Would BlooP allow for chained arrow notation, or would it be too restrictive for that?
Sadly, you need more than that: chained arrows can express the Ackermann function, which isn’t primitive recursive. But I guess you don’t really need them. Even if you just have Knuth’s up-arrows, and no way to abstract over the number of up-arrows, you can just generate a file containing two threes with a few million up-arrows sandwiched between them, and have enough compute for most purposes (and if your program still times out, append the file to itself and retry).
Sadly, you need more than that: chained arrows can express the Ackermann function, which isn’t primitive recursive. But I guess you don’t really need them. Even if you just have Knuth’s up-arrows, and no way to abstract over the number of up-arrows, you can just generate a file containing two threes with a few million up-arrows sandwiched between them, and have enough compute for most purposes (and if your program still times out, append the file to itself and retry).