String Length with Scalars and Vectors in APL

Question

I just started learning APL a couple of weeks ago, so this may sound like a newbie question.

Let B be a string, which in APL terms can be either a scalor or a vector. If it's a scalar, ⍴B returns null rather than the length of the string as I want.

B←'QR'
⍴B ⍝ returns 2

B←'Q'
⍴B ⍝ returns null

I discovered one way around that:

⍴1↓'X',B ⍝ concatenating X and then removing it returns a value of 1

That works, but it seems a little hokey, so I'm wondering if there is a more standard way to find string length.

Is it just me or does this seem a little inconsistent? The tutorial I read said to think of a scalar as a point similar to the way it is in vector algebra. But how is it that concatenating a scalar to a scalar makes a vector, but dropping a scalar from a vector never results in a scalar?

I'm really enjoying APL, so this question isn't meant as criticism. My question is, what's the best way to find string length? And, if anyone can shed a little light on this seeming inconsistency, it would be appreciated.

Answer 1

The reasons that concatenating X and removing it works, is that the catenation produces a vector. Removing X with 1↓ then leaves it as a vector, as an empty vector to be precise. And the length of vectors can be measured with ⍴. That is also what CrazyMetal's solution does: monadic , transforms its argument (scalar or array of any dimension) into a vector. And measuring its rho gives you the answer you were looking for: the standard way to find string length.

⍴,B

Answer 2

The behaviour that you see is caused by an inconsistency in the APL syntax. A sequence of characters enclosed in single-quotes creates an array of those characters. For example, 'foo' creates an array of the characters f, o and o. Calling ⍴ on this array shows the expected result:

      ⍴'foo'
3

However, these is an exception to this rule, and this is where the syntax is inconsistent. When you specify a single character inside the single quotes, you do not create an array of a single character, but rather the character itself is returned. This is why ⍴'f' returns an empty array, since the value is a scalar.

As was suggested by Pé de Leão, you can use the , function to ensure that a scalar value becomes an array which is why using ⍴, works regardless of whether its argument is a scalar or an array.

Because of this inconsistency, GNU APL has an extension that allows you to use " instead of ' when typing strings. The only difference between them is that " always creates an array, even for single characters.