Differentiable Programming Mega-Proposal

Firstly: Swift is a formal language based on the natural language English. Every single standard library function, including argument labels. But not only that, even if we exclude the standard library, and look at the core language, even then we can clearly see that Swift is based on English. We use words such as class, func, as, try, do, catch, throws, let, etc. Swift is English, whether we like it or not. And differentiable functions, is a mathematical concept. Whatever we call it, should be based on standard mathematical terminology in English.

Secondly: With respect to is a term of art, and has been used in mathematics since Leibniz' time. In other languages, there may be other phrasings (e.g in my mother language Norwegian, we say "den x-deriverte av f", literally "the x-derivative of f"). But still, in English it is a term of art.

Thirdly: Words such as "by" or "in" have different meanings in mathematics, which may be confusing. A function can e.g. be differentiable in a range or domain, or in some neighbourhood of a point.

I'm fine with spelling it out, but to replace it with another term would almost certainly be more confusing at best, and incorrect at worst.

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