There is also https://stitch-maps.com/ which semi-pictorially shows the effect of a knitting pattern on the shape of the resulting fabric.

I haven't tried writing a knitting interpreter, even though that it extremely within the Venn diagram intersection of my interests. I have spent some time thinking about trying to formalizing knitting pattern notation. Right now, it's, like mostly there, but every pattern tweaks things in ways that are often arbitrary and confusing.

Knitting patterns are an interesting programming language. Ignoring the resulting fabric for a moment, one way to think of them is that they are an encoding of a linear series of steps the knitter is supposed to perform.

As any programmer knows, there are a whole bunch of possible programs that produce the same output:

    print(1)
    print(2)
    print(3)
    print(4)
    print(5)

Versus:

    for (i from 1 to 5):
      print(i)

One of the challenges of designing a knitting pattern is coming up with a good encoding for the series of stitches to be created. You might think that the shortest encoding is best, but what you're really trying to optimize for is how easy is it mentally keep track of where you are.

A knitting pattern that, say, has deeply nested loops, can require the knitter to hold multiple indexes in their head (or using external counters) and increases the odds of making a mistake. Unrolled some of those loops manually might be more verbose but less error prone. Or not! Maybe the extra verbosity of the long list of stitches makes it easier to lose your place.

Even things like choosing where to place stitch markers can have an effect on how user-friendly the pattern is.

It's an interesting design problem. You're trying to design a set of instructions to produce a good object, but you're also trying to design a set of instructions that yield a good experience producing that object.