# Using rule definition tools

Rule definition tools can help you write more frules and the rrules with less lines of code.

## @non_differentiable

For non-differentiable functions the @non_differentiable macro can be used. For example, instead of manually defining the frule and the rrule for string concatenation *(String..), the macro call

@non_differentiable *(String...)

defines the following frule and rrule automatically

function ChainRulesCore.frule(var"##_#1600", ::Core.Typeof(*), String::Any...; kwargs...)
return (*(String...; kwargs...), NoTangent())
end
function ChainRulesCore.rrule(::Core.Typeof(*), String::Any...; kwargs...)
return (*(String...; kwargs...), function var"*_pullback"(_)
(ZeroTangent(), ntuple((_->NoTangent()), 0 + length(String))...)
end)
end

Note that the types of arguments are propagated to the frule and rrule definitions. This is needed in case the function differentiable for some but not for other types of arguments. For example *(1, 2, 3) is differentiable, and is not defined with the macro call above.

## @scalar_rule

For functions involving only scalars, i.e. subtypes of Number (no structs, Strings...), both the frule and the rrule can be defined using a single @scalar_rule macro call.

Note that the function does not have to be $\mathbb{R} \rightarrow \mathbb{R}$. In fact, any number of scalar arguments is supported, as is returning a tuple of scalars.

See docstrings for the comprehensive usage instructions.