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with — derived definition (overriding public words)

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Category: derivation (premise-layer core) / Signature: Base with { w = … } : premise -> premise / name settled (spec §5.4)

Meaning

Builds a new premise on top of an existing one, replacing or adding only the public words you name (the premise → premise closure). Fiscal calendars, organization-specific calendars, added labels — all of these are this.

Name resolution is Mechanism A (ADR-17):

• Bare names re-resolve in the derived scope — inherited words that depend on an overridden word (quarter, yearStart on year) follow the new definition automatically.
• Base.word pins to the base’s value — the explicit means when you deliberately want to fix on the original definition.

A derivation moves only the window cuts; calendar dates stay fixed (I1). 2026-03-01 remains “March 1” under the fiscal calendar; only the year window it belongs to changes, to fiscal 2025 (Apr 2025–Mar 2026).

Examples

A fiscal calendar (April start) is one line — it never touches month, so calendar dates and month-ends stay fixed:

# eval: 2025-01-01..2028-01-01
premise Fiscal = Gregorian with { year = month span (_ => 12) phase: 3 label: (p => yearNo(p)) }
premise FY { calendar-system: Fiscal; tz: "Asia/Tokyo"; wkst: Mon }
@FY
everyDay |> within(year) |> first
#=> 2025-04-01 2026-04-01 2027-04-01

quarter’s inherited definition (year split … by: month) automatically follows the new year and becomes the fiscal quarter:

# eval: 2026-01-01..2027-01-01
premise Fiscal = Gregorian with { year = month span (_ => 12) phase: 3 label: (p => yearNo(p)) }
premise FY { calendar-system: Fiscal; tz: "Asia/Tokyo"; wkst: Mon }
@FY
everyDay |> within(quarter) |> first
#=> 2026-01-01 2026-04-01 2026-07-01 2026-10-01

Pitfalls

• A derivation cannot be expanded into the primitive (it is a new rule) — an asymmetry distinct from the sugar → core expansion (one-way) (spec §2.4).
• In a fiscal calendar, pins like month = Gregorian.month and cycle avoidance are unnecessary — thanks to the design in which month does not depend on year (“leap is a value, not a window”) (spec §3.6/§3.7).
• The numbering of fiscal years (is fiscal 2025 the starting or the ending calendar year?) is a labeling question independent of where the windows are cut (the label: attachment expression; spec §4.9).

Related

rephase (sugar over with) · span · split · Mechanism A (ADR-17) · I1.

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