בתאריך יום ג׳, 19 במרץ 2019, 0:41, מאת Greg Ewing < greg.ew...@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. Elazar
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