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

[Adam Nemecek]

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