Operator-sensitive promotion¶

In certain cases, the simple rules for promotion may not be sufficient. For example, consider a type that can represent an object with physical units, here restricted to a single unit like “meter”:

immutable MeterUnits{T,P} <: Number
val::T
end
MeterUnits{T}(val::T, pow::Int) = MeterUnits{T,pow}(val)

m  = MeterUnits(1.0, 1)   # 1.0 meter, i.e. units of length
m2 = MeterUnits(1.0, 2)   # 1.0 meter^2, i.e. units of area


Now let’s define the operations + and * for these objects: m+m should have the type of m but m*m should have the type of m2. When the result type depends on the operation, and not just the input types, promote_rule will be inadequate.

Fortunately, it’s possible to provide such definitions via promote_op:

Base.promote_op{R,S}(::Base.AddFun, ::Type{MeterUnits{R,1}}, ::Type{MeterUnits{S,1}}) = MeterUnits{promote_type(R,S),1}
Base.promote_op{R,S}(::Base.MulFun, ::Type{MeterUnits{R,1}}, ::Type{MeterUnits{S,1}}) = MeterUnits{promote_type(R,S),2}
Base.promote_op{R,S}(::Base.DotMulFun, ::Type{MeterUnits{R,1}}, ::Type{MeterUnits{S,1}}) = MeterUnits{promote_type(R,S),2}


The first one defines the promotion rule for +, and the second one for *. AddFun, MulFun, and DotMulFun are “functor types” defined in functor.jl.

It’s worth noting that as julia’s internal representation of functions evolves, this interface may change in a future version of Julia.