Nat Representations

(This section assumes you've already gone through the standard library tour. If not, you'll see some functions here with which you're not familiar.)

Bars and Strings

In the intro we briefly covered bars and strings, but it's worth saying a bit more about them here. Because bars are arrays of bytes (which we can interpret as UTF-8), and strings are stored as opaque nats, a bar representation and a string representation that look the same on the surface are not equivalent PLAN values:

=?= b#{a string} {a string}
;; # {ASSERTION FAILURE}

The bar a string is not the same PLAN value as the string a string.

=?= (barNat b#{a string}) {a string}
;; Assertion succeeds

The barNat function will return the bar's string representation, which will indeed be the same nat as an identical string.

Under the Hood of Strings and Nats

showNat %a
{97}

We've already seen how the string a (entered above as %a) is "shown", stringified, as {97}. This is because we use ASCII to encode strings as nats, according to which the "string" %a is actually just the natural number 0x61, or 97 in decimal form.

We can confirm this using hexadecimal notation:

0x61
%a

So what's happening is that when we want to print the string %a, that's actually asking to print the hexadecimal number 0x61, which is the same as the decimal number 97. So we get back the string {97}.

So what does the string aa look like? 97 twice? maybe the sum of 97 + 97...?

showNat %aa
{24929}

Okay, that's surprising! To understand what's going on here, remember that ASCII is typically written in hexadecimal notation since that allows bits to line up neatly with the individual digits. So %aa should be the same as 0x6161, which it seems to be:

0x6161
%aa

And the nat 24929 turns out to be the same value:

24929
%aa

There are two lessons to learn here: one is that at the end of the day, everything is stored as a natural number in memory, but these values can be presented different ways depending on the task at hand. The other is that the REPL can be misleading if you don't track exactly what it's doing.