| Some other nice things that come from having a type system for numerical work: - Forward mode automatic differentiation. Having a type system that allows `Dual` numbers to pass through your algorithm, simulation, or whatever means you can calculate derivatives, gradients, jacobians, and hessians efficiently (for small problems) and accurately without having to change any of your code. There are so many times where I say “hey, I wonder what the sensitivity of my simulation output to this input parameter is” and it’s really nice to be able to answer that question with one line of code. - Unitful numbers. It’s really nice to be able to pass numbers with units through a simulation (little to no performance penalty!) to make sure everything checks out in that respect. - Uncertainty. Both Measurements.jl and MonteCarloMeasurements.jl provide numbers that propagate (linear and nonlinear, respectively) uncertainty as the pass through calculations. Want to see how uncertainty in a parameter propagates through a calculation? Just change that one parameter to an uncertain number and let it run through your algorithm as-is and it will spit out an answer with uncertainty bounds on the other side. These are just a few examples of the stuff I use it for in my everyday work. Having a full type system for numerical work is one of those things that seems silly before you use it, but once you do, you wonder how you got by without it before. EDIT: BTW, these are just examples of numerical types. Sending specialized array types through a your code is also a thing. For example, if you have a `Diagonal` type matrix and you send it to an eigenvalue solve, it just pulls the elements from the diagonal without wasting any time trying to calculate anything. Or there are things like ComponentArrays.jl (full disclosure, I wrote this library), that let you pass arbitrarily deep structured information through a differential equation or optimization solver for much cleaner and more readable code than just indexing into a plain vector like you would usually have to do. And you can even put your weird numerical types inside of the weird array types and just send it on through. |