Interval arithmetic can prove a UI never fails across infinitely many props
shuding · x · 2026-10-27
Final part of Shu Ding's math-for-UI thread. Proof: interval arithmetic verifies properties like 'page height stays under the limit' across every viewport width and font scale at once—each operation runs on ranges, giving a guaranteed enclosure of f over a whole box B of props; green regions are proven to hold everywhere, red proven to fail. Gradient: state a design goal ('no cut-off descriptions on any common screen, shortest page height') and gradient descent finds the best prop combinations (gap, padding, card width) automatically.
Related event: Vercel's The Calculus of Interfaces Compiles React UI into Math Functions(11 posts)→
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