# Designing protocols operating over pairs of types

**URL:** <https://forums.swift.org/t/designing-protocols-operating-over-pairs-of-types/26948>\
**Category:** Discussion\
**Tags:** protocols\
**Created:** [July 14, 2019, 1:25pm UTC](https://forums.swift.org/t/designing-protocols-operating-over-pairs-of-types/26948 "2019-07-14T13:25:59Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![eaplatanios](https://sea2.discourse-cdn.com/swift/user_avatar/forums.swift.org/eaplatanios/32/5384_2.png) [@eaplatanios](https://forums.swift.org/u/eaplatanios)\
**Post date:** [July 14, 2019, 1:25pm UTC](https://forums.swift.org/t/designing-protocols-operating-over-pairs-of-types/26948/1 "2019-07-14T13:25:59Z")

</div>

Hi all,

I understand that the title of this topic is a bit confusing but I also wasn't sure how to call it. Basically, I want to achieve the following behavior:

```
public protocol KLDivergence where Self: Distribution {
  associatedtype TargetDistribution: Distribution

  static func callAsFunction(_ source: Self, _ target: TargetDistribution) -> Float
}

public struct Categorical: Distribution {
  ...
}

extension Categorical: KLDivergence where TargetDistribution == Categorical {
  ...

}

extension Categorical: KLDivergence where TargetDistribution == Other {
  ...
}

```

The last part is the tricky one. Multiple conformance extensions to the same protocol are not allowed in Swift. I am aware that there have been discussions in Swift about potentially handling mutually exclusive extensions and overlapping types. However, I believe this case is somewhat special in that the protocols we are conforming to can be thought of as being different. With a slight abuse of notation, the above can be thought of as:

```
extension Categorical: KLDivergence<Categorical> {
  ...

}

extension Categorical: KLDivergence<Other> {
  ...
}

```

So I am wondering if something like this could be supported or if there is another way to achieve the desired behavior; namely, having the protocol `KLDivergence` be defined over pairs of types (i.e., `SourceDistribution` and `TargetDistribution`) and then having the compiler be able to find the static `ccallAsFunction` defined in it given only `SourceDistribution` and `TargetDistribution` (so that the user does not also need to provide the a KL divergence type / instance. In Scala, we can achieve something like this using implicit instances of `KLDivergence`s, but I'm not sure if something similar can be achieved in Swift as there is no equivalent notion of implicits.

Thanks,  
Anthony

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<div class="post-metadata">

**Author:** ![anandabits](https://sea2.discourse-cdn.com/swift/user_avatar/forums.swift.org/anandabits/32/355_2.png) [@anandabits](https://forums.swift.org/u/anandabits)\
**Post date:** [July 14, 2019, 1:42pm UTC](https://forums.swift.org/t/designing-protocols-operating-over-pairs-of-types/26948/2 "2019-07-14T13:42:43Z")

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What you’re looking for is something similar to multi-parameter type classes in Haskell. This has come up occasionally in the past. I believe the most recent discussion happened here: [Improving the UI of generics - #53 by Joe\_Groff](https://forums.swift.org/t/improving-the-ui-of-generics/22814/53).

---

<div class="post-metadata">

**Author:** ![eaplatanios](https://sea2.discourse-cdn.com/swift/user_avatar/forums.swift.org/eaplatanios/32/5384_2.png) [@eaplatanios](https://forums.swift.org/u/eaplatanios)\
**Post date:** [July 14, 2019, 10:31pm UTC](https://forums.swift.org/t/designing-protocols-operating-over-pairs-of-types/26948/3 "2019-07-14T22:31:34Z")

</div>

Thanks! That would satisfy what I need. Do you know if there's been any further discussion about potentially supporting something like this?