Advanced APL: Comprehensions and Tacit Programming

October 1, 2024

Advanced APL: Comprehensions and Tacit Programming

In this lesson, we delve into advanced APL concepts that can significantly enhance your coding skills: array comprehensions and tacit programming. These techniques not only make your code more concise but also increase its expressiveness, allowing you to accomplish more with less.

Array Comprehensions

Array comprehensions in APL provide a powerful way to generate arrays in a succinct manner. They allow you to create new arrays by applying functions to existing arrays, all within a single expression. The general syntax for an array comprehension is:

result ← {function} array

Here’s a simple example of using an array comprehension to generate the squares of numbers from 1 to 5:

squares ← {⍵*2} 1 2 3 4 5

This will yield:

1 4 9 16 25

Array comprehensions can also include conditional logic. For instance, if we want to generate the squares of only even numbers from 1 to 10, we can use the following syntax:

evenSquares ← {⍵*2 | ⍵ mod 2 = 0} 1 2 3 4 5 6 7 8 9 10

In this case, the result will be:

4 16 36 64

Tacit Programming

Tacit programming, also known as point-free style, is another advanced technique in APL. It allows you to define functions without explicitly mentioning their arguments. This can lead to more elegant and often shorter code. The key to tacit programming is understanding how to compose functions together.

For example, consider the following explicit function that adds two numbers:

add ← {⍺ + ⍵}

In tacit style, we can define the same addition operation without mentioning the arguments:

addTacit ← +

Now, let’s see how we can use tacit programming to create a function that adds and then squares two numbers:

addAndSquare ← {(+ ⍵) * 2}

This can be rewritten in a tacit style as:

addAndSquareTacit ← {⍵ * 2} ∘ +

Here, we are using the composition operator (∘) to combine the addition and squaring operations.

Combining Comprehensions and Tacit Programming

One of the most powerful aspects of APL is the ability to combine array comprehensions with tacit programming. This can lead to highly expressive one-liners that perform complex operations. For instance, if we want to compute the cubes of the squares of even numbers from 1 to 10, we can do it like this:

cubesOfEvenSquares ← {⍵*3} ∘ {⍵*2 | ⍵ mod 2 = 0} 1 2 3 4 5 6 7 8 9 10

This results in:

64 4096 13824

In this example, we first apply the array comprehension to get the squares of even numbers, and then we apply the tacit function to cube the results.

Conclusion

In this post, we explored advanced APL concepts such as array comprehensions and tacit programming. By mastering these techniques, you can write more concise and expressive APL code, making your programming experience more enjoyable and efficient. Experiment with these concepts in your own projects and see how they can simplify your code!