Reversed arrow tips for \overleftarrow and \overrightarrow

Question

The post Change arrow tip of \overleftarrow-Command tells me how to change the size of the tips of arrows generated with \overleftarrow and \overrightarrow. But how can I get a different tip all together?

Ideally, I would like a reversed arrow tip (like --< but not dashed) or small vertical lines for the tip of arrows on top of a letter based on \overleftarrow and \overrightarrow.

Answer 1

I tried to use the code of these answers to come up with a solution for an inverted arrow. Note that this may look a bit strage if the text underneath is too short (only one letter, for example). Also note that this approach has not been excessively tested for use in superscript or subscript.

\documentclass{article}
\usepackage{amsmath,amssymb,trimclip}
\makeatletter
\def\lefttailfill@{\arrowfill@\relbar\relbar{\vcenter{\hbox{\clipbox{6pt 0pt 0pt 0pt}{\ensuremath\leftarrowtail}}}}}
\ams@newcommand{\overlefttail}{\mathpalette{\overarrow@\lefttailfill@}}
\makeatother
\newcommand{\olefttail}[2]{[\overlefttail{\mathstrut#1,#2}]}
\begin{document}
[
\olefttail{2}{5}
]
[
\overlefttail{abc}
]
[
\sum^{\overlefttail{abc}}
]
\end{document}

---

Edit: same thing for the right "arrow" and one with two tails:

\documentclass{article}
\usepackage{amsmath,amssymb,trimclip}
\makeatletter
\def\righttailfill@{\arrowfill@{\vcenter{\hbox{\clipbox{0pt 0pt 6pt 0pt}{\ensuremath\rightarrowtail}}}}\relbar\relbar}
\ams@newcommand{\overrighttail}{\mathpalette{\overarrow@\righttailfill@}}
\def\leftrighttailfill@{\arrowfill@{\vcenter{\hbox{\clipbox{0pt 0pt 6pt 0pt}{\ensuremath\rightarrowtail}}}}\relbar{\vcenter{\hbox{\clipbox{6pt 0pt 0pt 0pt}{\ensuremath\leftarrowtail}}}}}
\ams@newcommand{\overleftrighttail}{\mathpalette{\overarrow@\leftrighttailfill@}}
\makeatother
\newcommand{\orighttail}[2]{[\overrighttail{\mathstrut#1,#2}]}
\newcommand{\oleftrighttail}[2]{[\overleftrighttail{\mathstrut#1,#2}]}
\begin{document}
[
\orighttail{2}{5}
]
[
\overrighttail{abc}
]
[
\oleftrighttail{2}{5}
]
[
\overleftrighttail{abc}
]
\end{document}

Answer 2

Run with lualatex or xelatex:

\documentclass[border=12pt]{standalone}
\usepackage{amsmath,graphicx}
\usepackage{unicode-math}
\setmathfont{XITS Math}
\makeatletter
\newcommand\xlongrightreversedarrow[2][]{\ext@arrow 0055{\longrightreversedarrowfill@}{#1}{#2}} 
\def\longrightreversedarrowfill@{\arrowfill@{}{\relbar}{\char"2919}}
\makeatother
\begin{document}
$\xlongrightreversedarrow[y=f(x,v,w)]{x=f(w)}$
\end{document}

Answer 3

Here is a possibility with tikz. The commands \overrighttail, \overlefttail and \overleftrighttail produce the "arrows" using the syntax \overrighttail{abc}, etc.

An optional second argument allows for styling of the arrow, e.g.,

\overleftrighttail[red, semithick, densely dotted, line cap=round]{abc}

as seen above. The arrow shape can be changed by replacing to in the tikzset with whatever shape you want:

\tikzset{tail/.tip={Stealth[reversed, length=4pt]}}

To use as a limit in a \sum, see this related answer.

Here is the code:

\documentclass{article}
\usepackage{tikz, mathtools}
\usetikzlibrary{arrows.meta}
\tikzset{tail/.tip={to[reversed, length=1.5pt]}}
\newcommand{\overrighttail}[2][]{\tikz[baseline, anchor=base]{\nodeinner sep=0pt{$#2$};
    \draw[tail-, #1]([shift={(1pt,2pt)}]a.north west)--([shift={(-1pt,2pt)}]a.north east);}}
\newcommand{\overlefttail}[2][]{\tikz[baseline, anchor=base]{\nodeinner sep=0pt{$#2$};
    \draw[-tail, #1]([shift={(1pt,2pt)}]a.north west)--([shift={(-1pt,2pt)}]a.north east);}}
\newcommand{\overleftrighttail}[2][]{\tikz[baseline, anchor=base]{\nodeinner sep=0pt{$#2$};
    \draw[tail-tail, #1]([shift={(1pt,2pt)}]a.north west)--([shift={(-1pt,2pt)}]a.north east);}}
\begin{document}
[
\overrighttail{abc};\overlefttail{abc};\overleftrighttail{abc};
\overleftrighttail[red, semithick, densely dotted, line cap=round]{abc}
]
\end{document}