Kairos Language Specification — 6. Glossary
Translated from the canonical Japanese chapter spec/50-glossary.md. The
source_shaabove records the source revision; a consistency check flags this page when the Japanese original changes.
An index for lookup while reading the specification. Each entry is 〈term｜one-line
definition｜references〉. The naming status is §5.4 — every word is final; no placeholders
remain (the batch confirmation F51 of 2026-07-09 settled everything else as official names and
renamed the supply pair to sessionOpens/sessionCloses; the final rephase ruling of
2026-07-26, formerly shiftBoundary, completed the set). In the references, “§” points to
chapters of this specification and stdlib/… to the standard premise commentary.
6.1 Layers, types, and overall structure
| Term | Definition | References |
|---|---|---|
| Kairos | This language. A schedule definition language that, from the continuous base Chronos, weaves the set of meaningful instants at which things should fire (kairos) | §1.1 |
| Chronos | The single absolute continuous time axis, independent of TZ = the base. A uniform idealized scale without leap seconds (each UTC day = 86,400 s). Every calendar system and granularity is a projection onto it; it is never relativized. The lexical name is chronos (ADR-29/33) |
§1.3 · §2.2 |
TZ (tz:) |
A TZ is a versioned mapping from chronos to civil coordinates (wall-clock labels). tz: is the premise context value that gives its name (I6; declaration leans mandatory; enforced at point of use). Values: IANA region identifiers, fixed offsets (strict unique form "±HH:MM" only = ADR-43), and "UTC". Time literals that fall into a gap or overlap are errors (ADR-33) |
§3.2 · §3.3 · §3.6 · §5.5 |
| kairos | A “meaningful instant at which something should fire”, chosen on the base Chronos. The language’s output (each point of a time stream) | §1.1 |
| premise layer（premise 層） | The layer that builds and supplies calendar systems and calendars (DDL-like, declarative, multi-line) | §2.1 · §3 |
| body layer（本体層） | The layer that weaves schedules with the supplied vocabulary (DML-like, pipe-styled, one-line oriented) | §2.1 · §4 |
| time stream type（時間ストリーム型） | A lazy, infinite, ordered sequence of points on the base. The body layer’s first-class value = the extension | §2.2 |
| premise type（premise 型） | The generating rule itself for calendar systems and the like = the intension. Comes in primitive/derived variants, with premise → premise closure |
§2.2 |
| value type（値型） | Numbers, booleans, enumerations, lists, strings (ADR-32), and instants (ADR-43 = bare value bindings are also legal). The third type, used for leap tests and the n of shift(n) |
§2.2 · §3.5 |
| lambda (anonymous function)（ラムダ（無名関数）） | A nameless function passed in place. args => expression (the arrow => is distinct from the type notation ->) |
§3.5 |
| higher-order function（高階関数） | An operator that takes a function as an argument. filter, span, split qualify (cycle takes a list) |
§3.5 |
| predicate（述語） | A lambda returning a boolean. filter takes both premise predicates (on:) and value-expression predicates (lambdas) |
§3.5 · §4.6 |
| extension / intension（外延 / 内包） | Extension = the generated sequence of points (a time stream); intension = the generating rule (a premise) | §2.2 |
| evaluation annotation (out-of-coverage)（評価註釈（範囲外）） | A sequence of annotation intervals running alongside the result 〔[a,b), kind, source, covering, asof〕. For now the only kind is “out-of-coverage” = intervals where the result may depend on data outside the coverage. Attached even to non-empty results. Absence of annotations is not a proof of correctness | §4.10 · ADR-15/37 |
| effective coverage（実効被覆域） | The settled region, computed via the transport table, of the bindings a reference actually reads (= the complement of the annotation intervals). The criterion for the error classifier (out-of-coverage vs. mix-up) — not the raw table’s covering | §4.10 · ADR-37 |
| coverage claim（被覆主張） | A binding-postfix covering: = the unverifiable explicit claim “this composition is complete over this range” (the sole outlet for offsetting; governance on a par with source/asof) |
§3.8 · ADR-37 |
| coverage summary / runway（被覆サマリ / 残走路） | For each data source the evaluation referenced: 〔source, covering, asof, completeness claim, days remaining from the evaluation to (the runway)〕. An unclipped vessel for monitoring (separate from annotations) |
§4.10 · ADR-37 |
| closure（閉包） | Every operator is (stream…, premise) → stream. Derived results can be fed back in as inputs |
§2.3 |
| core family（core 族） | The body layer’s minimal, strict operator set (generators, point transforms, combinators, filters, windows, selectors, strides) | §2.4 · §4 |
| sugar（糖衣） | Shorthand that names a core composition. Erasable by expansion into core (one-way dependency) | §2.4 · §4.8 |
| primitive definition（原始的定義） | A calendar-system root with no derivation source (Gregorian, etc.). Carves windows from the base |
§3.6 · stdlib/gregorian.md |
| derived definition（派生的定義） | A calendar system built by overriding an existing premise (fiscal calendars, etc.). premise → premise closure |
§3.7 |
6.2 The premise and its components
| Term | Definition | References |
|---|---|---|
| premise（前提） | The umbrella term for the preconditions under which an expression’s interpretation holds. Isomorphic to a contract’s recitals | §3.1 |
| preamble（前文） | The declarations that set premises before the body expression. Definition premise Name {…} / lightweight @name / full form |
§3.2 |
| calendar system（暦法） | A set of window-partition definitions on the base. Determines what a “month” is. Gregorian is just one instance | §3.6 |
| calendar（カレンダー） | A business-day calendar referenced by name (a weekend → holiday → organization-holiday cascade). Its version is fixed by asof | table §3.3 |
| calendar entity（カレンダー実体） | The premise installed at calendar:. Having the public word nonWorking and declaring tz: are the requirements for qualifying as one (ADR-35) |
§3.9 |
nonWorking |
The calendar entity’s reserved public word (time stream type; no arguments; day alignment in the entity’s tz). Bundles the non-working set = the result of the cascade composition | §3.9 |
bizDay (standard derivation)（標準導出） |
The derivation sugar the language fixes uniformly: everyDay \ C.nonWorking (C = the in-scope calendar:). With a calendar: in scope it is a language-reserved derived name (manual binding is a static error). A premise name in axis position (on: TSE) is read as this derivation. Consumer-relative (an axis drawn from the reader’s own days) |
§3.9 |
sessionOpens/sessionCloses |
The entity’s paired reserved public words = the opening sequence and closing sequence (the supply convention for business hours; optional declaration). Points are facts in the entity tz’s civil coordinates (wall clock). A session = a union of half-open intervals; the consistency check is local alternation + joint effective coverage | §3.9.1 |
bizOpen/bizClose/isOpen (standard derivations)（標準導出） |
The business session’s opening sequence, closing sequence, and membership predicate. Entity-relative (the judgment material resolves in the entity’s culture = the entity’s tz and holidays; a role distinct from bizDay’s consumer-relative stance). Business-day-ness is read off the opening day | §3.9.1 |
| axis（軸） | The unit an operation counts in (bizDay/day/hour…). Named by on:/unit:, resolved against the in-scope calendar. A separate concept from the base chronos (ADR-29) |
§3.3 |
| roll convention（ロール規約） | The convention that moves invalid points to valid ones (Following/Preceding/Modified). Axis-independent | §4.4 · §6.6 |
| granularity（粒度） | Year, month, day, hour, minute, second, week, quarter… A display projection of position on an axis. Not carried in the type | §2.2 |
| width (conventions)（幅（規約）） | The length of an offset. The convention set of elapsed time vs. civil time + roll. grid’s 1d is a civil day (not 86400s = elapsed time) |
stdlib/gregorian.md §1 · ADR-11/12 |
| WKST | Where the week starts (the week window’s cut; the origin of “week N”). A culture-dependent premise member | §3.3 · stdlib/gregorian.md §4 |
| asof | The temporal version that fixes the calendar version. Defaults to the evaluation instant when omitted | table §3.3 |
| source（出所） | The authority of the data (official / organization-local). A premise alongside asof | table §3.3 |
| name resolution (premise-relative)（名前解決（premise 相対）） | Names resolve under the in-scope premises. When ambiguous, qualify as Gregorian.month |
§3.4 |
| scope defaults (folding)（スコープ既定（畳み込み）） | Declare axis:/roll: once in the preamble and omitted stages inherit them. Innermost wins (default → evaluation context → block → stage) |
§3.3 |
| Mechanism A（機構 A） | Name resolution in derivations = bare names re-resolve in the derived scope (dependent words follow automatically); Base.word pins to the base value |
§3.7 |
6.3 Calendar systems and windows (the premise layer’s window-generating words)
| Term | Definition | References |
|---|---|---|
| window（窓） | A sub-stream bundled by period. Two kinds: partition-type and interval-sequence-type | §2.6 (I5) · §4.2 |
| partition-type window（パーティション型窓） | A window that partitions the axis without remainder. Exhaustiveness and non-overlap are checkable (I5) | §4.2 |
| interval-sequence window（区間列型窓） | A window cut by markers. Exhaustiveness is not guaranteed; the gap policy is made explicit | §4.2 |
| window-generating words（窓生成語） | The words with which a primitive definition carves the base into windows. grid/span/split/cycle |
§3.6 |
chronos (bare name)（裸名） |
The lexical name referring to the continuous base Chronos (day = chronos grid 1d). Only grid accepts it. A separate concept from the operation axis axis: (ADR-29) |
§3.6 · §1.3 |
grid(w) |
Uniformly divides the continuous axis at width w (the atoms of a calendar). Example: day = chronos grid 1d. The phase is the default alignment (civil-time widths = the opening instant of each civil day 〈tz midnight on ordinary days〉; elapsed-time widths = the epoch), overridable with anchor: (ADR-31) |
§3.6 |
epoch (epoch:)（紀元） |
The origin for span window ordinals and epochOrdinal. Language default 1970-01-01T00:00 (in the in-scope tz = a different point on chronos for a different tz; ADR-33); overridable via the primitive definition’s member epoch: (cannot be placed in the preamble). Ordinals are 0-based; before the epoch they are negative |
§3.6 · ADR-31 |
span(f) |
Bundles finer units a variable/constant number at a time (bottom-up aggregation). f = n => count |
§3.6 |
split(g) by: u |
Divides a parent window at variable widths in unit u (top-down). Used for dependent windows |
§3.6 |
cycle(labels) anchor: |
Attaches repeating labels to a partition window. Labels, not windows. Period length and target are arbitrary (year cycle is fine). anchor:: the target window it falls in carries the head label. The binding name reads as a point → label value function |
§3.6 · stdlib/gregorian.md §4 · ADR-27 |
week window（week 窓） |
The 7-day tiled window at WKST phase. A Gregorian public word that lazily resolves wkst:. Partition-hood is certified by the I5 check |
§3.6 · stdlib/gregorian.md §4.5 |
| table literal（テーブルリテラル） | Promotion of an instant list to a time-stream constant ([2026-03-20, …]). Ascending order required; source governance; validity range via covering:. labels: gives a parallel label sequence (the definition of a point → label projection). The empty form [] covering: … requires an explicit covering (the primary form of “zero points but a coverage to claim”; ADR-45) |
§3.8 · ADR-26/30/45 |
external |
The external-supply declaration = a table literal resolved at run time. Restricted to the right-hand side (head position) of a premise binding. kind: = the alignment claim (dates/instants; holds as declared even when empty); labels: = the enumeration of the label range; covering/asof are always carried by the resolved value (the supply contract). Resolution is an adjunct of the evaluation context (one resolution per evaluation, demand-driven); failure is a supply error (machine-readable subcategories) |
§3.8 · ADR-46 |
| public word（公開語） | A top-level binding in a premise block. Referenced with . (Gregorian.month) |
§3.6 |
| public boundary word（公開境界語） | A public word that derives boundaries by reusing selectors (monthEnd = month \|> last). What generators really are |
§3.6 |
with |
The core of derivation. Overrides/adds the base’s public words (Fiscal = Gregorian with {…}) |
§3.7 |
rephase |
Derivation sugar that shifts window W’s cuts by δ in unit U (re-phase). Expands into a span phase shift |
§3.7 |
| phase（位相） | The phase origin of span/split (a fiscal calendar’s April start, etc.) |
§3.7 |
6.4 The body layer’s operator families
| Term | Definition | References |
|---|---|---|
| generator（生成子） | () → stream. Calendar-system-pure and calendar-independent (everyDay, everyInstant, public boundary words, table literals) |
§4.2 · I8 |
window within(w)（窓） |
Partition-type windowing. w is a window name (month/week/…) |
§4.2 |
window segmentBy(m, edges:, empties:)（窓） |
Interval-sequence windowing. Gap policy required | §4.2 |
selectors first/nth(n)/last（選択子） |
Pick the Nth / the last within a window. Default is the innermost window; make it explicit with of:. Window-relative |
§4.3 · I4 |
point transform roll(conv, on:)（点変換） |
Moves invalid points to valid ones by conv. on: is an axis name or a derived stream |
§4.4 |
point transform shift(n, unit:)（点変換） |
Moves by n (signed) in units of U. Direction is expressed by the sign | §4.4 |
point transform snapTo(w)（点変換） |
Maps each point to the first point of the w window containing it (floor; aligns granularity seams) = reconciliation by chronos membership |
§4.4 · ADR-27/30 |
point transform rebase(to:)（点変換） |
Preserves the date label and maps to the head of the same date’s civil day in the to tz = reconciliation by label correspondence (cross-tz “same date” composition = F69). Input restricted to the default-aligned day grid; nonexistent dates are explicit errors |
§4.4 · ADR-40 |
projection ordinalIn(u, w, d)（射影） |
Within the w window containing point d, the ordinal of the u window containing d (1-based; granularity-independent). The reverse of nth |
§4.9 · ADR-27/30 |
projection epochOrdinal(u, d)（射影） |
The running ordinal of u windows from the epoch (0-based; the epoch is the language default 1970-01-01, overridable with epoch:) |
§4.9 · ADR-27/30/31 |
| label projection (binding name)（ラベル射影（束縛名）） | The binding name of a labeled window/cycle/table doubles as the projection name (weekday(d), sekki(d)). Points store no labels; labels are read via projections (the generic word labelOf was retired; ADR-30) |
§4.9 · §3.6 |
window instance reference W(v)（窓インスタンス参照） |
Value application to a label-sourced window binding = the preimage (year(2020) = the days of that year; returned as a time stream). Union of all matches; empty is legitimate; outside a statically enumerable label range is a static error. The dual of binding-name projection; point vs. value branches on the argument expression’s type (decided after expansion = §2.7) |
§4.9 · §2.7 · ADR-42 |
| element point sequence（要素点列） | Of the input point sequence that window binding W’s definition bundled into windows, the points belonging to W’s windows (grid/span/split chains = equivalent to the atomic grid ticks; segmentBy = the input points). The carrier of window instance references. An internal concept (not a word users write) | §4.9 · ADR-42 |
| combinator（結合子） | Stream × stream → stream. Union \|, intersection &, difference \. Intersection and difference require matching alignment on both sides |
§4.5 |
| cascade（カスケード） | Prioritized overriding. Has no dedicated symbol; expressed by left-associative ordered application of union and difference (last wins) | §4.5 |
| alignment（整列） | The static property of a stream: “every point lies on the ticks of an atomic grid G = (width, normalized phase, tz name)”. &/\/axis membership require the same G (mismatch is a static error); snapTo is the explicit re-alignment. Not a type (ADR-05/36). The value is a G, “none”, or vacuous conformance (an empty table conforms vacuously to every alignment; it passes the check and combinations inherit the partner’s. ADR-45) |
§4.5 |
filter filter（フィルタ） |
Thins by predicate. Takes both premise predicates (on:) and value-expression predicates (lambdas) |
§4.6 |
stride stride(n, from:)（ストライド） |
Thins the input points to “every nth” (input-relative; no axis argument — what gets counted is decided by the preceding stage = ADR-38). n is an integer ≥ 1. Consumes no windows; ignores boundaries; continuous. Origin from: required (the first input point at or after from: is step 0) |
§4.7 · ADR-31/38 |
stride strideBy(w, from:)（ストライド） |
Steps by width (a physical magnitude across multiple axes; e.g. 1 sol). Origin from: required |
§4.7 · ADR-31 |
window-membership predicate coincides(S, w, d)（窓所属述語） |
Whether the w window containing point d holds a point of S (boolean = bounded existential quantification). Interval membership, so alignment is not required (only the tz name is checked); settled by the witness rule (true = a point in a non-annotated interval; false = the window lies within the effective coverage). The receiving vessel for F68 |
§4.9 · ADR-38 |
| sugar definition (base form B)（糖衣定義（基底 B）） | name(args) = s => s \|> core-chain. Binds the preceding stage with s => |
§4.8 |
| sugar definition (shorthand A)（糖衣定義（略記 A）） | When the preceding stage is straightforward, omit s => — point-free (eta reduction) |
§4.8 |
6.5 Symbols, prefixes, and named arguments
| Symbol | Meaning | References |
|---|---|---|
\|> |
Stage connection (body layer stream→stream / premise layer premise→premise) | §2.5 |
. |
premise qualification (Gregorian.month) |
§2.5 |
\| & \ |
Combinators: union, intersection, difference (\ = U+005C, not the yen sign ¥) |
§4.5 |
= / == |
Binding (definition) / equality comparison | §3.5 |
=> |
Lambda binding (distinct from the type notation ->) |
§3.5 |
+ - * / mod div |
Arithmetic (mod and div are words) |
§3.5 |
[…] / l[i] / in |
List literal, indexing (0-based), membership predicate | §3.5 |
a..b |
Date range (sugar expanding to consecutive days) | §3.8 |
"…" |
String literal (values for TZ and source; no newlines, no escapes) | §5.5 · ADR-32 |
and or not |
Logic (words; the symbols are reserved for the combinators) | §3.5 |
? : |
Ternary conditional | §3.5 |
@name（@名前） |
Lightweight reference to a premise bundle | §3.2 |
on: / unit: |
Names the axis a stage counts in (roll/filter / shift; stride is input-relative = takes no axis; ADR-38) | §3.3 |
of: |
Makes a selector’s target window explicit | §4.3 |
by: |
The unit of split’s widths |
§3.6 |
axis: |
The axis default in the preamble (folding; settled by ADR-29) | §3.3 |
phase: |
The phase origin of span/split |
§3.7 |
anchor: |
cycle’s label phase (which actual day carries the head label) |
§3.6 |
from: |
The origin for the stride family (stride/strideBy). Always required (supply from windows was retired by ADR-31) | §4.7 |
edges: / empties: |
segmentBy’s gap policy |
§4.2 |
roll: |
The roll-convention default in the preamble (folding; being explicit is recommended) | §3.3 |
covering: |
The validity range = the two-sided claim “complete inside, unknown outside”. Does not touch the values (inclusion of every element is statically checked). Open-ended 2021../.. (completeness claim, with governance), interval lists, and binding-postfix (coverage claim) are allowed. Omission = the sequence’s ends (narrowest) and .. = complete everywhere (widest) are polar opposites (an empty table has no ends, so omission is impossible = explicit covering required. ADR-45) |
§3.8 · §4.10 · ADR-26/37/45 |
label: |
The label-assignment expression at window-generation time. The lambda receives the window’s first point, and name(d) ≡ assignment-expression(first point) (at projection time, lazily evaluated). Window and projection references on the representative point are allowed; adjacent windows and self-reference are not |
§4.9 · ADR-30/34 |
labels: |
The parallel label sequence (the projection’s defining data). For tables = point labels (same length as the instant list; ADR-30) / for segmentBy window sequences = window labels (same length as the coverage-based window count, aligned by window-sequence ordinal; ADR-39 = the vessel for F62) | §3.8 · §4.2 · ADR-30/39 |
6.6 Roll conventions and enumeration values
| Term | Definition | References |
|---|---|---|
| Following / Preceding | Move an invalid point to the next / previous valid point | §4.4 |
| Modified | Takes a superordinate window as an argument and moves while staying within that window | §4.4 |
| Mon…Sun | Enumeration values for weekday labels (value type). Used in cycle’s cyclic list | §3.6 |
6.7 Invariants I1–I8
| No. | One-liner | References |
|---|---|---|
| I1 | Fixed base (every element is a point on the single base Chronos) | §2.6 |
| I2 | Closure (every operator is (stream…, premise) → stream) |
§2.6 |
| I3 | Explicit resolution (roll conventions and anchor resolution as mandatory arguments; silent bugs made syntactically impossible) | §2.6 |
| I4 | Window-relative (selectors are relative to a containing window; no window is a type error) | §2.6 |
| I5 | Exhaustiveness verification (partition-type is checkable for exhaustiveness and non-overlap; interval-sequence-type makes gaps explicit) | §2.6 |
| I6 | Context flow (TZ, WKST, asof, and out-of-coverage provenance 〈interval annotations〉 flow as evaluation context / annotations) | §2.6 · §4.10 |
| I7 | Pure and lazy (defined online over infinite streams) | §2.6 |
| I8 | Generator purity (generators depend only on the calendar system, never on calendars) | §2.6 |