# Canonical ordering of days of week

The entities representing the days of the week sort alphabetically:

Sort[{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}]

(* {Friday, Monday, Saturday, Sunday, Thursday, Tuesday, Wednesday} *)


(Note that these are not strings.)

Is there a better way to sort than using the following?

SortBy[PositionIndex[{Monday, Tuesday, Wednesday, Thursday, Friday}]]

• Wouldn't this be ill-defined because it is cyclic? I guess you could order them if you agree on which day is the first of the week… some say monday, others sunday… – SHuisman Sep 19 '19 at 11:28
• "Canonically" (i.e. according to the Bible) the first day was Sunday. – mikado Sep 19 '19 at 20:43
• I don't know if you can get more canonical than the Bible, but according to ISO 8601, the week begins on Monday. – Stephen Powell Sep 20 '19 at 7:30

It is not much shorter than your PositionIndex[{Monday, Tuesday, Wednesday, Thursday, Friday}], but you can also use SystemDateObjectDump$dowAssociation: SystemDateObjectDump$dowAssociation


<|Monday -> 1, Tuesday -> 2, Wednesday -> 3, Thursday -> 4, Friday -> 5, Saturday -> 6, Sunday -> 7|>

sortByDoW = SortBy[SystemDateObjectDump\$dowAssociation];


Examples:

sortByDoW @ {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}


{Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

sortByDoW @ RandomSample[{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}]


{Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

As you've noticed, the weekday symbols are by default sorted by their symbol names. This is because Monday,... are not true date specifications, but only day types. So there is not really a canonical ordering. However, you could do the following:

SortBy[DayPlus[DayPlus[Today, 1, Sunday], 1, #] &]@
{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
(* {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday} *)


This works by converting the day types into actual dates. This is done in three steps:

• Find the next Sunday after today (you could also hardcode the date of a sunday here, but this is more readable I think)
• Find the date of the first Monday/... after that point
• Sort these dates