Recurrences & Intervals

Empire City Elixir Conference 2018, May 19th - http://empex.co/nyc

This talk is retelling my journey down the rabbit hole of dealing with date & time.

We will start the journey with date/time recurrences. Then, we will look at time intervals and operations around them. Finally, we will look at Eric Evans' talk "Exploring Time" which gives a fresh look at date/time in general and intervals in particular (spoiler alert: there might be some relevant research from the 80s around that too!). We will model both recurrences and intervals as streams and we will try to show that Elixir's extensibility makes it a great language for developing business applications.

Transcript

1. Recurrences & Intervals Wojtek Mach @wojtekmach @wojtekmach
2. Parts 1. Recurrences 2. Intervals 3. „Exploring Time” 4. Libraries
3. Part I: Recurrences
4. Google Calendar
5. Apple iCal
6. iCalendar
7. iCalendar Example DTSTART;TZID=Europe/Warsaw:20180101T090000 RRULE:FREQ=WEEKLY;BYDAY=MO,TU;COUNT=4 2018-01-01 09:00 CET (Monday) 2018-01-02 09:00 CET (Tuesday) 2018-01-08 09:00 CET (Monday) 2018-01-09 09:00 CET (Tuesday)
9. Beginning of Recurrence
10. Beginning of Recurrence
11. Aside: Time zones
12. iCalendar Example DTSTART;TZID=Europe/Warsaw:20180101T090000 RRULE:FREQ=DAILY;BYDAY=MO,TU;COUNT=4 2018-01-01 09:00 CET 2018-01-02 09:00 CET 2018-01-08 09:00 CET 2018-01-09 09:00 CET
13. iCalendar Example DTSTART=20180101T090000Z RRULE:FREQ=DAILY;BYDAY=MO,TU;COUNT=4 2018-01-01 08:00 UTC (09:00 CET) 2018-01-02 08:00 UTC (09:00 CET) 2018-01-08 08:00 UTC (09:00 CET) 2018-01-09 08:00 UTC (09:00 CET)
14. iCalendar Example DTSTART=20180319T090000Z RRULE:FREQ=DAILY;BYDAY=MO,TU;COUNT=4 2018-03-19 08:00 UTC (09:00 CET) 2018-03-20 08:00 UTC (09:00 CET) 2018-03-26 08:00 UTC (10:00 CET) 2018-03-27 08:00 UTC (10:00 CET)
15. Code
16. defmodule Recurrence do def stream(start) do Stream.iterate(start, &Date.add(&1, 1)) end end
17. defmodule Recurrence do def stream(start) do Stream.iterate(start, &Date.add(&1, 1)) end end iex> stream = Recurrence.stream(~D[2018-01-01]) #Function<... in Stream…>
18. defmodule Recurrence do def stream(start) do Stream.iterate(start, &Date.add(&1, 1)) end end iex> stream = Recurrence.stream(~D[2018-01-01]) #Function<... in Stream…> iex> Enum.take(stream, 3) [~D[2018-01-01], ~D[2018-01-02], ~D[2018-01-03]]
19. Part II: Intervals
20. Examples • the court is open daily between 9am and 8pm • the court is already booked on January 1st 2018 between 10:00 and 10:30
21. Examples • the court is open daily between 9am and 8pm • the court is already booked on January 1st 2018 between 10:00 and 10:30
22. Problem • court's opening hours, e.g.: 10am - 6pm • time window for when we want to search, e.g.:
 2pm - 8pm on January 1st 2018 • already made bookings e.g.: 4pm - 5pm Given: Calculate: available spots to book
23. 10:00 - 18:00 - opening hours 14:00 - 20:00 - search window 16:00 - 17:00 - booking +-----------------------+ | | | +-----------|-----+ | | | | | | ### | | | | ### | | | | | | 10:00 12:00 14:00 16:00 18:00 20:00 

24. 10:00 - 18:00 - opening hours 14:00 - 20:00 - search window 16:00 - 17:00 - booking +-----------------------+ | | | +-----------|-----+ | | | | | | ### | | | | ### | | | | | | 10:00 12:00 14:00 16:00 18:00 20:00 ###### #### ###### #### 10:00 12:00 14:00 16:00 18:00 20:00 

25. 10:00 - 18:00 - opening hours 14:00 - 20:00 - search window 16:00 - 17:00 - booking +-----------------------+ | | | +-----------|-----+ | | | | | | ### | | | | ### | | | | | | 10:00 12:00 14:00 16:00 18:00 20:00 ###### #### ###### #### 10:00 12:00 14:00 16:00 18:00 20:00 
 Results: 14:00 - 16:00 - gap 1
 17:00 - 18:00 - gap 2
26. defmodule DateTimeRange do defstruct [:first, :last] def new(%NaiveDateTime{}, %NaiveDateTime{}), do: ... def intersection(range1, range2), do: ... def subtract(range1, range2), do: ... end
27. defmodule DateTimeRange do defstruct [:first, :last] def new(%NaiveDateTime{}, %NaiveDateTime{}), do: ... def intersection(range1, range2), do: ... def subtract(range1, range2), do: ... end iex> DateTimeRange.new(~N[2018-01-01 09:00:00], ~N[201 %DateTimeRange{first: ~N[2018-01-01 09:00:00], last: ~
28. defmodule DateTimeRange do defstruct [:first, :last] def new(%NaiveDateTime{}, %NaiveDateTime{}), do: ... def intersection(range1, range2), do: ... def subtract(range1, range2), do: ... end iex> r("2018-01-01 09:00..10:00") %DateTimeRange{first: ~N[2018-01-01 09:00:00], last: ~
29. defmodule DateTimeRange do defstruct [:first, :last] def new(%NaiveDateTime{}, %NaiveDateTime{}), do: ... def intersection(range1, range2), do: ... def subtract(range1, range2), do: ... end iex> r("2018-01-01 09:00..10:00") r("2018-01-01 09:00..10:00")
30. defmodule DateTimeRange do defstruct [:first, :last] def new(%NaiveDateTime{}, %NaiveDateTime{}), do: ... def intersection(range1, range2), do: ... def subtract(range1, range2), do: ... end iex> a = r("2018-01-01 09:00..10:00”) iex> b = r("2018-01-01 09:00..10:00") iex> a > b ???
31. Part III:
 “Exploring Time”
32. “Exploring Time” Eric Evans
 Explore DDD 2017 - Denver, Sept. 21-22
33. 14:10 - 15:00 Eric Evans - Exploring Time Conference schedule: {#DateTime<2017-09-21 14:10:00-07:00 PDT America/ Los_Angeles>, #DateTime<2017-09-21 14:10:00-07:00 PDT America/ Los_Angeles>}
34. 14:10 - 15:00 Eric Evans - Exploring Time Conference schedule: {~N[2017-09-21 14:10:00], ~N[2017-09-21 15:00:00]}
35. 14:10 - 15:00 Eric Evans - Exploring Time Conference schedule: {~N[2017-09-21 14:10:00.000000], ~N[2017-09-21 15:00:00.000000]}
36. Arithmetic ~D[2017-01-20] + "1 month" => ~D[2017-02-20]
37. Arithmetic ~D[2017-01-20] + "1 month" => ~D[2017-02-20] ~D[2017-01-20] + "2 months” => ~D[2017-03-20]
38. Arithmetic ~D[2017-01-20] + "1 month" => ~D[2017-02-20] ~D[2017-01-20] + "2 months” => ~D[2017-03-20] ~D[2017-01-31] + "1 month" => ~D[2017-02-28]
39. Arithmetic ~D[2017-01-20] + "1 month" => ~D[2017-02-20] ~D[2017-01-20] + "2 months” => ~D[2017-03-20] ~D[2017-01-31] + "1 month" => ~D[2017-02-28] ~D[2017-03-31] + "2 months" => ~D[2017-05-31]
40. Arithmetic ~D[2017-01-20] + "1 month" => ~D[2017-02-20] ~D[2017-01-20] + "2 months” => ~D[2017-03-20] ~D[2017-01-31] + "1 month" => ~D[2017-02-28] ~D[2017-03-31] + "2 months" => ~D[2017-05-31] ~D[2017-03-31] + "1 month" => ~D[2017-04-30]
41. Arithmetic ~D[2017-01-20] + "1 month" => ~D[2017-02-20] ~D[2017-01-20] + "2 months” => ~D[2017-03-20] ~D[2017-01-31] + "1 month" => ~D[2017-02-28] ~D[2017-03-31] + "2 months" => ~D[2017-05-31] ~D[2017-03-31] + "1 month" => ~D[2017-04-30] ~D[2017-04-30] + "1 month" => ~D[2017-05-30]
42. Arithmetic ~D[2017-01-20] + "1 month" => ~D[2017-02-20] ~D[2017-01-20] + "2 months” => ~D[2017-03-20] ~D[2017-01-31] + "1 month" => ~D[2017-02-28] ~D[2017-03-31] + "2 months" => ~D[2017-05-31] ^^ ~D[2017-03-31] + "1 month" => ~D[2017-04-30] ~D[2017-04-30] + "1 month" => ~D[2017-05-30] ^^
43. Arithmetic ~D[2017-01-20] + "1 month" => ~D[2017-02-20] ~D[2017-01-20] + "2 months” => ~D[2017-03-20] ~D[2017-01-31] + "1 month" => ~D[2017-02-28] ~D[2017-03-31] + "2 months" => ~D[2017-05-31] ^^ ~D[2017-03-31] + "1 month" => ~D[2017-04-30] ~D[2017-04-30] + "1 month" => ~D[2017-05-30] ^^ (a + b) + c != a + (b + c)
44. Time Count ..., 2018-01-01, 2018-01-02, 2018-01-03, ...
45. Time Count ..., 2018-01-01, 2018-01-02, 2018-01-03, ... ..., 2018-12-31, 2019-01-01, 2019-01-02, ...
46. Time Count iex> next("2018-12-31") "2019-01-01" ..., 2018-01-01, 2018-01-02, 2018-01-03, ... ..., 2018-12-31, 2019-01-01, 2019-01-02, ...
47. Time Count iex> next("2018-12-31") "2019-01-01" iex> next("2018-12") "2019-01" ..., 2018-01-01, 2018-01-02, 2018-01-03, ... ..., 2018-12-31, 2019-01-01, 2019-01-02, ...
48. Time Count iex> next("2018-12-31") "2019-01-01" iex> next("2018-12") "2019-01" iex> next("2018") "2019" ..., 2018-01-01, 2018-01-02, 2018-01-03, ... ..., 2018-12-31, 2019-01-01, 2019-01-02, ...
49. Time Count iex> next(~I"2018-12-31") ~I"2019-01-01" iex> next(~I"2018-12") ~I"2019-01" iex> next(~I"2018") ~I"2019" ..., 2018-01-01, 2018-01-02, 2018-01-03, ... ..., 2018-12-31, 2019-01-01, 2019-01-02, ...
50. Time Count: Nesting iex> nest(~I"2018") {~I"2018-01", “2018-12"}
51. Time Count: Nesting iex> nest(~I"2018") {~I"2018-01", "2018-12"} iex> nest(~I"2018-01") {~I"2018-01-01", “2018-01-31”}
52. Time Count: Nesting iex> nest(~I"2018") ~I"2018-01/12" iex> nest(~I"2018-01") ~I”2018-01-01/31"
53. Time Count: Nesting iex> nest(~I"2018") ~I"2018-01/12" iex> nest(~I"2018-01") ~I”2018-01-01/31" iex> nest(~I"2018", :minute) ~I"2018-01-01 00:00/12-31 23:59"
54. Time Count: Enclosing iex> enclose(~I"2018-06") ~I"2018"
55. Time Count: Enclosing iex> enclose(~I"2018-06") ~I”2018" iex> enclose(~I"2018-01-01 00:00", :month) ~I"2018-01"
56. Representation ~I"2018-01/12" ~I"2018-01"
57. Representation ~I"2018-01/12" ~I"2018-01/01"
58. Time Count: Composition ~I"2018-05-19 09:00"
59. Time Count: Composition ~I"2018-05-19 09:00" |> enclose(:month) # => ~I"2018-05"
60. Time Count: Composition ~I"2018-05-19 09:00" |> enclose(:month) # => ~I"2018-05" |> nest(:day) # => ~I"2018-05-01/31"
61. Time Count: Composition ~I"2018-05-19 09:00" |> enclose(:month) # => ~I"2018-05" |> nest(:day) # => ~I”2018-05-01/31" |> List.last() # => ~I”2018-05-31"
62. Time Count: Composition def end_of_month(interval) do interval |> enclose(:month) |> nest(:day) |> Enum.last() end iex> end_of_month(~I"2018-05-01 09:00") ~I"2018-05-31"
63. Time Count: Composition def days_in_month(interval) do interval |> enclose(:month) |> nest(:day) |> Enum.count() end iex> days_in_month(~I"2018-05-01 09:00") 31
64. Time Count: Composition def days_in_year(interval) do interval |> enclose(:year) |> nest(:day) |> Enum.count() end iex> days_in_year(~I"2018-05-01 09:00") 365
65. Time Count: Composition def days_in_year(interval) do interval |> enclose(:year) |> nest(:day) |> Enum.count() end iex> days_in_year(~I"2018-05-01 09:00") 365 iex> days_in_year(~I"2020-05-01 09:00") 366
66. Time Count: Comparisons iex> compare(~I"2018-01/03", ~I"2018-02/04") ???
67. Allen’s Interval Algebra
68. Allen’s Interval Algebra
69. Allen’s Interval Algebra: Examples relation(~I"2018", ~I"2018") # => :equal
70. Allen’s Interval Algebra: Examples relation(~I"2018", ~I"2018") # => :equal relation(~I"2015", ~I"2018") # => :before
71. Allen’s Interval Algebra: Examples relation(~I"2018", ~I"2018") # => :equal relation(~I"2015", ~I"2018") # => :before relation(~I"2017", ~I"2018") # => :meets
72. Allen’s Interval Algebra: Examples relation(~I"2018", ~I"2018") # => :equal relation(~I"2015", ~I"2018") # => :before relation(~I"2017", ~I"2018") # => :meets relation(~I"2018-03", ~I"2018-01/12") # => :during
73. Allen’s Interval Algebra: Examples relation(~I"2018", ~I"2018") # => :equal relation(~I"2015", ~I"2018") # => :before relation(~I"2017", ~I"2018") # => :meets relation(~I"2018-03", ~I"2018-01/12") # => :during relation(~I"2018-01", ~I"2018-01/12") # => :starts
74. Allen’s Interval Algebra: Examples relation(~I"2018", ~I"2018") # => :equal relation(~I"2015", ~I"2018") # => :before relation(~I"2017", ~I"2018") # => :meets relation(~I"2018-03", ~I"2018-01/12") # => :during relation(~I"2018-01", ~I"2018-01/12") # => :starts relation(~I"2018-01/12", ~I"2018-02") # => :contains
75. Allen’s Interval Algebra: Examples relation(~I"2018", ~I"2018") # => :equal relation(~I"2015", ~I"2018") # => :before relation(~I"2017", ~I"2018") # => :meets relation(~I"2018-03", ~I"2018-01/12") # => :during relation(~I"2018-01", ~I"2018-01/12") # => :starts relation(~I"2018-01/12", ~I"2018-02") # => :contains relation(~I"2018-01/04", ~I"2018-02/06") # => :overlaps
76. iex> relation(~I"2018-01/03", ~I"2018-02/04") :overlaps
77. Part IV: Libraries
79. defmodule CalendarInterval do defstruct [:first, :last, :precision] @type t() :: %CalendarInterval{ first: NaiveDateTime.t(), last: NaiveDateTime.t(), precision: precision() } @type precision() :: :year |:month | ... end
80. defmodule CalendarInterval do def sigil_I(string, _) do parse!(string) end defimpl Inspect do def inspect(interval, _) do ... end end end iex> next(~I"2018") ~I"2018"
81. defmodule CalendarInterval do defimpl Enumerable do def reduce(interval, acc, fun) do ... end def count(interval) do {:error, __MODULE__} end # ... end end iex> Enum.count(~I"2018-01/12") 12
82. defmodule CalendarInterval do defimpl Enumerable do def reduce(interval, acc, fun) do ... end def count(interval) do count = ... # math {:ok, count} end # ... end end iex> Enum.count(~I"2018-01/12") 12
84. defmodule CalendarRecurrence do defimpl Enumerable do def reduce(recurrence, acc, fun) do ... end # ... end end
85. NimbleParsec
86. 
 # lib/calendar_recurrence/rrule_parser.ex defmodule CalendarRecurrence.RRULE.Parser do @moduledoc false import NimbleParsec freqs = ~w(SECONDLY MINUTELY HOURLY DAILY WEEKLY MONTHLY YEARLY) freq = part("FREQ", any_of(freqs, &string/1)) until = part("UNTIL", wrap(choice([datetime, date]))) count = part("COUNT", integer(min: 1)) # ... part = choice([ freq, until, count, interval, bysecond, byminute, byhour, byday ]) defparsec(:parse, part)
87. defp deps() do [ {:nimble_parsec, "~> 0.3", only: [:dev, :test]} ] end
88. 
 # lib/calendar_recurrence/rrule_parser.ex defmodule CalendarRecurrence.RRULE.Parser do @moduledoc false import NimbleParsec freqs = ~w(SECONDLY MINUTELY HOURLY DAILY WEEKLY MONTHLY YEARLY) freq = part("FREQ", any_of(freqs, &string/1)) until = part("UNTIL", wrap(choice([datetime, date]))) count = part("COUNT", integer(min: 1)) # ... part = choice([ freq, until, count, interval, bysecond, byminute, byhour, byday ]) defparsec(:parse, part)
89. 
 # lib/calendar_recurrence/rrule_parser.ex.eex defmodule CalendarRecurrence.RRULE.Parser do @moduledoc false # parsec: CalendarRecurrence.RRULE.Parser import NimbleParsec freqs = ~w(SECONDLY MINUTELY HOURLY DAILY WEEKLY MONTHLY YEARLY) freq = part("FREQ", any_of(freqs, &string/1)) until = part("UNTIL", wrap(choice([datetime, date]))) count = part("COUNT", integer(min: 1)) # ... part = choice([ freq, until, count, interval, bysecond, byminute, byhour, byday ]) defparsec(:parse, part)
90. $ mix nimble_parsec.compile lib/calendar_recurrence/rrule_parser.ex.exs Generating lib/calendar_recurrence/rrule_parser.ex mix nimble_parsec.compile
91. # Generated from lib/calendar_recurrence/rrule_parser.ex.exs, do # Generated at 2018-05-16 23:42:45Z. defmodule CalendarRecurrence.RRULE.Parser do # ... defp parse__0(rest, acc, stack, context, line, offset) do parse__1(rest, [], [acc | stack], context, line, offset) end defp parse__1(rest, acc, stack, context, line, offset) do parse__82(rest, [], [{rest, context, line, offset}, acc | sta end defp parse__3(<<"BYDAY", "=", rest::binary>>, acc, stack, conte parse__4(rest, ["BYDAY"] ++ acc, stack, context, comb__line, end # ... end
92. Extensibility "FREQ=DAILY" |> CalendarRecurrence.RRULE.to_recurrence(~D"2018-01-01") # Date |> Enum.take(3) #=> [~D[2018-01-01], ~D[2018-01-02], ~D[2018-01-03]]
93. Extensibility "FREQ=DAILY" |> CalendarRecurrence.RRULE.to_recurrence(~I"2018-01-01") # Interval |> Enum.take(3) #=> [~I"2018-01-01", ~I"2018-01-02", ~I"2018-01-03"]
94. Extensibility "FREQ=DAILY" |> CalendarRecurrence.RRULE.to_recurrence(~I"2018-01-01") # Interval |> Enum.take(3) #=> [~I"2018-01-01", ~I"2018-01-02", ~I"2018-01-03"] |> CalendarRecurrence.RRULE.to_recurrence(~I"2018-01-01") # Interval Fast parser, no runtime dependency, extensible
95. Extensibility "FREQ=DAILY" |> CalendarRecurrence.RRULE.to_recurrence(~I"2018-01-01") # Interval |> Enum.take(3) #=> [~I"2018-01-01", ~I"2018-01-02", ~I"2018-01-03"] Fast |> Enum.take(3)
96. Extensibility "FREQ=DAILY" |> CalendarRecurrence.RRULE.to_recurrence(~I"2018-01-01") # Interval |> Enum.take(3) #=> [~I"2018-01-01", ~I"2018-01-02", ~I"2018-01-03"] Extensibility #=> [~I"2018-01-01", ~I"2018-01-02", ~I"2018-01-03"]
97. Further work • Implement remaining RRULE options • Support timezones in intervals • Support interval features from the new ISO 8601 draft
98. References • iCalendar: Internet Calendaring and Scheduling Core Object Specification • How to save datetimes for future events - (when UTC is not the right answer) - Lau Taarnskov • Exploring Time - Eric Evans • Maintaining Knowledge About Temporal Integrals - James F. Allen • https://github.com/wojtekmach/calendar_interval • https://github.com/wojtekmach/calendar_recurrence • https://hex.pm/packages/nimble_parsec • ISO 8601 Draft: Basic rules • ISO 8601 Draft: Extensions • Date.Range
99. Thank you!