On Fri, 7 Jul 2017 01:41 am, Marko Rauhamaa wrote: > Here's how identity is dealt with in First-Order Logic: > > <URL: https://en.wikipedia.org/wiki/First-order_logic#Semantics> > > In other words, identity is mapped to the "sameness" in a domain of > discourse.
Define "sameness". > In Second-Order Logic, you can define identity directly: > > ∀x ∀y x = y ↔ ∀P (P(x) ↔ P(y)) Translating to English: For all x, for all y, x equals y if and only if for all P (P(x) if and only if P(y)) That might be sufficient for second-order logic, but it won't do for programming. Defining if-and-only-if for functions that can return more than two values (true and false) requires having a definition of equality, which would make the definition circular. And what if there exists even a single non-deterministic function, or one that has hidden variables that may change state, or a constant function that always returns the same value? Such things are forbidden in second order logic but they exist in many programming languages. > Programming languages are different beasts, of course, but "objects" and > "identity" are such important foundational topics that you'd expect a > bit more than hand-waving when defining the data model. I wouldn't. I don't think identity is even capable of vigorous definition outside of pure mathematics, and even if it is, I don't see how it would make anyone a better programmer to have such a definition. In practice, identity is hardly important in Python, except for a few limited cases, and the prohibition against using `is` when you mean `==`. > As a good example of the style I'm looking for, take a look at: > > <URL: https://docs.oracle.com/javase/specs/jls/se7/html/jls-17.html> Neither the word "identity" nor "identical" exists on that page, so I don't see how that solves your problem. -- Steve “Cheer up,” they said, “things could be worse.” So I cheered up, and sure enough, things got worse. -- https://mail.python.org/mailman/listinfo/python-list
