[Python-ideas] Why operators are useful

Elazar elazarg at gmail.com
Mon Mar 18 18:56:56 EDT 2019

בתאריך יום ג׳, 19 במרץ 2019, 0:41, מאת Greg Ewing ‏<
greg.ewing at canterbury.ac.nz>:

> Rémi Lapeyre wrote:
> > You can make "inferences from the way things are used". But the
> > comparison with maths stops here, you don’t make such inferences because
> your
> > object must be well defined before you start using it.
> In maths texts it's very common to see things like 'Let y = f(x)...'
> where it's been made clear beforehand (either explicitly or implicitly)
> what type f returns.
> That's completely analogous to inferring the type bound to a Python
> name from an assignment statement.
>  > You can track types with
> > comments but you need to comment each line.
> No, you don't, because most lines in most programs allow types to
> be inferred. The reason that things like MyPy are possible and
> useful is that Python programs in practice are usually well-typed.
> > In maths, an given object is not duck because it quacks and walks like
> > a duck, it’s
> > either part of the set of all ducks, or not.
> But there's no restriction on how you define the set of all ducks.
> It could be "the set of all things that quack". Duck typing is
> totally possible in mathematics, even common.
> For example, in linear algebra the ducks are "anything you can
> apply a linear operator to". That can cover a surprisingly large
> variety of things.
> > But the equation is only meaningful in a given context. Asking whether
> > f: x -> 1/x
> > is differentiable is only meaningful if we know whether x is in R, C,
> > [1; +oo[...
> That depends on what you want to say. You can say "let f be a
> differentiable function" and then go on to talk about things that
> depend only on the differentiability of f, without knowing
> exactly what types f operates on. Then later you can substitute
> any function you know to be differentiable, and all of those
> thing will be true for it.
> Mathematicians abstract things this way all the time. Groups,
> fields, vector spaces, etc. are all very abstract concepts,
> defined only as a set of objects having certain properties.
> If that's not duck typing, I don't know what is.

Technically, that's structural typing. Duck typing is only relevant when
there is some kind of control flow, and things need not always have all the
properties in question.

But I don't think this difference is that important in the context.

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