Problem when using type Any for mutiple-dispatch in Julia

Question

I am trying to write a function that receives a tuple and a dictionary as arguments.

function findBestAction(state::Tuple{Int64, Int64}, qTable::Dict{Any, Matrix{Float64}})
   doSomething()
end

I want the function to receive dictionaries whose keys can be of any possible type. I run the following command but receive error messages:

findBestAction((0, 0), qTable) #qTable::Dict{String, Matrix{Float64}}

Error Messages:

Stacktrace:
 [1] top-level scope
   @ e:\Master Thesis\lu_jizhou\Learning\q_learning.jl:33

ERROR: MethodError: no method matching findBestAction(::Tuple{Int64, Int64}, ::Dict{String, Matrix{Float64}})
Closest candidates are:
  findBestAction(::Tuple{Int64, Int64}, ::Dict{Any, Matrix{Float64}}) at e:\Master Thesis\lu_jizhou\Learning\q_learning.jl:33
Stacktrace:
 [1] top-level scope
   @ e:\Master Thesis\lu_jizhou\Learning\q_learning.jl:48

How should I do that?

Answer 1

This is because Dict{String, ...) is not a subtype of Dict{Any, ...) .

This is the way parametric types (ie types with other types in their curly braces) behave in Julia. From the Julia manual section on Parametric types :

 julia> Point{Float64} <: Point{Real} false

Warning

This last point is very important: even though Float64 <: Real we DO NOT have Point{Float64} <: Point{Real} .

In other words, in the parlance of type theory, Julia's type parameters are invariant

You can instead write the function as

function findBestAction(state::Tuple{Int64, Int64}, qTable::Dict{<:Any, Matrix{Float64}})
   doSomething()
end

which explicitly says that any subtype of Any is allowed as the key type in the Dict .

You can also consider changing the Dict to an AbstractDict , and the value type of it to be something like <:AbstractMatrix{<:Real} , if your code is written generically in a way that works for any AbstractMatrix and any Real subtype.