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

[Adam Nemecek]

>  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.

> 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. A better question is why does
thread currently implement a default constructor?

> 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. Which means that the binary operation must
be addition. If I call String() I get "" which is the identity of the +
String operation.

> 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 other one would returns the default value. Fundamentally
the default constructibles are useful in numerical computations e..g.
dealing with tensors.


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