/**
 * Return how many distinct calendar dates two date intervals share.
 *
 * - Counts the number of dates touched by the closed intersection
 *   `[max(aStart, bStart), min(aEnd, bEnd)]` — inclusive of both endpoints.
 * - Adjacent intervals (e.g. `aEnd === bStart`) share one date and count as `1`.
 * - Returns `0` when the intervals do not overlap at all (a well-defined answer, not
 *   invalid input).
 * - Returns `null` if either interval is invalid (`start > end`).
 * - Returns `null` on invalid input (wrong type, malformed strings).
 * - Diverges from date-fns's `getOverlappingDaysInIntervals`, which rounds up elapsed
 *   24-hour periods instead of counting calendar dates (its own doc example — Jan 10-20 vs
 *   Jan 17-21 — returns 3 there, 4 here). To reproduce date-fns's number, compose
 *   `intervalIntersectionDate` with `intervalCountDate`:
 *   `const span = intervalIntersectionDate(aStart, aEnd, bStart, bEnd); span ? intervalCountDate(span.start, span.end, "day") : 0;`
 *
 * - Accepts GMT calendar-annotated PlainDate strings — E5 (issue #78). A day is a day in every
 *   supported calendar, so this returns the same count whether or not the endpoints are
 *   calendar-tagged, and arguments may carry different or no tags (D4).
 *
 * @param aStart ISO 8601 date string for the first interval start, optionally calendar-annotated
 * @param aEnd ISO 8601 date string for the first interval end, optionally calendar-annotated
 * @param bStart ISO 8601 date string for the second interval start, optionally calendar-annotated
 * @param bEnd ISO 8601 date string for the second interval end, optionally calendar-annotated
 * @returns number of shared calendar dates, `0` when disjoint, or null on invalid input
 *
 * @example intervalOverlappingDaysDate("2024-01-01", "2024-06-30", "2024-04-01", "2024-12-31") // 91
 * @example intervalOverlappingDaysDate("2024-01-01", "2024-12-31", "2024-02-01", "2024-02-29") // 29
 * @example intervalOverlappingDaysDate("2024-01-01", "2024-06-30", "2024-06-30", "2024-12-31") // 1 (adjacent)
 * @example intervalOverlappingDaysDate("2024-01-01", "2024-06-30", "2024-07-01", "2024-12-31") // 0 (disjoint)
 * @example intervalOverlappingDaysDate("invalid", "2024-06-30", "2024-04-01", "2024-12-31") // null
 */
export declare function intervalOverlappingDaysDate(aStart: string, aEnd: string, bStart: string, bEnd: string): number | null;