional Programming Languages

ML has a binary operator for composing two functions, o (a lowercase

“oh”). For example, to build a function h that first applies function f and then

applies function g to the returned value from f, we could use the following:

val h = g o f;

Strictly speaking, ML functions take a single parameter. When a func-

tion is defined with more than one parameter, ML considers the parameters

to be a tuple, even though the parentheses that normally delimit a tuple value

are optional. The commas that separate the parameters (tuple elements) are

required.

The process of currying replaces a function with more than one parameter

with a function with one parameter that returns a function that takes the other

parameters of the initial function.

ML functions that take more than one parameter can be defined in curried

form by leaving out the commas between the parameters (and the delimiting

parentheses).^11 For example, we could have the following:

fun add a b = a + b;

Although this appears to define a function with two parameters, it actually

defines one with just one parameter. The add function takes an integer param-

eter (a) and returns a function that also takes an integer parameter (b). A call

to this function also excludes the commas between the parameters, as in the

following:

add 3 5;

This call to add returns 8 , as expected.

Curried functions are interesting and useful because new functions can be

constructed from them by partial evaluation. Partial evaluation means that the

function is evaluated with actual parameters for one or more of the leftmost

formal parameters. For example, we could define a new function as follows:

fun add5 x = add 5 x;

The add5 function takes the actual parameter 5 and evaluates the add function

with 5 as the value of its first formal parameter. It returns a function that adds 5

to its single parameter, as in the following:

val num = add5 10;

The value of num is now 15. We could create any number of new functions

from the curried function add to add any specific number to a given parameter.

11. This form of functions is named for Haskell Curry, a British mathematician who studied them.