How to properly unwrap nested structs to access internals?

General Usage
5 
struct TheStruct{T<:SomeAbstractType}
    x::T
end

is very different in performance from

struct TheStruct
    x::SomeAbstractType
end

And that is the whole point with the parametric types.

In the latter case, the type TheStruct provides basically no information on what the inner layout of an object is, because one can subtype SomeAbstractType with arbitrarily complex type. So, the compiler can only produce slow generic code with unboxing etc.
In the former case, any concrete object cannot be of type TheStruct, it will be of type TheStruct{SomeType}. If SomeType is a concrete type, then the compiler has information of the data layout from the type of object alone and can produce fast machine code.

Moreover, all types in your OP must be parametric for performance:

struct CArray{T<:Dict} <: AbstractArray
    cool_mapping::T
end

struct BArray{T<:AbstractArray} <: AbstractArray
    data::T
end

const AllowableATypes = Union{CArray, BArray{<:CArray}}

struct AArray{T<:AllowableATypes} <: AbstractArray
    arr::T
end

Note that you can’t have BArray{CArray} in AllowableATypes, because that would disallow BArray{CArray{SomeConcreteDictType}} (cf. Array{Int} and Array{Integer}). You need a BArray parameterized by a type that is a subtype of CArray, that’s why a longer signature is required.

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