Calendars is a collection of calendars based on the Calixir package. Calixir is a port of the Lisp calendar software 'calendrica-4.0.cl' to Elxir. 'calendrica-4.0.cl' is the software that comes with the book 'Calendrical Calculations - The Ultimate Edition' by Edward M. Reingold and Nachum Dershowitz, Cambridge University Press, 2018.

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Programming language: Elixir
License: Apache License 2.0
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Calendars is a collection of calendars that is based on the calendars contained in the 4th edition of the book (from here on referenced as DR4)

Calendrical Calculations - The Ultimate Edition
by Edward M. Reingold and Nachum Dershowitz
Cambridge University Press, 2018

The calendars are just thin wrappers around the Calixir package. Calixir is a port of the Lisp calendar software calendrica-4.0.cl that comes with DR4.


The package is available in Hex and can be installed by adding calendars to your list of dependencies in mix.exs:

def deps do
    {:calendars, "~> 0.1.0"}


Documentation has been generated with ExDoc and published on HexDocs. The docs can be found at https://hexdocs.pm/calendars.

The Calixir library and its sample data are made public under the following conditions:

  • The code and data can be used for personal use.
  • The code can data be used for demonstrations purposes.
  • Non-profit reuse with attribution is fine.
  • Commercial use of the algorithms should be licensed and are not allowed from this library.

The permissions above are granted as long as attribution is given to the authors of the original algorithms, Nachum Dershowitz and Edward M. Reingold.

About the Calendars

In this software, I distinguish monotonous and cyclical calendars:

A monotonous calendar has a distinct origin or epoch and stretches from there (potentially) to negative and positive infinity. All its values or dates are distinct. The most common example is probably the Gregorian calendar.

A cyclical calendar does not have an origin. It consists of periods or cycles of the same length that return indefinitely. All the values or dates within one cycle are unique, but they return from cycle to cycle, so that it is not possible, to assign such a value to a distinct point in time. The most common example is probably the week with its weekdays.

One could argue that cycles shouldn't be called 'calendars'. But that's the way they are treated in DR4. So I'm using the attributes monotonous and cyclical to distinguish calendars if and when it matters.

About the Calendar Conversions

To facilitate the conversion of calendar dates between different calendars is one of the main functions of Calendars. To minimize the number of conversion
functions to be written the common star pattern is used. Each conversion from one calendar to another is split in two steps:

  1. Conversion of the date of the source calendar into a common 'canonical' date.
  2. Conversion of the 'canonical' date into a date of the target calendar.

The 'canonical' date is the central hub for all conversions. Thus, every calendar must only know how to convert its dates into and from the corresponding date of some 'canonical' calendar. Prime candidates for a 'canonical' calendar are calendars that don't have an internal structure of their own (i.e. a hierarchy of units like 'year', 'month', and 'day'), but work with one unit only (usually the 'day').

One candidate could have been the Julian Day number (JD in this package) or variants thereof (i.e. the Modified Julian Day number, MJD). But the authors of DR4 have chosen to create their own 'canonical' calendar, the RataDie calendar, that is closely aligned with the Gregorian calendar.

The base unit of the RataDie is the day. Throughout the book (DR4) a
variable containing a day of this calendar is referred by the term date while functions working with such a variable use the term fixed, i.e.:

gregorian-from-fixed(date) = [year, month, day]  # DR4 62 (2.23)

I consider this unfortunate, because date is a broader term that can be (and commonly is) used for all calendars. So throughout Calixir and Calendars, I use the term fixed instead of date for dates of the RataDie calendar, i.e.:

gregorian_from_fixed(fixed) = {year, month, day}  # DR4 62 (2.23)

The fixed dates of the RataDie calendar form the basis for all calendar conversions in Calixir and Calendars.

  • Both, monotonous and cyclical calendars must have a from_fixed function that converts a fixed date into their own corresponding dates.

  • In addition, monotonous calendars must have a to_fixed function that converts their own dates into the corresponding fixed dates.

Additionally, the calendars have two pairs of conversion functions that are just syntactic sugar:

  • from_jd and to_jd for Julian Day numbers
  • from_date and to_date for direct conversions from and into another calendar.

The WHYs and the WHY-NOTs

In this section, I detail some of my decisions why this software is how it is. It might help you to understand its structure.

Before I published the Calixir and Calendars packages I tried various ways to refactor the monolithic calendrica-4.0 Lisp package, but always ended in some form of 'dependency hell'. So I finally decided to keep Calixir as a single monolithic block and implement the calendars as thin wrappers around Calixir.

This approach offers an additional advantage: The Calendars collection can be extended just by adding calendar modules to lib/calendars. Additional calendars can but don't need to reference Calixir. To allow for conversions they only have to implement their own from_fixed, to_fixed, from_date, and to_date functions. from_jd and to_jd are not required.

If you need additional functionality for a calendar create a new module and use
existing functionality by creating defdelegates to the base calendar or Calixir.


Here is an example for the interactive use of Calendars:

D:\Projects\calendars>iex -S mix
Interactive Elixir (1.9.4) - press Ctrl+C to exit (type h() ENTER for help)
iex(1)> alias Calendars.Gregorian
iex(2)> g_date = Gregorian.date(2020, 7, 24)
{2020, 7, 24}
iex(3)> fixed = Gregorian.to_fixed(g_date)
iex(4)> alias Calendars.Julian
iex(5)> j_date = Julian.from_fixed(fixed)
{2020, 7, 11}
iex(6)> Julian.to_date(j_date, Gregorian)
{2020, 7, 24}

The same example in a module:

defmodule ExampleConverter do

  alias Calendars.{Gregorian, Julian}

  def gregorian_to_julian_conventional do
    g_date = Gregorian.date(2020, 7, 24)  # create Gregorian date 
    fixed = Gregorian.to_fixed(g_date)    # convert Gregorian date to fixed
    j_date = Julian.from_fixed(fixed)     # convert fixed into Julian date
    Julian.to_date(j_date, Gregorian)     # should return {2020, 7, 24}

Using a pipeline:

defmodule PipelineConverter do

  alias Calendars.{Gregorian, Julian, Hebrew}

  def check_pipeline do
    gregorian_date = Gregorian.date(2020, 7, 24)

    if (gregorian_date
        |> Gregorian.to_fixed
        |> Julian.from_fixed
        |> Julian.to_fixed
        |> Gregorian.from_fixed) == gregorian_date,
    do:   {:ok, "Pipeline works."},
    else: {:error, "Pipeline is broken."}   

  def check_pipeline_using_from_date do
    gregorian_date = Gregorian.date(2020, 7, 28)

    if (gregorian_date
        |> Julian.from_date(Gregorian)
        |> Hebrew.from_date(Julian)
        |> Gregorian.from_Hebrew()) == gregorian_date,
    do:   {:ok, "Pipeline works."},
    else: {:error, "Pipeline is broken."}   

  def check_pipeline_using_to_date do
    gregorian_date = Gregorian.date(2020, 7, 28)

    if (gregorian_date
        |> Gregorian.to_date(Julian)
        |> Julian.to_date(Hebrew)
        |> Hebrew.to_date(Gregorian)) == gregorian_date,
    do:   {:ok, "Pipeline works."},
    else: {:error, "Pipeline is broken."}   


Of course, this works for any combination of monotonous calendars.



  • Added functions date_text to Gregorian, Julian, and Hebrew.


  • Fixed and renamed _as_date functions.


  • Added function today to Gregorian.
  • Added function start_of_year to Gregorian.
  • Added function end_of_year to Gregorian.
  • Added function start_of_month to Gregorian.
  • Added function end_of_month to Gregorian.
  • Added function start_of_week to Gregorian.
  • Added function end_of_week to Gregorian.
  • Added function month_names_as_list to Gregorian.
  • Added function day_names_as_list to Gregorian.
  • Added function month_names_as_list to Hebrew.
  • Added holiday functions to Gregorian.
  • Added holiday functions to Hebrew.
  • Added the corresponding tests.


  • Fixed docs in RataDie calendar.
  • Fixed from_jd and to_jd functions in in RataDie calendar.
  • Added is_leap? and days_in_month functions to Gregorian calendar.
  • Added is_leap? and days_in_month functions to Julian calendar.

*Note that all licence references and agreements mentioned in the Calendars README section above are relevant to that project's source code only.