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

[Xiaodi Wu]

On Sun, Dec 25, 2016 at 9:40 PM, Adam Nemecek <adamnemecek at gmail.com> 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.
>

Whoops, I missed a few items here. In your first post, you stated that you
wanted your proposed protocol to apply to "basically at least every type
that currently has a constructor without any arguments." Is that not the
case?

> 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.
>

In Swift, protocols do not merely guarantee particular spellings, but
particular semantics as well. If "not all of this applies" to
"resource-like" types, what semantic guarantees are you proposing for
`DefaultConstructible`, and to what types would they completely apply?

> 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-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 <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.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> _______________________________________________
>>>>>>>>>> swift-evolution mailing list
>>>>>>>>>> swift-evolution at swift.org
>>>>>>>>>> https://lists.swift.org/mailman/listinfo/swift-evolution
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>
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>>>>>> swift-evolution mailing list
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>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>
>>>
>>
>
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