Compile a dashboard into one math function, and all of mathematics comes with it
This projects page is an ordinary React component, <ProjectsPage {...props} />. It is compiled into a pure math function, UI = f(props), from the props to the position and size of every card. Once it is math, you can differentiate it to tune the design for every device at once, bound it to prove a rule for every screen width, find its discontinuities, integrate it over real devices, compress it like a signal, soften it until it animates itself, and even ask what the page looks like at an imaginary width.
Interactive model
How the function is built
The page is written once as a straight list of operations with no branches or loops, following the approach of chenglou/handwired. Every operation is a weighted sum, a product, a ReLU, or a step function. An if becomes a step that blends both outcomes, and Math.max becomes a ReLU:
The column count is a sum of steps, one per possible count, and the layout is computed for every count and blended by which one is on. Word wrapping is one step per line: for each commit message there is a width below which it needs another line.
So f is piecewise smooth, and the same list of operations can be evaluated four ways: exactly; with every step replaced by a sigmoid; with forward-mode differentiation; and with interval arithmetic. The tools above combine those four evaluations.
Limits
- The page is written by hand in this form. Nothing converts existing React or HTML into it yet.
- Messages are set in a monospace font and wrapped by character count, so line counts are computed rather than measured from rendered text.
- Proofs hold for exact arithmetic. They do not account for floating point rounding.
- Projects, device shares, and font scale shares are sample data.