Add syntactic sugar for the common folds {①②③⑤} #36

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opened 2026-07-03 00:31:00 +00:00 by toph · 0 comments

toph commented

2026-07-03 00:31:00 +00:00

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Surface-layer follow-up to the two-layer principle now in spec §1 ("Two layers: capability and surface"). Reasoning in notes/2026-07-03.md.

What

Design and add syntactic sugar for the frequently-folded axioms — the sugar-worthy core {①, ②, ③, ⑤} (⑥ optionally). Current primitive forms:

① through .x .y
② map .x onto .y
③ perp --l through .p
⑤ map --l1 onto --l2 toward .p

Why

These dominate real paper folding, so they deserve short, intuitive syntax. The capability layer already ships all of ①–⑦ exactly — this is purely surface. The boundary follows fold frequency, not the degree ladder: ④ (project onto a line) is degree-1 but rarely folded and stays verbose, while ⑤ (angle bisector) needs √ but is everywhere and gets sugar.

Open questions

Surface forms for ①②③⑤ — what reads naturally (corner-to-corner, edge-to-edge, diagonal, book fold, …)?
How sugar composes with @ (fold) vs. a bare precrease.
Multi-solution selectors (toward / second solution) under sugar.
Whether ⑥ earns a sugar form too.

Non-goals

No new capability — ①–⑦ already exist.
No sugar for ④ or ⑦.
No semantic or number-kernel changes.

Surface-layer follow-up to the two-layer principle now in spec §1 ("Two layers: capability and surface"). Reasoning in `notes/2026-07-03.md`. ## What Design and add syntactic sugar for the frequently-folded axioms — the sugar-worthy core **{①, ②, ③, ⑤}** (⑥ optionally). Current primitive forms: - ① `through .x .y` - ② `map .x onto .y` - ③ `perp --l through .p` - ⑤ `map --l1 onto --l2 toward .p` ## Why These dominate real paper folding, so they deserve short, intuitive syntax. The capability layer already ships all of ①–⑦ exactly — this is purely surface. The boundary follows fold frequency, not the degree ladder: ④ (project onto a line) is degree-1 but rarely folded and stays verbose, while ⑤ (angle bisector) needs √ but is everywhere and gets sugar. ## Open questions - Surface forms for ①②③⑤ — what reads naturally (corner-to-corner, edge-to-edge, diagonal, book fold, …)? - How sugar composes with `@` (fold) vs. a bare precrease. - Multi-solution selectors (`toward` / second solution) under sugar. - Whether ⑥ earns a sugar form too. ## Non-goals - No new capability — ①–⑦ already exist. - No sugar for ④ or ⑦. - No semantic or number-kernel changes.

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