This is one of the reasons I included all arithmetic operations in ax:
https://github.com/mnemnion/ax/blob/master/ax%20spec.md
Also because once you say 'natural number', the arithmetic operations are already in scope, so to speak.
https://github.com/mnemnion/ax/blob/master/ax%20spec.md
Also because once you say 'natural number', the arithmetic operations are already in scope, so to speak.
Not that there's anything wrong with defining a language that is usable out of the box, but at the same time muh intellectual purity.
A spec which includes the term 'natural numbers' but not subtraction might even be argued to be incomplete, rather than minimal. Ymmv.
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.