examples/prayer-times.umsg
%unimsg 0 worship/prayer-times/v1 · 283 lines · 15058 bytes of text · 11506 bytes canonical · the raw file
Point at anything below — a sigil, a literal, a brace — and the card says what it is. Keyboard: tab through the document. Every explanation is also printed in full beneath the source.
%unimsg 0 worship/prayer-times/v1
-- The calculation of Islamic prayer times: one astronomical core, and the
-- several conventions layered on it.
--
-- This document exists because prayer times are the clearest real case of the
-- thing this format was made for. There is one piece of astronomy, agreed by
-- everyone, and a set of rules about how to apply it, not agreed by everyone.
-- Every implementation in the wild hard-codes those rules as a table in its
-- source. They are not code. They are data with authorities attached, and they
-- belong somewhere a person can read, compare and cite.
--
-- READ THIS BEFORE USING ANY NUMBER HERE. The parameters below carry religious
-- weight: an angle that is wrong by a degree moves the start of a fast. They
-- are recorded to the best of the author's knowledge, each with the authority
-- it is attributed to, and they must be checked against that authority before
-- anyone prays by them. The document's structure is offered with confidence;
-- its parameter values are offered for verification.
--
-- The format takes no position on which convention is correct. It could not:
-- this is ikhtilāf — a difference of opinion among scholars, each reasoned and
-- each held by a recognised authority — and it is not a question an encoding
-- gets a vote on. What the format can do is carry all of them, side by side,
-- each saying whose it is.
prayer-times @worship/prayer-times/v1 {
title "Prayer time calculation, with its conventions carried as data"
status :provisional
scope {
is "the astronomical core, the convention parameters, the schools for Asr,
the strategies for latitudes where the core has no solution, and
vectors that pin computed times"
is-not [
"a ruling on which convention applies to anyone",
"a timetable — a timetable is this, evaluated, for one place and year",
"an ephemeris: the solar position here is the standard low-precision
series, good to well under a minute of time, which is finer than the
rounding every convention applies afterwards"
]
on-precision "Worth stating plainly, because it is the question that
prompted this document. Nothing here needs exact decimals.
The arithmetic is trigonometric and the target is about a
second; a double carries fifteen significant digits and is
comfortable. Exact decimals earn their place where values
differ beyond that — money, and amounts denominated in very
small units. What this calculation stresses instead is
transcendental functions, which is a different axis, and one
the store's formula grammar deliberately does not reach."
}
-- ===================================================================
-- THE CORE
-- ===================================================================
-- Inert data. These steps describe a computation and do not perform one; a
-- reader that has sine, cosine and an arc-cosine can carry them out.
solar !formula/procedure {
yields "the sun's declination and the equation of time, for an instant"
given [ "a calendar date", "a longitude, to place the instant" ]
needs [ :sin, :cos, :arcsin, :arctan2 ]
steps [
| n name rule
| 1 "julian day" "the standard civil-to-Julian conversion, less longitude / (15 x 24)"
| 2 "days from epoch" "d = jd - 2451545.0"
| 3 "mean anomaly" "g = 357.529 + 0.98560028 x d"
| 4 "mean longitude" "q = 280.459 + 0.98564736 x d"
| 5 "true longitude" "L = q + 1.915 x sin(g) + 0.020 x sin(2g)"
| 6 "obliquity" "e = 23.439 - 0.00000036 x d"
| 7 "right ascension" "RA = arctan2(cos(e) x sin(L), cos(L)) / 15"
| 8 "declination" "dec = arcsin(sin(e) x sin(L))"
| 9 "equation of time" "eqt = q / 15 - RA, brought into [-12, 12] hours"
]
accuracy "Under a minute of time for any date within a century or so of the
epoch. Every convention rounds to the minute afterwards, so the
series is finer than the answer."
}
hour-angle !formula/procedure {
yields "the hours between solar noon and the sun standing at a given altitude"
rule "T(a) = arccos( ( -sin(a) - sin(dec) x sin(lat) ) / ( cos(dec) x cos(lat) ) ) / 15"
no-solution "When the quotient falls outside [-1, 1] the sun never reaches
that altitude on that day at that latitude, and T has no
value. This is not an error and not a missing datum: it is a
correct answer of the form `there is none`. See
undefined-is-not-missing below."
}
noon {
rule "dhuhr = 12 + timezone - longitude / 15 - equation-of-time"
note "The only prayer time that is not an hour angle. Every other time is
noon plus or minus one."
}
from-noon [
| prayer at altitude-or-rule
| :fajr "noon - T(fajr-angle)" "the convention's Fajr angle below the horizon"
| :sunrise "noon - T(0.833)" "the sun's upper limb at the horizon, with refraction"
| :dhuhr "noon" "the sun on the meridian"
| :asr "noon + A(shadow-factor)" "the shadow rule below"
| :maghrib "noon + T(0.833)" "sunset, the mirror of sunrise"
| :isha "noon + T(isha-angle)" "or a fixed interval after Maghrib, per convention"
]
asr !formula/procedure {
rule "A(f) = arccos( ( sin(arccot(f + tan(|lat - dec|))) - sin(dec) x sin(lat) ) / ( cos(dec) x cos(lat) ) ) / 15"
meaning "The moment an object's shadow exceeds its noon shadow by f times
the object's own height."
schools [
| school shadow-factor followed-by
| :standard 1 "Shafi'i, Maliki and Hanbali"
| :hanafi 2 "Hanafi"
]
note "One number, and it moves Asr by well over an hour in summer. See
vectors p-001 and p-006, which differ in nothing else."
}
-- ===================================================================
-- THE CONVENTIONS
-- ===================================================================
-- The rules-as-data section, and the reason the document exists. Each row is
-- a position held by a named body. The format holds them all; it adjudicates
-- none of them.
--
-- `isha-minutes` where present replaces the angle: Isha falls a fixed
-- interval after Maghrib rather than at a solar altitude.
conventions [
| id attributed-to fajr-angle isha-angle isha-minutes
| :mwl "Muslim World League" 18.0 17.0 0
| :isna "Islamic Society of North America" 15.0 15.0 0
| :egyptian "Egyptian General Authority of Survey" 19.5 17.5 0
| :umm-al-qura "Umm al-Qura University, Makkah" 18.5 0.0 90
| :karachi "University of Islamic Sciences, Karachi" 18.0 18.0 0
| :tehran "Institute of Geophysics, University of Tehran" 17.7 14.0 0
| :jafari "Shia Ithna Ashari, Leva Research Institute, Qum" 16.0 14.0 0
]
convention-notes {
verify-these "Every number in that table is a parameter with religious
consequence and is recorded here from secondary knowledge. An
implementer must confirm each against the body it is
attributed to. The attribution column exists so that this is
possible rather than merely advisable."
umm-al-qura-ramadan "Umm al-Qura is commonly cited as using 120 minutes
rather than 90 during Ramadan. A convention whose
parameter depends on the season is exactly the kind of
rule that ends up buried in code; if it is adopted it
belongs here as a second row, not as a branch."
maghrib-is-not-always-sunset "Some conventions, Tehran and Jafari among
them, place Maghrib at a small angle below
the horizon rather than at sunset. Not
modelled in the table above, and that is a
gap rather than a decision."
}
-- ===================================================================
-- WHERE THE SUN DOES NOT COOPERATE
-- ===================================================================
high-latitude {
problem "Above roughly 48 degrees the sun does not descend far enough below
the horizon in summer for Fajr or Isha to exist. Further north it
does not set at all, and Maghrib and sunrise go with them."
undefined-is-not-missing "Four states that all look like `no value` if they
are not distinguished, and an implementation that
conflates them will be wrong in a way nobody
notices:"
states [
| state means reader-should
| :computed "the equation had a solution" "show the time"
| :undefined "the sun never reaches that altitude here today" "say so, and name the strategy if one is applied"
| :approximated "no solution, and a named strategy supplied a time" "show the time and the strategy together"
| :failed "the calculation could not be carried out at all" "report the fault, never a time"
]
strategies [
| id rule
| :none "leave Fajr and Isha undefined and say so"
| :middle-of-night "the night, sunset to sunrise, halved"
| :one-seventh "a seventh of the night from sunset, and from sunrise"
| :angle-based "a portion of the night set by the convention's own angle, night / (60 / angle)"
| :nearest-latitude "compute as though at 48.5 degrees"
]
which-strategy "A choice, and not one this document makes. The strategies
are recorded because they exist and are used; selecting one
is a matter for whoever prays by the result."
}
-- ===================================================================
-- VECTORS
-- ===================================================================
-- Computed from the rules above, with no strategy applied for high latitudes,
-- so the undefined cases show as undefined. Times are local, rounded to the
-- nearest minute, and Asr uses the standard factor except where stated.
--
-- These make the document falsifiable: an implementation derived from it
-- either reproduces them or does not.
vectors {
rounding "to the nearest minute; a convention that rounds differently will
differ from these by up to a minute, which is a real difference
and should be declared rather than absorbed"
asr-factor "1 everywhere except p-006, which is the same instant computed
with 2 and differs in nothing else"
times [
| id place date convention fajr sunrise dhuhr asr maghrib isha
| :p-001 "Makkah" "2026-08-04" :mwl "04:35" "05:55" "12:27" "15:46" "18:59" "20:14"
| :p-002 "Makkah" "2026-08-04" :isna "04:49" "05:55" "12:27" "15:46" "18:59" "20:05"
| :p-003 "Makkah" "2026-08-04" :egyptian "04:27" "05:55" "12:27" "15:46" "18:59" "20:17"
| :p-004 "Makkah" "2026-08-04" :umm-al-qura "04:32" "05:55" "12:27" "15:46" "18:59" "20:29"
| :p-005 "Makkah" "2026-08-04" :karachi "04:35" "05:55" "12:27" "15:46" "18:59" "20:19"
| :p-006 "Makkah" "2026-08-04" :mwl "04:35" "05:55" "12:27" "17:01" "18:59" "20:14"
| :p-010 "London" "2026-08-04" :mwl "02:44" "05:28" "13:07" "17:15" "20:45" "23:15"
| :p-011 "London" "2026-06-21" :mwl "-" "04:43" "13:02" "17:25" "21:21" "-"
| :p-012 "Tromso" "2026-06-21" :mwl "-" "-" "12:46" "17:58" "-" "-"
]
undefined-vectors {
p-011 "London on the summer solstice: the sun sets and rises, so Maghrib
and sunrise exist, and it never falls 18 degrees below the horizon,
so Fajr and Isha do not. A dash here is the answer, not a gap."
p-012 "Tromso on the same day: the sun does not set. Sunrise, Maghrib,
Fajr and Isha are all undefined together, and only Dhuhr and Asr
survive — the two that do not depend on the horizon."
p-010 "London five weeks later, everything defined, and Fajr at 02:44
with Isha at 23:15. Nothing is wrong with it, and it is the case
that makes people reach for a strategy."
}
what-would-falsify-this "Any of these times differing by more than a minute
from an implementation of the steps above, or a
dash where a time was computed, or a time where a
dash was expected."
}
-- ===================================================================
-- PROVENANCE
-- ===================================================================
provenance {
astronomy "The low-precision solar series is standard and long published;
it is not anyone's proprietary work and is reproduced here as
steps rather than as code."
parameters "Recorded from secondary knowledge and attributed per row. Not
verified against the issuing bodies by the author of this file.
This is stated in the header, in convention-notes, and here,
because it is the one thing about this document that could
cause harm if skimmed."
vectors-from "Evaluating the steps in this document, not from any published
timetable. They test that an implementation matches this
document. They do not test that this document matches the
authorities — only checking the parameters can do that, and
that check has not been done."
method-note "Written after a session in which prose specifications were
repeatedly found to be satisfied by whatever the reader
understood them to mean. The conventions are a table, the
states are a table, the strategies are a table, and the
vectors carry numbers, for that reason."
}
}
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20 64 65 63 69 73 69 6f 6e 2eexamples/prayer-times.umsg 11506 bytesEvery construct on this page
The formal columns are read from the specification when this page is generated. The last column is this site's plain-language gloss and is not normative — where they differ, the specification is right.
| construct | glyph | carries | example | gloss |
|---|---|---|---|---|
| :annotation | — | — | — | A bare name qualifying the value after it—for example a language tag or a unit such as kg. It is not a value itself; a bare name with nothing after it is an error, not a guess. |
| :array | ^ | type, or type:shape; then [ elements ] | ^f64 [ 1.5, 2.5 ] or ^i16:2x3 [ … ] | A packed, homogeneous numeric array. The ^ marker gives every element its type and may also give the row-major shape: ^f64:2x3 [ … ]. |
| :array-element | — | — | — | One element of a typed array. Its type comes from the ^ marker, so 1.5 inside ^f64 is binary64 rather than an exact decimal. |
| :array-missing | — | — | — | A missing position in a typed array. null here is not an element value: it adds a validity mask while preserving the array's shape. |
| :block | — | — | — | A block: named pairs, in braces. Its keys are sorted in the encoding and shown here as written. |
| :bytes | ~ | encoding:data | ~hex:ff00 or ~b64:iVBORw0KGgo= | Raw octets, carried as octets. No base64 tax, no pretending they are text. |
| :comment | -- | to end of line | -- a note | A note for people. It travels with the pair it precedes and never reaches the bytes. |
| :decimal | — | — | — | An exact decimal. 19.99 is nineteen and ninety-nine hundredths, not the nearest double to it. |
| :extension | ! | name, then value | !acme/hint { zone 4 } | A qualifier this reader may not know. It survives the round trip intact, and stays legible on the way past — the rule that separates an extension from a private convention. |
| :float | — | — | — | A binary float, marked so it can never be mistaken for the exact decimal beside it. |
| :hash | # | algorithm:hex | #sha256:deadbeef | The digest of some content, with the algorithm said out loud so it is still meaningful in ten years. |
| :header | % | unimsg only | %unimsg 0 label | Declares the format version and what this document is. Optional, and useful exactly when a file arrives without context. |
| :identifier | @ | word | @ord-88213 | Gives this value a name, so another document can point at it without copying it. |
| :integer | — | — | — | A whole number of any size. Past 2^53 it is still exact, which is the whole reason this is not JSON. |
| :key | — | — | — | A field name: the first thing in a pair. It is bare when possible and quoted when needed, and names the content without becoming part of the value. |
| :reference | -> | an identifier or a path | -> @cust-4471, -> @lexicon.entries.kitāb | Points at a name. Nothing follows it while reading — resolution is somebody else's job, deliberately. |
| :reserved-literal | — | — | — | One of six bare words that are values rather than names. The list is fixed, so no value is coerced by what it looks like. |
| :sequence | — | — | — | An ordered list. Order is preserved and is meaning. |
| :string | — | — | — | Text. May span lines, so prose does not have to be escaped into one. |
| :symbol | : | word | :dispatched | A name from a fixed vocabulary, not free text. :high is a value someone chose; "high" is a phrase someone typed. |
| :table-row | | | cells | | sku qty | One record of a table. A table is sugar for a sequence of blocks with the same keys, and encodes identically to the longhand. |
| — | — | — | A temporal value at the precision written. 2026-08 stays a month, and 03:52 stays a wall-clock time; neither is widened into an invented instant. |