Introduction to Programming Languages/Partial Application

From Wikibooks, open books for an open world
< Introduction to Programming Languages
Jump to: navigation, search

Partial Application[edit]

In many programming languages, most notably in members of the functional paradigm such as ML and Haskell, every function takes only one argument as an input parameter. For instance, a ML function such as add(x, y) does not receive two parameters, x and y, as one could, at first think. It receives one parameter: the tuple (x, y):

- fun add(x, y) = x + y;
val add = fn : int * int -> int
 
- val t = (2, 3);
val t = (2,3) : int * int
 
- add t;
val it = 5 : int

In order to give developers the illusion that a function takes several parameters, these languages resort to a technique called currying. A curried function such as f(x)(y) takes an argument x, and returns a new function that takes another argument y, and might use the value of x inside its body. As an example, the function below is the curried version of the previous implementation of add:

- fun add_curry x y = x + y;
val add_curry = fn : int -> int -> int
 
- add_curry 2 3;
val it = 5 : int

Usually we do not need to pass all the sequence of arguments expected by a curried function. If we pass only the prefix of this sequence of arguments, then we have a Partial Application. The result of a partial application is normally implemented as a closure. For instance, below we are using our add_curry function as a function factory:

- fun add_curry a b = a + b;
val add_curry = fn : int -> int -> int
 
- val inc = add_curry 1;
val inc = fn : int -> int
 
- inc 2;
val it = 3 : int
 
- val sum2 = add_curry 2;
val sum2 = fn : int -> int
 
- sum2 2;
val it = 4 : int

Closures · Noticeable High-Order Functions