Recurrence, Cleanly

One question decides everything.

The One Question

Does the pattern look the same in every parent cycle?

• “Hours 0, 4, 8, 12, 16, 20”: same every day, forever. → calendar-locked. The calendar field itself tells you the answer.
• “Every 14 months from March 2018”: hits 2018-03, 2019-05, 2020-07… the month drifts each year. → anchor-based. No calendar field can tell you; only elapsed time since a start date can.

These are two different kinds of recurrence; forcing both through one syntax is how recurrence grammars collapse. DTRExp gives each its own construct.

Construct 1 — Stride /interval[/duration] (calendar-locked)

Attach /<interval>[/<duration>] to a normal selector: from the range start, every interval-th unit, covering duration units (default 1).

Expression	Meaning	Covered
H0/4	every 4th hour from hour 0, each day	00, 04, 08, 12, 16, 20
M1/3	every 3rd month from January, each year	Jan, Apr, Jul, Oct
M1/5/2	every 5 months, 2 months long	Jan–Feb, Jun–Jul, Nov–Dec
Y2020:2040/3	every 3rd year of that range	2020, 2023, 2026, … 2038

Rules:

• Legal only when it fits inside the parent cycle (n ≤ parent’s span). M3/14 is a syntax error: 14 months can’t repeat inside one year; that’s a cadence (below).
• The range start is the anchor. Y2020:2040/3 anchors at 2020. Bare Y*/3 is a syntax error: no start, no anchor. (This kills the old “every 3 years… from when?” / year-0 problem by construction.)
• The first number after / is always the interval; the optional second is the duration, the same order as cadences (20180301/14M/2M). 1 ≤ duration < interval.
• Evaluation is one modulo: (value − start) % interval < duration. No dates, no iteration.

Stride is pure convenience; H0/4 and H0,4,8,12,16,20 are the same expression. It adds terseness, not power.

Construct 2 — Anchored Cadence <date>/<n><unit>[/<n><unit>] (anchor-based)

A component that starts with a date literal: from this date, repeat every <period>, covering <duration> each time (default: 1 period-unit).

Expression	Meaning	Covered
20180301/14M	every 14 months from 2018-03-01	2018-03, 2019-05, 2020-07, …
20200106/10D	every 10 days from 2020-01-06	Jan 6, 16, 26, Feb 5, …
20200106/10D/3D	every 10 days, 3 days long	Jan 6–8, 16–18, 26–28, …

Rules:

• The anchor date is required and part of the literal; a cadence without an anchor cannot be written, so it can never be ambiguous.
• Evaluation is still O(1): elapsed = unitsBetween(anchor, instant); covered iff elapsed % period < duration.
• This is the thing cron famously cannot express (“every 10 days”) and RRULE expresses only via DTSTART + INTERVAL. It maps 1:1 to ISO 8601 repeating intervals (R/2018-03-01/P14M), so toRRule() / ISO interop falls out for free.

Composing Them

Components still just intersect, like everything else in DTRExp:

Expression	Meaning
T0900:1200 20200106/10D	09:00–12:00, on every 10th day from 2020-01-06
m0:19 H0/4	first 20 minutes of every 4th hour (da Vinci’s sleep)
E1 20180301/14M	Mondays that fall inside each 14-month recurrence window

Cheat Sheet

Same pattern every year/day/hour? → selector + /n stride. Pattern drifts across the calendar? → date-anchored cadence. Want only some recurrences? → bound it with a date range.