# Parametric types as subtypes of the type parameter

**URL:** <https://discourse.julialang.org/t/parametric-types-as-subtypes-of-the-type-parameter/11821>\
**Category:** New to Julia\
**Tags:** parametric-types\
**Created:** [June 20, 2018, 12:34pm UTC](https://discourse.julialang.org/t/parametric-types-as-subtypes-of-the-type-parameter/11821 "2018-06-20T12:34:51Z")\
**Posts on this page:** 9\
**Page:** 1

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**Author:** ![FMeirinhos](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fmeirinhos/32/19527_2.png) [@FMeirinhos](https://discourse.julialang.org/u/FMeirinhos)\
**Post date:** [June 20, 2018, 12:34pm UTC](https://discourse.julialang.org/t/parametric-types-as-subtypes-of-the-type-parameter/11821/1 "2018-06-20T12:34:51Z")

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I want my **parametric types to be subtypes of the type parameter**.

Consider a wrapper for floats:

```julia
struct wrapper{T} <: T where {T <: Union{Real}}
    bar::T
end

```

This example works fine. Now consider making the type `T` to be a subtype of `Union{Real,Complex}`. This throws an

> invalid subtyping in definition of

Since `Real` and `Complex` are subtypes of `Number`, something such as

```julia
struct wrapper{T<: Union{Real, Complex}} <: Number
    bar::T
end

```

would be a possible solution for _most_ cases.

However, this would be a quick fix and would defeat to the purpose of the **parametric type to be a subtype of the type parameter**. How does one achieve this?

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**Author:** ![quinnj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/quinnj/32/11_2.png) [@quinnj](https://discourse.julialang.org/u/quinnj)\
**Post date:** [June 20, 2018, 12:48pm UTC](https://discourse.julialang.org/t/parametric-types-as-subtypes-of-the-type-parameter/11821/2 "2018-06-20T12:48:15Z")

</div>

I don’t think it’s possible to make a subtype relation parametric; even in your first example, `Union{Real}` evaluates to just `Real`, so the `supertype` of any instance will always be `Real`, like

```julia
julia> wrapper(1)
wrapper{Int64}(1)

julia> supertype(typeof(ans))
Real

julia> wrapper("hey")
wrapper{String}("hey")

julia> supertype(typeof(ans))
Real

julia> wrapper(1.0)
wrapper{Float64}(1.0)

julia> supertype(typeof(ans))
Real

```

Maybe you can elaborate the use-case and why having the parametric subtype relation seems to be important?

---

<div class="post-metadata">

**Author:** ![FMeirinhos](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fmeirinhos/32/19527_2.png) [@FMeirinhos](https://discourse.julialang.org/u/FMeirinhos)\
**Post date:** [June 20, 2018, 1:29pm UTC](https://discourse.julialang.org/t/parametric-types-as-subtypes-of-the-type-parameter/11821/3 "2018-06-20T13:29:08Z")

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I am extending the ForwardDiff package to work with R –\> C functions (currently it is limited to R –\> R functions).

This requires the use of Dual Numbers, originally defined as

```julia
Dual{T,V<:Real,N} <: Real

```

where `V` is the “machine” type of the number (e.g., Float64) and T and N are not really important in this discussion.

I believe an extension to complex numbers would be correct with a redefinition such as

```julia
Dual{T,V,N} <: V where {V <: Union{Real, Complex}}

```

allowing the Dual number to **either** be Real or Complex but this seems to result in a

> invalid subtyping in definition of

error.

---

<div class="post-metadata">

**Author:** ![dpsanders](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dpsanders/32/3573_2.png) [@dpsanders](https://discourse.julialang.org/u/dpsanders)\
**Post date:** [June 20, 2018, 1:35pm UTC](https://discourse.julialang.org/t/parametric-types-as-subtypes-of-the-type-parameter/11821/4 "2018-06-20T13:35:16Z")

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Why don’t you just use a function from R to R^2 for the derivative and then convert to a complex?

Eg see the realify function in IntervalRootFinding.jl

---

<div class="post-metadata">

**Author:** ![FMeirinhos](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fmeirinhos/32/19527_2.png) [@FMeirinhos](https://discourse.julialang.org/u/FMeirinhos)\
**Post date:** [June 20, 2018, 2:04pm UTC](https://discourse.julialang.org/t/parametric-types-as-subtypes-of-the-type-parameter/11821/6 "2018-06-20T14:04:35Z")

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Because I don’t think that should be the way to solve the problem. There have been issues reported since 2016 hinting for support for R –\> C function differentiation and I thought I would take upon the task myself.  
The end goal is to differentiate eigenvalues (hence R^n –\> C^{m x m}) so I would stay away from such conversions, no?

But we digress. The question at hand is how to make a parametric type be a subtype of the type parameter with Unions.

---

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**Author:** ![ExpandingMan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/expandingman/32/866_2.png) [@ExpandingMan](https://discourse.julialang.org/u/ExpandingMan)\
**Post date:** [June 20, 2018, 2:16pm UTC](https://discourse.julialang.org/t/parametric-types-as-subtypes-of-the-type-parameter/11821/7 "2018-06-20T14:16:24Z")

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What you are asking for is not possible, because it would make the direct supertype of the declared type ambiguous.

To see why this is the case, consider

```julia
struct Wrapper{T<:Number} <: Number
    x::T 
end

```

Now, clearly `Number` is a supertype of `Wrapper{Float64}`. However, `Wrapper` (which you should think of as an abstract type) is also a supertype of `Wrapper{Float64}`. What is the supertype of `Wrapper`? Well, in this case `Number` is still a supertype of `Wrapper`, but if we had made it parametric as you are suggesting, it would be undefined. Julia does not allow this, since in Julia `T` is always a supertype of `T{U}`. This isn’t done arbitrarily, in fact this is one of the most common method signatures (e.g. `::AbstractVector` is a very common type of function argument to see).

I’m not quite sure what you’re trying to do, but I suspect that pattern that would be best for you would be what I showed above. (Also note that the reason your first example worked without error was because it’s equivalent to what I showed above.) This still gives you a lot of flexibility, and you can still do it with arbitrarily complicated `Union` types.

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<div class="post-metadata">

**Author:** ![Non-Contradiction](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/non-contradiction/32/2208_2.png) [@Non-Contradiction](https://discourse.julialang.org/u/Non-Contradiction)\
**Post date:** [June 20, 2018, 2:28pm UTC](https://discourse.julialang.org/t/parametric-types-as-subtypes-of-the-type-parameter/11821/8 "2018-06-20T14:28:38Z")

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I don’t think it is possible to make a type subtype of `Complex` since it is not an abstract type, so the `Complex` will break the subtyping anyway, even it is not in a union.

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**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:** [June 20, 2018, 3:07pm UTC](https://discourse.julialang.org/t/parametric-types-as-subtypes-of-the-type-parameter/11821/9 "2018-06-20T15:07:51Z")

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Could you make a `Complex{Dual}` instead of a `Dual <: Complex`?

---

<div class="post-metadata">

**Author:** ![dpsanders](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dpsanders/32/3573_2.png) [@dpsanders](https://discourse.julialang.org/u/dpsanders)\
**Post date:** [June 20, 2018, 5:49pm UTC](https://discourse.julialang.org/t/parametric-types-as-subtypes-of-the-type-parameter/11821/10 "2018-06-20T17:49:22Z")

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You don’t need to make it a subtype of Complex.