<div dir="ltr">On Sun, Dec 25, 2016 at 9:40 PM, Adam Nemecek <span dir="ltr"><<a href="mailto:adamnemecek@gmail.com" target="_blank">adamnemecek@gmail.com</a>></span> wrote:<br><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><span class=""><div>> <span style="font-size:12.8px">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()`.</span></div><div><span style="font-size:12.8px"><br></span></div></span><div><span style="font-size:12.8px">Right, it's an empirical argument.</span></div></div></blockquote><div><br></div><div>My question was about the semantics of `init()`; it can't be answered empirically and requires no argument.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><span class="">> <span style="font-size:12.8px">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()`.</span><div><span style="font-size:12.8px"><br></span></div></span><div><span style="font-size:12.8px">Let's not talk about those then. This would not apply to every single type in existence, as I've stated previously.</span></div><span class=""><div><span style="font-size:12.8px"><br></span></div><div><span style="font-size:12.8px">> </span><span style="font-size:12.8px">It gives you something different every time. How can this be squared with your stated motivation regarding concepts of zero and concepts of equality?</span></div><div><span style="font-size:12.8px"><br></span></div></span><div><span style="font-size:12.8px">Due to the fact that it's a resource, not a value. As I've stated above, not all of this applies to types that are more resource-like.</span></div><span class=""><div><br></div><div>> <span style="font-size:12.8px">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.</span><br></div></span><div><div><span style="font-size:12.8px"><br></span></div><div><span style="font-size:12.8px">This is an appeal to tradition.</span></div></div></div></blockquote><div><br></div><div>I'm saying that `init()` does not, afaik, currently have the semantics that you state it does. I am not making an argument.</div><div><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><span class=""><div><span style="font-size:12.8px">> </span><span style="font-size:12.8px">The statement I wrote was in JavaScript, so I'm not sure what you mean by returning an optional. `[]</span><span style="font-size:12.8px">.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.</span></div><div><span style="font-size:12.8px"><br></span></div></span><div><span style="font-size:12.8px">I was talking about their </span><span style="font-size:12.8px">analogous </span><span style="font-size:12.8px">swift implementations.</span></div></div></div></blockquote><div><br></div><div>Can you elaborate, perhaps in code, as to what you would improve about reduce? </div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><span class=""><div>> <span style="font-size:12.8px">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?</span></div><div><span style="font-size:12.8px"><br></span></div></span><div><span style="font-size:12.8px">If it's implemented as either nested collections or numbers.</span></div></div></blockquote><div><br></div><div>I'm not sure I follow. Can you give an example of such an algorithm?</div><div><br></div><div><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="HOEnZb"><div class="h5"><div class="gmail_extra"><div class="gmail_quote">On Sun, Dec 25, 2016 at 6:00 PM, Xiaodi Wu <span dir="ltr"><<a href="mailto:xiaodi.wu@gmail.com" target="_blank">xiaodi.wu@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><span>On Sun, Dec 25, 2016 at 7:30 PM, Adam Nemecek <span dir="ltr"><<a href="mailto:adamnemecek@gmail.com" target="_blank">adamnemecek@gmail.com</a>></span> wrote:<br></span><div class="gmail_extra"><div class="gmail_quote"><span><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><span class="m_-4682646206182832717m_1176161565890972384gmail-"><span style="font-size:12.8px">> 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? </span><br><div><span style="font-size:12.8px"><br></span></div></span><div><span style="font-size:12.8px">Int() == 0, String() == "" so to some extent by convention, a lot of types have a default value as is.</span></div></div></blockquote><div><br></div></span><div>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()`.</div><div><br></div><div>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."</div><div><br></div><div>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?</div><span><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><span class="m_-4682646206182832717m_1176161565890972384gmail-"><div><span style="font-size:12.8px">> Is the thread that I get by writing `let t = Thread()` some kind of zero in any reasonable sense of the word?</span><span style="font-size:12.8px"><br></span></div><div><span style="font-size:12.8px"><br></span></div></span><div><span style="font-size:12.8px">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.</span></div></div></blockquote><div><br></div></span><div>It gives you something different every time. How can this be squared with your stated motivation regarding concepts of zero and concepts of equality?</div><span><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div><span style="font-size:12.8px">A better question is why does thread currently implement a default constructor? </span></div></div></blockquote><div><br></div></span><div>It's an initializer that takes no arguments, because none are needed for a new thread. How else would you write it?</div><span><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><span class="m_-4682646206182832717m_1176161565890972384gmail-"><div><div style="font-size:12.8px">> 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.</div></div><div style="font-size:12.8px"><br></div></span><div style="font-size:12.8px">I do. The justification is that if I call the default constructor of Int currently, I get the value of 0.</div></div></blockquote><div><br></div></span><div>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.)</div><span><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div style="font-size:12.8px">Which means that the binary operation must be addition.</div></div></blockquote><div><br></div></span><div>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.</div><span><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div style="font-size:12.8px">If I call String() I get "" which is the identity of the + String operation.</div></div></blockquote><div><br></div></span><div>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.</div><span><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><span class="m_-4682646206182832717m_1176161565890972384gmail-"><div style="font-size:12.8px">> <span style="font-size:12.8px">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?</span></div><div style="font-size:12.8px"><span style="font-size:12.8px"><br></span></div></span><div style="font-size:12.8px">These two will have different signatures. The reduce you describe returns an optional,</div></div></blockquote><div><br></div></span><div>The statement I wrote was in JavaScript, so I'm not sure what you mean by returning an optional. `[]<span style="font-size:12.800000190734863px">.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.</span></div><span><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div style="font-size:12.8px">the other one would returns the default value.</div></div></blockquote><div><br></div></span><div>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.</div><span><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div style="font-size:12.8px">Fundamentally the default constructibles are useful in numerical computations e..g. dealing with tensors.</div></div></blockquote><div><br></div></span><div>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`.)</div><div><div class="m_-4682646206182832717h5"><div><br></div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div class="m_-4682646206182832717m_1176161565890972384gmail-HOEnZb"><div class="m_-4682646206182832717m_1176161565890972384gmail-h5"><div class="gmail_extra"><div class="gmail_quote">On Sun, Dec 25, 2016 at 3:30 PM, Xiaodi Wu <span dir="ltr"><<a href="mailto:xiaodi.wu@gmail.com" target="_blank">xiaodi.wu@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><span>On Sun, Dec 25, 2016 at 5:27 PM, Adam Nemecek <span dir="ltr"><<a href="mailto:adamnemecek@gmail.com" target="_blank">adamnemecek@gmail.com</a>></span> wrote:<br></span><div class="gmail_extra"><div class="gmail_quote"><span><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><span class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-"><div>> <span style="font-size:12.8px">*Which* APIs become more ergonomic?</span></div><div><span style="font-size:12.8px"><br></span></div></span><div>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). </div><span class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-"><div><br></div><div>> <span style="font-size:12.8px">1) How does this square with Swift’s general philosophy to not default initialize values to “zero”?</span></div><div><span style="font-size:12.8px"><br></span></div></span><div><span style="font-size:12.8px">I actually wasn't aware of this philosophy. Despite this philosophy, look at how many types actually currently implement a default constructor.</span></div></div></blockquote><div><br></div></span><div>(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?</div><span><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div><span style="font-size:12.8px">Also can I ask what's the motivation behind this philosophy? </span></div><div><span style="font-size:12.8px">I think that in Swift, default constructibility makes complete sense for (most?) structs, maybe less so for classes. </span></div><span class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-"><div><br></div>> <span style="font-size:12.8px">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.</span><div><span style="font-size:12.8px"><br></span></div></span><div><span style="font-size:12.8px">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.</span></div></div></blockquote><div><br></div></span><div>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.</div><div><br></div><div>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?</div><div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376h5"><div><br></div><div><div><br></div></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-HOEnZb"><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-h5"><div class="gmail_extra"><div class="gmail_quote">On Sun, Dec 25, 2016 at 1:24 PM, Chris Lattner <span dir="ltr"><<a href="mailto:clattner@apple.com" target="_blank">clattner@apple.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div style="word-wrap:break-word"><span>On Dec 25, 2016, at 12:54 PM, Adam Nemecek via swift-evolution <<a href="mailto:swift-evolution@swift.org" target="_blank">swift-evolution@swift.org</a>> wrote:</span><div><span><blockquote type="cite"><div><div dir="ltr">Does enabling a lot of small improvements that make APIs more ergonomic count as practical?</div></div></blockquote><div><br></div></span><div>Yes, that would count as practical, but Xiaodi’s question is just as important. *Which* APIs become more ergonomic?</div><div><br></div><div>Here are a couple of more questions:</div><div><br></div><div>1) How does this square with Swift’s general philosophy to not default initialize values to “zero”?</div><div><br></div><div>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.</div><span class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596HOEnZb"><font color="#888888"><div><br></div><div>-Chris</div></font></span><div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596h5"><br><blockquote type="cite"><div><div class="gmail_extra"><br><div class="gmail_quote">On Sun, Dec 25, 2016 at 12:19 PM, Xiaodi Wu <span dir="ltr"><<a href="mailto:xiaodi.wu@gmail.com" target="_blank">xiaodi.wu@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><span>On Sun, Dec 25, 2016 at 3:07 PM, Adam Nemecek <span dir="ltr"><<a href="mailto:adamnemecek@gmail.com" target="_blank">adamnemecek@gmail.com</a>></span> wrote:<br></span><div class="gmail_extra"><div class="gmail_quote"><span><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr">There's a book that provides quite a bit of info on this <div><br></div><div><a href="https://smile.amazon.com/Elements-Programming-Alexander-Stepanov/dp/032163537X?sa-no-redirect=1" target="_blank">https://smile.amazon.com/Eleme<wbr>nts-Programming-Alexander-Step<wbr>anov/dp/032163537X?sa-no-redir<wbr>ect=1</a><br></div><div><br></div><div>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.</div><div><br></div><div>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. </div><div><span style="color:rgb(80,0,80)"></span></div></div></blockquote><div><br></div></span><div>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?</div><span><div><br></div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div><span style="color:rgb(80,0,80)">On Sun, Dec 25, 2016 at 11:37 AM, Xiaodi Wu </span><span dir="ltr" style="color:rgb(80,0,80)"><<a href="mailto:xiaodi.wu@gmail.com" target="_blank">xiaodi.wu@gmail.com</a>></span><span style="color:rgb(80,0,80)"> wrote:</span><br></div></div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289HOEnZb"><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289h5"><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">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.<br><div class="gmail_quote"><div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951h5"><div dir="ltr">On Sun, Dec 25, 2016 at 14:23 Adam Nemecek via swift-evolution <<a href="mailto:swift-evolution@swift.org" target="_blank">swift-evolution@swift.org</a>> wrote:<br></div></div></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951h5"><div dir="ltr" class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg">This protocol is present in C++ <a href="http://en.cppreference.com/w/cpp/concept/DefaultConstructible" class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg" target="_blank">http://en.cppreference.com<wbr>/w/cpp/concept/DefaultConstruc<wbr>tible</a> as well as in Rust <a href="https://doc.rust-lang.org/std/default/" class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg" target="_blank">https://doc.rust-lang.org/std/<wbr>default/</a><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"><br class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"></div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg">It's the identity element/unit of a monoid or a zero.<br class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"><br class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"></div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg">The Swift implementation is very simple (I'm open to different names)<br class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"></div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"><br class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"></div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg">protocol DefaultConstructible {</div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"> init() </div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg">}</div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"><br class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"></div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg">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.</div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"><br class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"></div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg">The RangeReplaceableCollection protocol would inherit from this protocol as well. <br class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"></div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"><br class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"></div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg">This protocol would simplify a lot of generic algorithms where you need the concept of a zero (which shows up a lot)</div></div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"><br class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"></div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg">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.</div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"><br class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"></div><div class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"><br class="m_-4682646206182832717m_1176161565890972384gmail-m_2687622816934730376m_-5821329404718624302gmail-m_3993794689939404596m_-267952324834337685m_8912025549324475289m_699475458640075951m_-6015751673947924360gmail_msg"></div><div 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