Another alternative: the Nam-Shub of Enki, in Neal Stephenson's Snow Crash.Here, the conceptual basis of a 'spell' is that the Sumerians were aware of a foundational language (an Ur-language, if you will) or an 'Assembly Code' layer of cognition which can be compiled or scripted from repetitive phrases and recursive narratives uttered (or heard) in the correct tones and rhythm.A properly constructed Nam-Shub programs the individual: their loyalty, or motivation, or their actions in surprisingly complex directions for agricultural labour. It is binding on the subject - or subjects, a labour gang or an entire village - and it may be permanent; or it may require reinforcement in a daily chant led by the village priest.
Mmmm. That one did spring to my mind while I was making notes towards this post, but I discarded it for not quite being magical in the sense of supernatural. If I'd left it in, I probably would have considered it to be an honorary member of the 'one true Language Of Magic' category; that's where I had it listed in my notes.But now you point it out, I suppose it does count as different, because the Language Of Magic in this case is not a property of the universe as a whole, but rather it's a property of the people at whom you're aiming the spell. If the human race of Snow Crash made contact with aliens, then the question would doubtless arise of whether the aliens had a similar cognitive substructure with an analogous back door; and if they did, then (barring some exceptionally implausible cosmic coincidence) there'd be a different language of magic depending on who you were aiming the magic at – which puts it outside all my categories in which the LoM is universal, or varies with the caster, or with the location. This one would vary with the victim!
Yes, I think your argumenrt stands up: there won't be a common 'programming language'......Unless 'cognition' is a very special, well-defined, unique algorithm. I consider that unlikely, but I could explore some ideas around it:among them, a fairly high probability that there's a universal 'stop' or 'factory reset' command.