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cycle — parallel repeating labels (labels, not windows)

Translated from the canonical Japanese page reference/cycle.md. The source_sha above records the source revision; a consistency check flags this page when the Japanese original changes.

Category: window-generating word (premise layer) / Signature: cycle(labels) anchor: r : Stream -> Stream(labeled) / name settled (spec §5.4)

Meaning

Attaches repeating labels to a target partition window. It creates no windows — just as weekdays do not partition the days, labels are a concept parallel to windows (ADR-03). The period length is arbitrary (7, 10, 12, 60, …), and so is the target window (not only weekdays over day — it can be laid over month and year too; the twelve earthly branches are year cycle […]).

• The list gives only the cyclic order; the head carries no meaning of “start” (where the week starts is WKST’s job. stdlib/gregorian.md §4.1).
• anchor: is the actual day that pins the phase — “the target window containing the anchor carries the head label”.
• The binding name reads as a value-expression “point → label” function — weekday(d), yearBranch(d). Resolution is the two steps point → containing window → label (ADR-27/30).

Examples

The yearly earthly branches — with 2020 (子, the Rat) as anchor, selecting New Year’s Day of a 午 (Horse) year:

# eval: 2020-01-01..2028-01-01
premise JPEto = Gregorian with {
  tz: "Asia/Tokyo"                  # needed to anchor the date literal in anchor: (ADR-33)
  yearBranch = year cycle [子, 丑, 寅, 卯, 辰, 巳, 午, 未, 申, 酉, 戌, 亥] anchor: 2020-01-01
}
@JPEto
everyDay |> within(year) |> first |> filter(d => yearBranch(d) == 午)
#=> 2026-01-01

Reading the standard weekday (Gregorian.weekday) in a predicate:

# eval: 2026-01-01..2026-01-20
@JP
everyDay |> filter(d => weekday(d) == Mon)
#=> 2026-01-05 2026-01-12 2026-01-19

Pitfalls

• cycle is a rhythm (calendar-system-pure, infinite) — a 1-to-1 label over finite data, like the names of the 24 solar terms, is not a cycle but a table’s labels: (table literal; the source differs, but the reading side is the same binding-name projection). Attaching a fixed period to a data-derived window sequence is segmentBy’s labels: cycle form (ADR-47 — the same “the window containing the anchor carries the first label” as this page).
• Rotating the list (rewriting [Mon, …, Sun] as [Sun, Mon, …], etc.) gives the same calendar only if the anchor is also re-taken to a corresponding real day — with the anchor fixed, every label rotates at once (the phase is decided by “the window containing the anchor = the first label”. The old wording “the same anchor gives the same calendar” was wrong — corrected 2026-07-25). That the list order has nothing to do with the week’s start (WKST) still holds.
• A composite period like the 60-term sexagenary cycle may be a single 60-element cycle, or the two cycles of the ten heavenly stems and the twelve earthly branches composed in a predicate (a zip product of cycles is not introduced — open item F16).

Related

filter (label predicates) · table literal (data-derived labels) · the separation from WKST (stdlib/gregorian.md §4) · ADR-03/27/30.

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