You can synthesize subtraction from recursion and addition. Peano numbers really only have successor, but is still a valid encoding.
Really, you aren't wrong. But then how would we be able to advertise how stupid Nock is for those sweet internet points? It can't even do subtraction! Come see, tickets one dollar!
Addition is kinda the prime operation that is needed - everything else can be dissolved into it, but without it the jet system doesn't hold up because your language can't really /do/ anything. If you didn't require jets to be transparent to the reduction, you could just have /all/ operations be jets and not even pretend Nock was useful without them.
Check out https://github.com/tibru/tibru No primitive arithmetic operations at all, no need for jets but the same time complexity as arithmetic in C just with a higher constant factor.
Really, you aren't wrong. But then how would we be able to advertise how stupid Nock is for those sweet internet points? It can't even do subtraction! Come see, tickets one dollar!
Addition is kinda the prime operation that is needed - everything else can be dissolved into it, but without it the jet system doesn't hold up because your language can't really /do/ anything. If you didn't require jets to be transparent to the reduction, you could just have /all/ operations be jets and not even pretend Nock was useful without them.