[swift-evolution] [Pitch] Add the DefaultConstructible protocol to the standard library

[Daniel Leping]

Usually it's a generic function that needs to return a value from some
other function or a default value (zero) in a case of some conditions.
Optional value is an arguable solution in quite some scenarios. Afaik,
sometimes it can be used for optional resolution.

Also, generic factories. Widely used in ORM solutions.

As mentioned above, algorythmical stuff that requires Zero.

On Mon, 26 Dec 2016 at 8:38 Xiaodi Wu <xiaodi.wu at gmail.com> wrote:

> Can you give some examples of what you used this approach to do?
>
>
> On Sun, Dec 25, 2016 at 9:49 PM, Daniel Leping <daniel at crossroadlabs.xyz>
> wrote:
>
> +1 to this approach. I remember I had to create it on my own for my
> projects. Would be nice to have it out of the box.
>
> On Mon, 26 Dec 2016 at 8:11 Adam Nemecek via swift-evolution <
> swift-evolution at swift.org> wrote:
>
> > 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()`.
>
> Right, it's an empirical argument.
>
> > 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()`.
>
> Let's not talk about those then. This would not apply to every single type
> in existence, as I've stated previously.
>
> > It gives you something different every time. How can this be squared
> with your stated motivation regarding concepts of zero and concepts of
> equality?
>
> 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.
>
> > 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.
>
> This is an appeal to tradition.
>
> > 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.
>
> I was talking about their analogous swift implementations.
>
> > 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?
>
> If it's implemented as either nested collections or numbers.
>
>
>
> On Sun, Dec 25, 2016 at 6:00 PM, Xiaodi Wu <xiaodi.wu at gmail.com> wrote:
>
> On Sun, Dec 25, 2016 at 7:30 PM, Adam Nemecek <adamnemecek at gmail.com>
> 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 <xiaodi.wu at gmail.com> wrote:
>
> On Sun, Dec 25, 2016 at 5:27 PM, Adam Nemecek <adamnemecek at gmail.com>
> 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 <clattner at apple.com> wrote:
>
> On Dec 25, 2016, at 12:54 PM, Adam Nemecek via swift-evolution <
> swift-evolution at swift.org> 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 <xiaodi.wu at gmail.com> wrote:
>
> On Sun, Dec 25, 2016 at 3:07 PM, Adam Nemecek <adamnemecek at gmail.com>
> wrote:
>
> There's a book that provides quite a bit of info on this
>
>
> https://smile.amazon.com/Elements-Programming-Alexander-Stepanov/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 <xiaodi.wu at gmail.com> 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 <
> swift-evolution at swift.org> 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.
>
>
>
>
>
>
>
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