In order to understand future examples, we first have to discuss how to use higher-order functions in Java, and how to write anonymous inner classes. This post will have nothing to do with multi-stage programming.

Let’s write a program that can print out data tables for different mathematical functions. For example, for a function that multiplies by two, *f(x) = 2x*, we want to print something like this:

x f(x) -5.0000000000 -10.0000000000 -4.0000000000 -8.0000000000 -3.0000000000 -6.0000000000 -2.0000000000 -4.0000000000 -1.0000000000 -2.0000000000 0.0000000000 0.0000000000 1.0000000000 2.0000000000 2.0000000000 4.0000000000 3.0000000000 6.0000000000 4.0000000000 8.0000000000 5.0000000000 10.0000000000

We can write a function like this:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | public static void printTableTimesTwo(double x1, double x2, int n) { assert n>1; double x = x1; double delta = (x2-x1)/(double)(n-1); System.out.println("x f(x)"); System.out.printf("%20.10f %20.10f\n", x, x*2); for(int i=0; i<(n-1); ++i) { x += delta; System.out.printf("%20.10f %20.10f\n", x, x*2); } } |

The parameter `x1`

determines the lower end of the interval, `x2`

the upper end, and `n`

determines how many values should be printed. `n`

needs to be at least `2`

to print out the values at `x1`

and `x2`

. We can generate the table above with this call:

1 | printTableTimesTwo(-5, 5, 11); |

What if we want to print out the values of a different function, for example f(x) = x + 4? We can write a new function:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | public static void printTablePlusFour(double x1, double x2, int n) { assert n>1; double x = x1; double delta = (x2-x1)/(double)(n-1); System.out.println("x f(x)"); System.out.printf("%20.10f %20.10f\n", x, x+4); for(int i=0; i<(n-1); ++i) { x += delta; System.out.printf("%20.10f %20.10f\n", x, x+4); } } |

This involves a lot of code duplication, though. The only parts that actually differ are the two occurrences of `x*2`

and `x+4`

. How can we factor that difference out?

Let’s write an interface that we can use for any kind of function that takes in one parameter and returns one parameter *f(x) = y* is an example of such a function.

1 2 3 | public interface ILambda<R,P>; { public R apply(P param); } |

This interface is called `ILambda`

and it has one method, `apply`

. We used Java generics and didn’t specify the return type and the type of the parameter; instead, we just called them `R`

and `P`

, respectively. A function that takes in a `Double`

and that returns a `Double`

, like *f(x) = y*, can be expressed using a `ILambda<Double,Double>`

. A function taking a `String`

and returning an `Integer`

would use `ILambda<String,Integer>`

.

Now we can write our *f(x) = 2x* and *f(x) = x + 4* functions using `ILambda`

:

1 2 3 4 5 6 |

Now we can write one `printTable`

method that takes in an `ILambda<Double,Double>`

called `f`

representing the function, in addition to the parameters `x1`

, `x2`

and `n`

, as before:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | public static void printTable(ILambda<Double,Double> f, double x1, double x2, int n) { assert n>1; double x = x1; double delta = (x2-x1)/(double)(n-1); // f.apply(x) just means what f(x) means in math! double y = f.apply(x); System.out.println("x f(x)"); System.out.printf("%20.10f %20.10f\n", x, y); for(int i=0; i<(n-1); ++i) { x += delta; y = f.apply(x); System.out.printf("%20.10f %20.10f\n", x, y); } } |

Note that when we want to print out the y-value, we just write `f.apply(x)`

, which looks very similar to f(x) in mathematics. It means exactly the same.

We can print out the tables for our two functions using:

1 2 | printTable(new TimesTwo(), -5, 5, 11); printTable(new PlusFour(), -5, 5, 11); |

We have to create new objects for the functions: The first time we call `printTable`

we pass a new `TimesTwo`

object; the second time, we pass a new `PlusFour`

object.

We can now define as many functions as we like without having to rewrite the `printTable`

function. For example, we can easily write a square root function and use it very easily:

1 2 3 4 5 6 7 8 9 |

The really neat thing is that we can even define a new function on-the-fly, without having to give it a name. We do that using anonymous inner classes in Java. Here, we call `printTable`

and pass it a new object that implements `ILambda<Double,Double>`

.

1 2 3 4 5 |

We define a new `ILambda`

from `Double`

to `Double`

without giving it a name. When we use anonymous inner classes, we need to fill in all the methods that are still abstract. Here, it is just the `apply`

method.

The method `printTable`

is now a “higher order function”, because conceptually it is a function that takes another function as input.

Questions:

- What does the anonymous
`ILambda<Double,Double>`

in the example above compute? What’s the mathematical function it represents? - How would you print a table for the function
*f(x) = x*?^{2}+ 2x

You can download the complete source code for the examples here:

`HigherOrder1.java`

: Example without`ILambda`

`HigherOrder2.java`

: Example with`ILambda`

`ILambda.java`

:`ILambda`

interface for the`HigherOrder2.java`

example

(Re-posted from The Java Mint Blog)