# Multiple dispatch and type conversion for cousins of a type hierarchy

**URL:** <https://discourse.julialang.org/t/multiple-dispatch-and-type-conversion-for-cousins-of-a-type-hierarchy/53787>\
**Category:** General Usage\
**Tags:** question\
**Created:** [January 22, 2021, 3:49pm UTC](https://discourse.julialang.org/t/multiple-dispatch-and-type-conversion-for-cousins-of-a-type-hierarchy/53787 "2021-01-22T15:49:41Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![marty0801](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/marty0801/32/12715_2.png) [@marty0801](https://discourse.julialang.org/u/marty0801)\
**Post date:** [January 22, 2021, 3:49pm UTC](https://discourse.julialang.org/t/multiple-dispatch-and-type-conversion-for-cousins-of-a-type-hierarchy/53787/1 "2021-01-22T15:49:41Z")

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I have the following type hierarchy:

```julia
abstract type U end 
struct A <: U ... end 
struct B <: U ... end 

```

(I’ve omitted the details, but `A` and `B` both have identical field-names and types, but the semantic meaning of their fields is quite different, hence using two structs instead of one.) I also have a conversion function from `A` to `B`:

```julia
a2b(a::A)::B= (...) 

```

I have written several functions that apply only to data of type `B` such as :

```julia
+(b::B, x::Number)= ... 
*(b::B, x::Number)= ...
+(b::B, b::B)= ...
...

```

I want the ability to use these functions when the arguments of type `B` are replaced with arguments of type `A`. What is the most concise way of doing this? I see the following options:

1. For each function above, manually write a method for type `A` arguments using `convert` as in…

```julia
+(a::A, x::Number)= +(a2b(a), x) 

```

1. Use a macro to accomplish #1. I’m just cutting my teeth here on Julia, so I’d rather avoid this option if a better one exists.
2. Use the type system in a different way that I’m doing here?

I’m hoping (and suspecting) #3 is the correct answer, I just don’t see how to do it.

Please help!! And thanks!

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<div class="post-metadata">

**Author:** ![rdeits](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rdeits/32/286_2.png) [@rdeits](https://discourse.julialang.org/u/rdeits)\
**Post date:** [January 22, 2021, 3:59pm UTC](https://discourse.julialang.org/t/multiple-dispatch-and-type-conversion-for-cousins-of-a-type-hierarchy/53787/2 "2021-01-22T15:59:08Z")

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I would suggest something like:

- Implement `+(u::U, x::Number) = ` in terms of some set of _methods_ that define whatever API you expect `A` and `B` to implement
- Implement those methods for both `A` and `B`
- That’s it

This has a bunch of advantages:

- It removes the assumption that A and B must have identical fields or be perfectly convertible from one to the other. That’s true now, but will it always hold?
- It makes it more clear what the new type `C <: U` should do when you inevitably decide you need it

This is a super common pattern in Julia. One example is `AbstractArray`: There are lots of methods which work on any kind of `AbstractArray` because they use the common methods like `size()` and `getindex()`. It’s easy to implement a new kind of `AbstractArray` by just defining `size()` and `getindex()` for your new type, and then all the existing functions of `AbstractArray` should just work.

Your proposal to use `a2b` internally would be like forcing all array-like functions to first convert their inputs to a dense `Matrix` before operating on them. That would be unnecessarily slow at best and impossible at worst. Using a set of common methods, instead, and requiring users to implement those methods for their new types, makes things much easier to manage.

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<div class="post-metadata">

**Author:** ![marty0801](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/marty0801/32/12715_2.png) [@marty0801](https://discourse.julialang.org/u/marty0801)\
**Post date:** [January 22, 2021, 5:47pm UTC](https://discourse.julialang.org/t/multiple-dispatch-and-type-conversion-for-cousins-of-a-type-hierarchy/53787/3 "2021-01-22T17:47:56Z")

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Awesome. Thank you; exactly what I needed!