TOL

A quick and dirty implementation of TOL time representation, in pure Julia.

To install the yet unregistered packages

using Pkg
Pkg.add("https://github.com/gvdr/TOL.jl")

What's in the package

For the moment we have just some bare structures, types, and functions that come from the TOL ideas.

The calendarization is dynamic, and it is lifted from Dates.TimeType: this means that we can use Date (i.e., "2023-06-23"), Time (i.e., "12:33:08.336"), or DateTime (i.e., "2023-06-23T02:03:08.336").

There are, for the moments, three kinds of fechados, namely:

• Day_of_Month: a Day_of_Month(4) includes all dates (or datetimes) that are on the 4th day of a month (i.e., all days like "yyyy-mm-04").
• Day_of_Week: a Day_of_Week(4) includes all dates (or datetimes) that are on the 4th day of a week (i.e., Thursdays).
• Month_of_Year: a Month_of_Year(4) includes all dates (or datetimes) that are on the 4th Month of a year (i.e., April).

We have operators working on date (or datetimes) and fechados.

• ∈ : This is most fundamental operator, as it fundamentally defines the fechados, determing whether a certain date is in it or not. The converse operator ∋ comes for free 😄
• ∩ and ∪: creates respectively intersections and unions of fechados. The resulting objects are of type IntFechado and UnFechado respectively. Composition happens from the left: Day_of_Week(1) ∩ Day_of_Month(1) ∩ Month_of_Year(1) is the same of ((Day_of_Week(1) ∩ Day_of_Month(1)) ∩ Month_of_Year(1)). We also have the convenience constructor functions IntFechados() and UnFechados() that work with arrays fechados (i.e., IntFechados([Day_of_Week(1), Day_of_Month(1), Month_of_Year(1)])).
• Functions C() to build complementary sets (all the fechados in a range minus one), and - to subtract sets.
• succ() and prec() : these functions returns either successors or predecessors of dates or fechados. The last argument is always compulsory, and it is the number of succ (or prec) steps to take.

Examples

using TOL
using Dates

today = now()

today ∈ Day_of_Week(1) ∩ Day_of_Month(1) ∩ Month_of_Year(1)

today ∈ Day_of_Week(4) ∪ Day_of_Week(5)

succ(Month_of_Year(1),1)
prec(Month_of_Year(1),2)

Ω(Month_of_Year(1))

succ(today,Month_of_Year(1),2)

Extension

An atomic fechado is defined by three main object. The first two are mandatory:

• a struct inhering from AtomicFechado, that has the only field core:

  struct Day_of_Week <: AtomicFechado
      core::Atomic
  end

• a constructor for the atomic fechado, that provides the default information regarding the range and the comparison function, for example, to define an atomic fechado that considers the dayofweek of a date (or datetime) and has a range from 0 to 6, we write:

  Day_of_Week(n::N) where {N<:Int}  = Day_of_Week(Atomic(n, collect(1:1:7), dayofweek))

  In general, a range and n can be defined using whatever number (in this example we forec n to be an integer). The comparison function defines the inclusion by determining whether comparison_function(a_date) == n, and can be any of the Dates functions or user defined.
• optionally, a collection of succ() functions, determing what is the next date, when considering it as an element of a certain atomic fechado. For example:

  succ(a_date::Tt,T::Day_of_Week,k) where {Tt<:TimeType} = a_date + Day(k)

  The general successor function for the class of any defined Atomic Fechados is defined in src/Utilities.jl; a method overriding it can be provided by a function of signature function succ(T::ASF,k) where ASF is the name of the user defined Atomic Fechado.

For convenience, we keep them all in src/Fechados/.

TODO

• implement a stronger logic for the operators (checking for equality, so to simplify algebraic operations)
• introduce comparison for composed objects
• maybe experiment with different operator symbols to better capture the algebraic properties.