> 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 7:30 PM, Adam Nemecek <adamnemecek@gmail.com> wrote:
On Sun, Dec 25, 2016 at 3:30 PM, Xiaodi Wu <xiaodi.wu@gmail.com> wrote:
On Sun, Dec 25, 2016 at 5:27 PM, Adam Nemecek <adamnemecek@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@apple.com> >>> wrote:
On Dec 25, 2016, at 12:54 PM, Adam Nemecek via swift-evolution < >>>> swift-evolution@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@gmail.com> >>>> wrote:
On Sun, Dec 25, 2016 at 3:07 PM, Adam Nemecek <adamnemecek@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@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@swift.org> wrote:
This protocol is present in C++ http://en.cppreference.com
/w/cpp/concept/DefaultConstructible as well as in Rust
std::default - Rust
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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