Checking for Palindromes

APL is an old language, and it’s very different from most other languages. It’s an array language: you’re manipulating blocks of data rather than stepping over parts of that block. Think in a similar way to how R is vectorised.

One thing it’s known for is its very terse ways to solve problems. I’m just brushing the surface at the moment but I wanted to share a well known example of APL code to show how powerful it can be. I hope to write more about APL later, but for now here’s how you can check whether a string is a palindrome:

⌽≡⊢

That’s it. Three glyphs.

In use, this is what it looks like:

      (⌽≡⊢)'racecar'
1
      (⌽≡⊢)'risetovotesir'
1
      (⌽≡⊢)'thisisnotapalindrome'
0

(Boolean True/False in APL is shown by 1 or 0).

When you break it down, it’s really simple:

• ⌽ reverses an array, e.g. if you have an array of 1 2 3, ⌽1 2 3 gives you 3 2 1.
• ≡ checks whether two arrays are the same, 1 2 3≡1 2 3 would give you 1 (i.e true), 1 2 3≡3 4 5 would five you 0 (false).
• ⊢ just returns the argument on the right.

The arrangement of these glyphs uses what’s called a “fork”. Essentially when you have three functions in a row acting on some value ⍵, i.e. (fgh)⍵, this expands to (f⍵)g(h⍵).

In our case, we end up with (⌽⍵)≡(⊢⍵) which is equivalent to (⌽⍵)≡(⍵), or in English, “is the reverse of this array equal to the array itself?”.

Wonderful.