julia> type_morespecific(a, b) = ccall(:jl_type_morespecific, Cint, (Any,Any), a, b)
type_morespecific (generic function with 1 method)
julia> types = [Tuple{Int, Int}, Tuple{Integer, Integer}, Tuple{T, T} where T<: Real, Tuple{Int, Integer}];
julia> sort(types, lt = Bool∘type_morespecific)
4-element Vector{Type}:
Tuple{Int64, Int64}
Tuple{Int64, Integer}
Tuple{Integer, Integer}
Tuple{T, T} where T<:Real
(thanks to @jakobnissen for linking More about types · The Julia Language) but that doesn’t necessarily give an answer to which method your input tuple would be dispatched to (e.g. consider Tuple{Int64, Float64}).