On Sun, Dec 25, 2016 at 7:30 PM, Adam Nemecek <[email protected]> wrote:
> > Is it well settled, either in Swift or in C++/Rust/etc., that the value > returned by a default initializer/constructor is regarded as an identity > element or zero? > > Int() == 0, String() == "" so to some extent by convention, a lot of types > have a default value as is. > Yes, those particular types have initializers that take no arguments. That does not address my question. You merely restated your initial observation that many types in Swift have implemented `init()`. I didn't think the value returned by `init()` was regarded as any sort of zero--or even any sort of "default." In fact, some types in Foundation have a static property called `default` distinct from `init()`. In Rust, the Default trait requires a function called `default()`, which is documented as being useful when you want "some kind of default value, and don't particularly care what it is." I was asking whether there's some understanding, of which I've been unaware, that the result of `init()` (or the equivalent in other languages) is expected to be some sort of zero or an identity element. I'm not aware of any evidence to that effect. Are you? > Is the thread that I get by writing `let t = Thread()` some kind of zero > in any reasonable sense of the word? > > DefaultConstructibility makes less sense for types that represent some > sort of resource but make sense for things that are values. But even in > this case, Thread() gives you a default value for example if you are > working with a resizable collection of threads. > It gives you something different every time. How can this be squared with your stated motivation regarding concepts of zero and concepts of equality? A better question is why does thread currently implement a default > constructor? > It's an initializer that takes no arguments, because none are needed for a new thread. How else would you write it? > Do you mean to argue that for an integer the additive identity should be > considered "more prominent and useful" than the multiplicative identity? > I'm not aware of any mathematical justification for such a conclusion. > > I do. The justification is that if I call the default constructor of Int > currently, I get the value of 0. > This is backwards. Why do you believe that the value you obtain from `init()` is intended to be an identity element at all, let alone the most important one? (It's also circular reasoning. Since `init()` only ever gives you one value at a time, by your reasoning it demonstrates that every type must have one "more prominent and useful" identity, which is begging the question.) Which means that the binary operation must be addition. > Based on the value of `Int.init()`, you conclude that addition of integers is a "more prominent and useful" operation than multiplication? Again, this is backwards. Rather, we know that each numerical type belongs to multiple ring algebras; there is no basis for reckoning any as "more useful." Since `init()` can only ever give us one value at a time, we know that `init()` cannot give a value that is a meaningful default with respect to any particular operation. If I call String() I get "" which is the identity of the + String operation. > Or, it's what you get because that's the most trivial possible string. Quite simply, I do not think the designer of most types that implement `init()` have paused to wonder whether the value that you get is the identity element associated with the most useful and prominent operation that can be performed on that type. I certainly never have. > Going to your original example, I should add: other languages provide a > version of `reduce` that doesn't require an initial result (for instance, > JavaScript). In JavaScript, `[1, 2, 3].reduce((a, b) => a + b)` uses the > element at array index 0 as the initial result, and the accumulator > function is invoked starting with the element at array index 1. This is > precisely equivalent to having `reduce` use the additive identity as the > default initial result when + is the accumulator function and the > multiplicative identity when * is the accumulator function (with the > accumulator function being invoked starting with the element at array index > 0). It does not require a DefaultConstructible protocol. What more > ergonomic solution could be implemented using a monoidic wrapper type? > > These two will have different signatures. The reduce you describe returns > an optional, > The statement I wrote was in JavaScript, so I'm not sure what you mean by returning an optional. `[].reduce((a, b) => a + b)` results in an error in JavaScript. In Swift, such a function may also be implemented with a precondition that the array is not empty and would not return an optional. the other one would returns the default value. > In what scenario would you prefer to propagate a default after reducing a potential empty collection _without supplying an explicit default_ for that operation? This would certainly violate the Swift convention of not defaulting to zero and, I suspect, most users of Swift would not regard that as ergonomic at all. > Fundamentally the default constructibles are useful in numerical > computations e..g. dealing with tensors. > Can you give an example of an algorithm dealing with tensors where you would use a `DefaultConstructible` generic over all types that have `init()`, as opposed to working with the existing `Integer`, `FloatingPoint`, and other numerical protocols? (I should also add, FWIW, I have never seen a generic algorithm written for integers or FP types that has preferred the use of `T()` over `0`.) On Sun, Dec 25, 2016 at 3:30 PM, Xiaodi Wu <[email protected]> wrote: > >> On Sun, Dec 25, 2016 at 5:27 PM, Adam Nemecek <[email protected]> >> wrote: >> >>> > *Which* APIs become more ergonomic? >>> >>> I'll get back to this question in a second if I may. This would be a >>> longer discussion and I first want to make sure that before we get into the >>> details that there is a possibility of this being introduced (I'm asking if >>> violating the no zero defaults is more important than slightly more >>> ergonomic APIs). But to give a broad answer I think that the concept of a >>> zero is closely related to the concept of equality (and all the things that >>> build up on equality such as comparability and negation). >>> >>> > 1) How does this square with Swift’s general philosophy to not >>> default initialize values to “zero”? >>> >>> I actually wasn't aware of this philosophy. Despite this philosophy, >>> look at how many types actually currently implement a default constructor. >>> >> >> (Not a rhetorical question:) Is it well settled, either in Swift or in >> C++/Rust/etc., that the value returned by a default initializer/constructor >> is regarded as an identity element or zero? Is the thread that I get by >> writing `let t = Thread()` some kind of zero in any reasonable sense of the >> word? >> >> >>> Also can I ask what's the motivation behind this philosophy? >>> I think that in Swift, default constructibility makes complete sense for >>> (most?) structs, maybe less so for classes. >>> >>> > 2) To your original example, it isn’t immediately clear to me that >>> reduce should choose a default identity. Some types (e.g. integers and FP) >>> belong to multiple different ring algebras, and therefore have different >>> identity values that correspond to the relevant binary operations. >>> >>> This is a good point that I've considered as well but felt that for the >>> most part, there is one particular identity and associated operation that >>> is more prominent and useful than others. Furthermore, modeling different >>> algebras isn't mutually exclusive with writing generic algorithms that rely >>> on this protocol, you can always introduce some monoidic wrapper type that >>> defines the more appropriate default value and operation. >>> >> >> Do you mean to argue that for an integer the additive identity should be >> considered "more prominent and useful" than the multiplicative identity? >> I'm not aware of any mathematical justification for such a conclusion. >> >> Going to your original example, I should add: other languages provide a >> version of `reduce` that doesn't require an initial result (for instance, >> JavaScript). In JavaScript, `[1, 2, 3].reduce((a, b) => a + b)` uses the >> element at array index 0 as the initial result, and the accumulator >> function is invoked starting with the element at array index 1. This is >> precisely equivalent to having `reduce` use the additive identity as the >> default initial result when + is the accumulator function and the >> multiplicative identity when * is the accumulator function (with the >> accumulator function being invoked starting with the element at array index >> 0). It does not require a DefaultConstructible protocol. What more >> ergonomic solution could be implemented using a monoidic wrapper type? >> >> >> On Sun, Dec 25, 2016 at 1:24 PM, Chris Lattner <[email protected]> >>> wrote: >>> >>>> On Dec 25, 2016, at 12:54 PM, Adam Nemecek via swift-evolution < >>>> [email protected]> wrote: >>>> >>>> Does enabling a lot of small improvements that make APIs more ergonomic >>>> count as practical? >>>> >>>> >>>> Yes, that would count as practical, but Xiaodi’s question is just as >>>> important. *Which* APIs become more ergonomic? >>>> >>>> Here are a couple of more questions: >>>> >>>> 1) How does this square with Swift’s general philosophy to not default >>>> initialize values to “zero”? >>>> >>>> 2) To your original example, it isn’t immediately clear to me that >>>> reduce should choose a default identity. Some types (e.g. integers and FP) >>>> belong to multiple different ring algebras, and therefore have different >>>> identity values that correspond to the relevant binary operations. >>>> >>>> -Chris >>>> >>>> >>>> On Sun, Dec 25, 2016 at 12:19 PM, Xiaodi Wu <[email protected]> >>>> wrote: >>>> >>>>> On Sun, Dec 25, 2016 at 3:07 PM, Adam Nemecek <[email protected]> >>>>> wrote: >>>>> >>>>>> There's a book that provides quite a bit of info on this >>>>>> >>>>>> https://smile.amazon.com/Elements-Programming-Alexander-Step >>>>>> anov/dp/032163537X?sa-no-redirect=1 >>>>>> >>>>>> They say that DefaultConstructible is one of the essential protocols >>>>>> on which most algorithms rely in one way or another. One of the authors >>>>>> is >>>>>> the designer of the C++ STL and basically the father of modern generics. >>>>>> >>>>>> This protocol is important for any algebraic structure that deals >>>>>> with the concept of appending or addition (as "zero" is one of the >>>>>> requirements of monoid). There isn't a good short answer to your >>>>>> question. >>>>>> It's a building block of algorithms. Think about why a >>>>>> RangeReplaceableCollection can provide you with a default constructor >>>>>> but a >>>>>> Collection can't. >>>>>> >>>>> >>>>> It's well and fine that most algorithms rely on the concept in one way >>>>> or another. Yet the Swift standard library already implements many generic >>>>> algorithms but has no DefaultConstructible, presumably because there are >>>>> other protocols that guarantee `init()` and the algorithms being >>>>> implemented don't need to be (practically speaking) generic over all >>>>> DefaultConstructible types. My question is: what practical use cases are >>>>> there for an explicit DefaultConstructible that are impractical today? >>>>> >>>>> >>>>> On Sun, Dec 25, 2016 at 11:37 AM, Xiaodi Wu <[email protected]> >>>>>> wrote: >>>>>> >>>>>>> Can you give some other examples of generic algorithms that would >>>>>>> make use of this DefaultConstructible? I'm having trouble coming up with >>>>>>> any other than reduce. >>>>>>> On Sun, Dec 25, 2016 at 14:23 Adam Nemecek via swift-evolution < >>>>>>> [email protected]> wrote: >>>>>>> >>>>>>>> This protocol is present in C++ http://en.cppreference.com >>>>>>>> /w/cpp/concept/DefaultConstructible as well as in Rust >>>>>>>> https://doc.rust-lang.org/std/default/ >>>>>>>> >>>>>>>> It's the identity element/unit of a monoid or a zero. >>>>>>>> >>>>>>>> The Swift implementation is very simple (I'm open to different >>>>>>>> names) >>>>>>>> >>>>>>>> protocol DefaultConstructible { >>>>>>>> init() >>>>>>>> } >>>>>>>> >>>>>>>> A lot of the standard types could then be made to conform to this >>>>>>>> protocol. These include all the numeric types, collection types (array, >>>>>>>> set, dict), string, basically at least every type that currently has a >>>>>>>> constructor without any arguments. >>>>>>>> >>>>>>>> The RangeReplaceableCollection protocol would inherit from this >>>>>>>> protocol as well. >>>>>>>> >>>>>>>> This protocol would simplify a lot of generic algorithms where you >>>>>>>> need the concept of a zero (which shows up a lot) >>>>>>>> >>>>>>>> Once introduced, Sequence could define an alternative >>>>>>>> implementation of reduce where the initial result doesn't need to be >>>>>>>> provided as it can be default constructed. >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> _______________________________________________ >>>>>>>> swift-evolution mailing list >>>>>>>> [email protected] >>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>>>>>> >>>>>>> >>>>>> >>>>> >>>> _______________________________________________ >>>> swift-evolution mailing list >>>> [email protected] >>>> https://lists.swift.org/mailman/listinfo/swift-evolution >>>> >>>> >>>> >>> >> >
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