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  "path": "/t/ann-interval-patterns-0-8-2/14044?page=2#post_24",
  "publishedAt": "2026-05-12T06:26:20.000Z",
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  "textContent": "tonyday567:\n\n> The symbols attach to the numbers ⟦2 5⟧ is function application and hence a blank.\n\nInteresting idea. Reminds me of bra-ket notation in physics. Perhaps we can interpret `⟦2` as an idempotent function, for example `max 2`. Likewise, `5⟧` would be `min 5`. The final convex set is then obtained by applying the chain of functions to `Whole`, just like what `ShowS` does.\n\nThe idea of describing points or sets by iterated functions is not new, of course. It is the basis of Conway’s surreal numbers and of signed-digit exact reals. There, the basic functions (digits) are certain contractions, represented as mid-pointing with a dyadic number.\n\nBy the way, Escardo and Simpson have a paper where they exhibit the closed real interval as the free mid-point algebra over two points. You might find that interesting. More general version here.",
  "title": "[ANN] interval-patterns-0.8.2"
}