% arara: pdflatex
% arara: pdflatex
\documentclass{memoir}

\usepackage[en-GB,showdow]{datetime2}

\usepackage{lipsum}% dummy text
\usepackage[hidelinks]{hyperref}

\newcommand*{\numdash}{\texorpdfstring{\,--\,}{--}}

% \DTMmonthname is robust and can't be used in the bookmarks
% or headings so use \DTMenglishmonthname since this
% document is in English.
\newcommand*{\entrymonth}[2]{\DTMenglishmonthname{#2} #1}

% A range of dates.
% Syntax: \daterange{yyyy1}{mm1}{dd1}{yyyy2}{mm2}{dd2}
\newcommand*{\daterange}[6]{%
  \ifnum#1=#4 
% Same year
    \ifnum#2=#5
% Same month
      \ifnum#3=#6
% Same day - not a range!
       \DTMdisplaydate{#1}{#2}{#3}%
      \else
% Range within the same month.
% This needs to be done explicitly but match the separators
% with the en-GB style.
       \DTMenglishordinal{#3}\numdash\DTMenglishordinal{#6}%
       \DTMenGBdaymonthsep
       \DTMenglishmonthname{#2}%
       \DTMenGBmonthyearsep\number#1
      \fi
    \else
% Not the same month
      \DTMdisplaydate{#1}{#2}{#3}{-1}\numdash\DTMdisplaydate{#4}{#5}{#6}{-1}%
    \fi
  \else
% Not same year
   \DTMdisplaydate{#1}{#2}{#3}{-1}\numdash\DTMdisplaydate{#4}{#5}{#6}{-1}%
  \fi
}

% range of months
% Syntax: \monthspan{yyyy1}{mm1}{yyyy2}{mm2}
\newcommand*{\monthspan}[4]{%
 \ifnum#1=#3
% Same year
   \DTMenglishmonthname{#2}\numdash\DTMenglishmonthname{#4}%
   \DTMenGBmonthyearsep\number#1
 \else
% Not the same year
   \DTMenglishmonthname{#2}%
   \DTMenGBmonthyearsep\number#1
   \numdash\DTMenglishmonthname{#4}%
   \DTMenGBmonthyearsep\number#3
 \fi
}

\newcommand*{\entrydate}[3]{\DTMdisplaydate{#1}{#2}{#3}{-1}}
\newcommand*{\titleentrydate}[3]{\DTMdate{#1-#2-#3}}

\renewcommand*{\printchaptertitle}[1]{%
 {%
   \let\entrydate\titleentrydate
   \chaptitlefont{#1}%
 }%
}

\setsecheadstyle{\let\entrydate\titleentrydate
 \Large\bfseries\memRTLraggedright}

\begin{document}

\frontmatter
\tableofcontents

\mainmatter
\chapter{Introduction}

This is a test document that illustrates the use of dates within
chapter titles.

\section{Sample}

An example section.

\chapter{\entrymonth{2016}{01}}

\lipsum

\section{\entrydate{2016}{01}{01}}

\lipsum[1-10]

\section{\entrydate{2016}{01}{02}}

\lipsum

\section{\daterange{2016}{01}{04}{2016}{01}{12}}

\lipsum[1-3]

\chapter{\entrydate{2016}{02}{03}}

\lipsum

\chapter{\monthspan{2016}{02}{2016}{03}}

\lipsum

\section{\daterange{2016}{02}{04}{2016}{03}{01}}

\lipsum

\chapter{\monthspan{2015}{12}{2016}{01}}

\lipsum

\section{\daterange{2015}{12}{20}{2016}{01}{01}}

\lipsum


\end{document}
