# Parametric types and where keyword in Julia v0.6

**URL:** <https://discourse.julialang.org/t/parametric-types-and-where-keyword-in-julia-v0-6/5123>\
**Category:** General Usage\
**Tags:** question, parametric-types\
**Created:** [July 29, 2017, 2:14pm UTC](https://discourse.julialang.org/t/parametric-types-and-where-keyword-in-julia-v0-6/5123 "2017-07-29T14:14:01Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![scidom](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/scidom/32/882_2.png) [@scidom](https://discourse.julialang.org/u/scidom)\
**Post date:** [July 29, 2017, 2:14pm UTC](https://discourse.julialang.org/t/parametric-types-and-where-keyword-in-julia-v0-6/5123/1 "2017-07-29T14:14:01Z")

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The following typealias used to work in Julia v0.5:

typealias RealLowerTriangular{T\<:Real, S\<:AbstractMatrix} LowerTriangular{T, S}

Upon upgrading to Julia v0.6, I received a suggestion on the REPL to use instead the following:

RealLowerTriangular{T\<:Real, S\<:AbstractMatrix} = LowerTriangular{T, S}

However, trying out the supposed fix yields the following error:

RealLowerTriangular(ones(2))  
ERROR: MethodError: Cannot `convert` an object of type Array{Float64,1} to an object of type LowerTriangular{T,S} where S\<:(AbstractArray{T,2} where T) where T\<:Real  
This may have arisen from a call to the constructor LowerTriangular{T,S} where S\<:(AbstractArray{T,2} where T) where T\<:Real(…),  
since type constructors fall back to convert methods.  
Stacktrace:  
[1] LowerTriangular{T,S} where S\<:(AbstractArray{T,2} where T) where T\<:Real(::Array{Float64,1}) at ./sysimg.jl:24

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**Author:** ![cstjean](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/cstjean/32/1444_2.png) [@cstjean](https://discourse.julialang.org/u/cstjean)\
**Post date:** [July 29, 2017, 2:29pm UTC](https://discourse.julialang.org/t/parametric-types-and-where-keyword-in-julia-v0-6/5123/2 "2017-07-29T14:29:16Z")

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That’s the same in 0.5

```julia
julia> typealias RealLowerTriangular{T<:Real, S<:AbstractMatrix} LowerTriangular{T, S}
LowerTriangular{T<:Real,S<:AbstractArray{T,2}}

julia> RealLowerTriangular(ones(2))
ERROR: MethodError: Cannot `convert` an object of type Array{Float64,1} to an object of type LowerTriangular{T<:Real,S<:AbstractArray{T,2}}
This may have arisen from a call to the constructor LowerTriangular{T<:Real,S<:AbstractArray{T,2}}(...),
since type constructors fall back to convert methods.
 in LowerTriangular{T<:Real,S<:AbstractArray{T,2}}(::Array{Float64,1}) at ./sysimg.jl:53

```

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<div class="post-metadata">

**Author:** ![scidom](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/scidom/32/882_2.png) [@scidom](https://discourse.julialang.org/u/scidom)\
**Post date:** [July 29, 2017, 2:39pm UTC](https://discourse.julialang.org/t/parametric-types-and-where-keyword-in-julia-v0-6/5123/3 "2017-07-29T14:39:16Z")

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That’s because there was a small typo in my example, sorry. Here is what I meant, which I just tried it in Julia v0.5.2 and it works:

```julia
julia> typealias RealLowerTriangular{T<:Real, S<:AbstractMatrix} LowerTriangular{T, S}
LowerTriangular{T<:Real,S<:AbstractArray{T,2}}

julia> RealLowerTriangular(ones(2, 2))
2×2 LowerTriangular{Float64,Array{Float64,2}}:
 1.0 ⋅ 
 1.0 1.0

```

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**Author:** ![Dan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dan/32/42581_2.png) [@Dan](https://discourse.julialang.org/u/Dan)\
**Post date:** [July 29, 2017, 3:31pm UTC](https://discourse.julialang.org/t/parametric-types-and-where-keyword-in-julia-v0-6/5123/4 "2017-07-29T15:31:48Z")

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maybe it’s because `ones(2,2)` is not lower triangular, and older version had bug?

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**Author:** ![scidom](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/scidom/32/882_2.png) [@scidom](https://discourse.julialang.org/u/scidom)\
**Post date:** [July 29, 2017, 4:02pm UTC](https://discourse.julialang.org/t/parametric-types-and-where-keyword-in-julia-v0-6/5123/5 "2017-07-29T16:02:41Z")

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Thanks Dan, this wasn’t meant to be an accurate example, you are right that `ones(2, 2)` is not lower triangular. What I am getting at is that the equivalent proposed by Julia v0.6 no longer works, one could use for instance `eye(2)` above instead of `ones(2, 2)` to make this point.

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**Author:** ![Dan](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dan/32/42581_2.png) [@Dan](https://discourse.julialang.org/u/Dan)\
**Post date:** [July 29, 2017, 10:00pm UTC](https://discourse.julialang.org/t/parametric-types-and-where-keyword-in-julia-v0-6/5123/6 "2017-07-29T22:00:51Z")

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Indeed there is a problem getting to the constructor of `LowerTriangular` from the typedef-ed `RealLowerTriangular`. A solution can be to define the outer constructor:

```julia
# first we do the typedef
RealLowerTriangular{T,S} = LowerTriangular{T,S} where {T<:Real,S<:AbstractMatrix{T}}

# now the outer constructor
RealLowerTriangular(m) = LowerTriangular(m)

```

The logic is as follows: Calling a constructor is basically calling a method with the type as its name. The outer constructor `LowerTriangular` is simply a method named `LowerTriangular{T,S} where S where T`. A `RealLowerTriangular` is defined as `LowerTriangular{T,S} where S<:AbstractMatrix{T} where T<:Real` so Julia doesn’t find a method with this name and defaults to the `convert` constructor for a generic type.

In general, the non-parametrized names of parametric types are equivalent to the types with appropriate `where T` clauses added (for each parameter).

Hope this somehow makes more sense.  
And

```julia
julia> RealLowerTriangular(ones(2,2))
2×2 LowerTriangular{Float64,Array{Float64,2}}:
 1.0 ⋅ 
 1.0 1.0

```

works with these definitions.

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**Author:** ![scidom](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/scidom/32/882_2.png) [@scidom](https://discourse.julialang.org/u/scidom)\
**Post date:** [July 29, 2017, 10:14pm UTC](https://discourse.julialang.org/t/parametric-types-and-where-keyword-in-julia-v0-6/5123/7 "2017-07-29T22:14:24Z")

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Brilliant, this makes sense, and works.