From 134349701bddf7cbbacf6030c6b9f9838aff96fa Mon Sep 17 00:00:00 2001
From: Karl Berry <karl@freefriends.org>
Date: Mon, 23 Jul 2012 17:15:00 +0000
Subject: l3kernel 3990 (17jul12)

git-svn-id: svn://tug.org/texlive/trunk@27108 c570f23f-e606-0410-a88d-b1316a301751
---
 .../texmf-dist/source/latex/l3kernel/l3coffins.dtx | 1587 +++++++-------------
 1 file changed, 563 insertions(+), 1024 deletions(-)

(limited to 'Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx')

diff --git a/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx b/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
index 54575bde8ce..b4242b6d8ed 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
@@ -36,8 +36,8 @@
 %
 %<*driver|package>
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3coffins.dtx 3482 2012-03-03 18:48:06Z bruno $
-  {L3 Experimental coffin code layer}
+\GetIdInfo$Id: l3coffins.dtx 3986 2012-07-15 19:23:51Z joseph $
+  {L3 Coffin code layer}
 %</driver|package>
 %<*driver>
 \documentclass[full]{l3doc}
@@ -94,10 +94,19 @@
 % \begin{function}[added = 2011-08-17]
 %  {\coffin_set_eq:NN, \coffin_set_eq:Nc, \coffin_set_eq:cN, \coffin_set_eq:cc}
 %   \begin{syntax}
-%    \cs{coffin_set_eq:NN} \meta{coffin1} \meta{coffin2}
+%    \cs{coffin_set_eq:NN} \meta{coffin_1} \meta{coffin_2}
 %   \end{syntax}
-%   Sets both the content and poles of \meta{coffin1} equal to those
-%   of \meta{coffin2} within the current \TeX\ group level.
+%   Sets both the content and poles of \meta{coffin_1} equal to those
+%   of \meta{coffin_2} within the current \TeX\ group level.
+% \end{function}
+%
+% \begin{function}[EXP, pTF, added = 2012-06-20]
+%   {\coffin_if_exist:N, \coffin_if_exist:c}
+%   \begin{syntax}
+%     \cs{coffin_if_exist_p:N} \meta{box}
+%     \cs{coffin_if_exist:NTF} \meta{box} \Arg{true code} \Arg{false code}
+%   \end{syntax}
+%   Tests whether the \meta{coffin} is currently defined.
 % \end{function}
 %
 % \section{Setting coffin content and poles}
@@ -127,7 +136,7 @@
 %   environment in a coffin.
 % \end{function}
 %
-% \begin{function}[added = 2011-08-17, updated = 2011-09-03]
+% \begin{function}[added = 2011-08-17, updated = 2012-05-22]
 %   {\vcoffin_set:Nnn, \vcoffin_set:cnn}
 %   \begin{syntax}
 %     \cs{vcoffin_set:Nnn} \meta{coffin} \Arg{width} \Arg{material}
@@ -138,7 +147,7 @@
 %   size of the typeset material.
 % \end{function}
 %
-% \begin{function}[added = 2011-09-10]
+% \begin{function}[added = 2011-09-10, updated = 2012-05-22]
 %   {\vcoffin_set:Nnw, \vcoffin_set:cnw, \vcoffin_set_end:}
 %   \begin{syntax}
 %     \cs{vcoffin_set:Nnw} \meta{coffin} \Arg{width} \meta{material} \cs{vcoffin_set_end:}
@@ -180,42 +189,6 @@
 %   the \meta{coffin}.
 % \end{function}
 %
-% \section{Coffin transformations}
-%
-% \begin{function}[added = 2011-09-02]{\coffin_resize:Nnn, \coffin_resize:cnn}
-%   \begin{syntax}
-%     \cs{coffin_resize:Nnn} \meta{coffin} \Arg{width} \Arg{total-height}
-%   \end{syntax}
-%   Resized the \meta{coffin} to \meta{width} and \meta{total-height},
-%   both of which should be given as dimension expressions. These may
-%   include the terms \cs{TotalHeight}, \cs{Height}, \cs{Depth} and
-%   \cs{Width}, which will evaluate to the appropriate dimensions of
-%   the \meta{coffin}.
-%
-%  \textbf{This function is experimental.}
-% \end{function}
-%
-% \begin{function}[added = 2011-09-02]{\coffin_rotate:Nn, \coffin_rotate:cn}
-%   \begin{syntax}
-%     \cs{coffin_rotate:Nn} \meta{coffin} \Arg{angle}
-%   \end{syntax}
-%   Rotates the \meta{coffin} by the given \meta{angle} (given in
-%   degrees counter-clockwise). This process will rotate both the
-%   coffin content and poles. Multiple rotations will not result in
-%   the bounding box of the coffin growing unnecessarily.
-% \end{function}
-%
-% \begin{function}[added = 2011-09-02]{\coffin_scale:Nnn, \coffin_scale:cnn}
-%   \begin{syntax}
-%     \cs{coffin_scale:Nnn} \meta{coffin} \Arg{x-scale} \Arg{y-scale}
-%   \end{syntax}
-%   Scales the \meta{coffin} by a factors \meta{x-scale} and
-%   \meta{y-scale} in the horizontal and vertical directions,
-%   respectively. The two scale factors should be given as real numbers.
-%
-%  \textbf{This function is experimental.}
-% \end{function}
-%
 % \section{Joining and using coffins}
 %
 % \begin{function}
@@ -225,19 +198,19 @@
 %   }
 %   \begin{syntax}
 %     \cs{coffin_attach:NnnNnnnn}
-%     ~~\meta{coffin1} \Arg{coffin1-pole1} \Arg{coffin1-pole2}
-%     ~~\meta{coffin2} \Arg{coffin2-pole1} \Arg{coffin2-pole2}
+%     ~~\meta{coffin_1} \Arg{coffin_1-pole_1} \Arg{coffin_1-pole_2}
+%     ~~\meta{coffin_2} \Arg{coffin_2-pole_1} \Arg{coffin_2-pole_2}
 %     ~~\Arg{x-offset} \Arg{y-offset}
 %   \end{syntax}
 %   This function attaches <coffin_2> to <coffin_1> such that the bounding box
-%   of \meta{coffin1} is not altered, \emph{i.e.}~\meta{coffin2} can
+%   of \meta{coffin_1} is not altered, \emph{i.e.}~\meta{coffin_2} can
 %   protrude outside of the bounding box of the coffin. The alignment
-%   is carried out by first calculating \meta{handle1}, the
-%   point of intersection of \meta{coffin1-pole1} and
-%   \meta{coffin1-pole2}, and \meta{handle2}, the point of intersection
-%   of \meta{coffin2-pole1} and \meta{coffin2-pole2}. \meta{coffin2} is
-%   then attached to \meta{coffin1} such that the relationship between
-%   \meta{handle1} and \meta{handle2} is described by the \meta{x-offset}
+%   is carried out by first calculating \meta{handle_1}, the
+%   point of intersection of \meta{coffin_1-pole_1} and
+%   \meta{coffin_1-pole_2}, and \meta{handle_2}, the point of intersection
+%   of \meta{coffin_2-pole_1} and \meta{coffin_2-pole_2}. \meta{coffin_2} is
+%   then attached to \meta{coffin_1} such that the relationship between
+%   \meta{handle_1} and \meta{handle_2} is described by the \meta{x-offset}
 %   and \meta{y-offset}. The two offsets should be given as dimension
 %   expressions.
 % \end{function}
@@ -249,19 +222,19 @@
 %   }
 %   \begin{syntax}
 %     \cs{coffin_join:NnnNnnnn}
-%     ~~\meta{coffin1} \Arg{coffin1-pole1} \Arg{coffin1-pole2}
-%     ~~\meta{coffin2} \Arg{coffin2-pole1} \Arg{coffin2-pole2}
+%     ~~\meta{coffin_1} \Arg{coffin_1-pole_1} \Arg{coffin_1-pole_2}
+%     ~~\meta{coffin_2} \Arg{coffin_2-pole_1} \Arg{coffin_2-pole_2}
 %     ~~\Arg{x-offset} \Arg{y-offset}
 %   \end{syntax}
 %   This function joins <coffin_2> to <coffin_1> such that the bounding box
-%   of \meta{coffin1} may expand. The new bounding
+%   of \meta{coffin_1} may expand. The new bounding
 %   box will cover the area containing the bounding boxes of the two
 %   original coffins. The alignment is carried out by first calculating
-%   \meta{handle1}, the point of intersection of \meta{coffin1-pole1} and
-%   \meta{coffin1-pole2}, and \meta{handle2}, the point of intersection
-%   of \meta{coffin2-pole1} and \meta{coffin2-pole2}. \meta{coffin2} is
-%   then attached to \meta{coffin1} such that the relationship between
-%   \meta{handle1} and \meta{handle2} is described by the \meta{x-offset}
+%   \meta{handle_1}, the point of intersection of \meta{coffin_1-pole_1} and
+%   \meta{coffin_1-pole_2}, and \meta{handle_2}, the point of intersection
+%   of \meta{coffin_2-pole_1} and \meta{coffin_2-pole_2}. \meta{coffin_2} is
+%   then attached to \meta{coffin_1} such that the relationship between
+%   \meta{handle_1} and \meta{handle_2} is described by the \meta{x-offset}
 %   and \meta{y-offset}. The two offsets should be given as dimension
 %   expressions.
 % \end{function}
@@ -272,7 +245,7 @@
 %     ~~\Arg{x-offset} \Arg{y-offset}
 %   \end{syntax}
 %   Typesetting is carried out by first calculating \meta{handle}, the
-%   point of intersection of \meta{pole1} and \meta{pole2}. The coffin
+%   point of intersection of \meta{pole_1} and \meta{pole_2}. The coffin
 %   is then typeset such that the relationship between the current
 %   reference point in the document and the \meta{handle} is described
 %   by the \meta{x-offset} and \meta{y-offset}. The two offsets should
@@ -310,7 +283,7 @@
 % \section{Coffin diagnostics}
 %
 % \begin{function}[updated = 2011-09-02]
-%   {\coffin_display_handles:cn, \coffin_display_handles:cn}
+%   {\coffin_display_handles:Nn, \coffin_display_handles:cn}
 %   \begin{syntax}
 %     \cs{coffin_display_handles:Nn} \meta{coffin} \Arg{colour}
 %   \end{syntax}
@@ -329,8 +302,8 @@
 %     \cs{coffin_mark_handle:Nnnn} \meta{coffin} \Arg{pole_1} \Arg{pole_2} \Arg{colour}
 %   \end{syntax}
 %   This function first calculates the \meta{handle} for the
-%   \meta{coffin} as defined by the intersection of \meta{pole1} and
-%   \meta{pole2}. It then marks the position of the \meta{handle}
+%   \meta{coffin} as defined by the intersection of \meta{pole_1} and
+%   \meta{pole_2}. It then marks the position of the \meta{handle}
 %   on the \meta{coffin}. The \meta{handle} will be labelled as part of
 %   this process: the location of the \meta{handle} and the label are
 %   both printed in the \meta{colour} specified.
@@ -353,6 +326,19 @@
 %   the later, rather than the absolute values, which determines the
 %   direction of the pole.
 % \end{function}
+% 
+% \subsection{Constants and variables}
+%
+% \begin{variable}{\c_empty_coffin}
+%   A permanently empty coffin.
+% \end{variable}
+% 
+% \begin{variable}[added = 2012-06-19]{\l_tmpa_coffin, \l_tmpb_coffin}
+%   Scratch coffins for local assignment. These are never used by
+%   the kernel code, and so are safe for use with any \LaTeX3-defined
+%   function. However, they may be overwritten by other non-kernel
+%   code and so should only be used for short-term storage.
+% \end{variable}
 %
 % \end{documentation}
 %
@@ -363,183 +349,148 @@
 %    \begin{macrocode}
 %<*initex|package>
 %    \end{macrocode}
+%    
+%    \begin{macrocode}
+%<@@=coffin>
+%    \end{macrocode}
 %
 %    \begin{macrocode}
 %<*package>
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
-\package_check_loaded_expl:
+\__expl_package_check:
 %</package>
 %    \end{macrocode}
 %
 % \subsection{Coffins: data structures and general variables}
 %
-% \begin{variable}{\l_coffin_internal_box}
-% \begin{variable}{\l_coffin_internal_dim}
-% \begin{variable}{\l_coffin_internal_fp}
-% \begin{variable}{\l_coffin_internal_tl}
+% \begin{variable}{\l_@@_internal_box}
+% \begin{variable}{\l_@@_internal_dim}
+% \begin{variable}{\l_@@_internal_tl}
 %   Scratch variables.
 %    \begin{macrocode}
-\box_new:N \l_coffin_internal_box
-\dim_new:N \l_coffin_internal_dim
-\fp_new:N  \l_coffin_internal_fp
-\tl_new:N  \l_coffin_internal_tl
+\box_new:N \l_@@_internal_box
+\dim_new:N \l_@@_internal_dim
+\tl_new:N  \l_@@_internal_tl
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 % \end{variable}
-% \end{variable}
 %
-% \begin{variable}{\c_coffin_corners_prop}
+% \begin{variable}{\c_@@_corners_prop}
 %   The \enquote{corners}; of a coffin define the real content, as
 %   opposed to the \TeX{} bounding box. They all start off in the same
 %   place, of course.
 %    \begin{macrocode}
-\prop_new:N \c_coffin_corners_prop
-\prop_put:Nnn \c_coffin_corners_prop { tl } { { 0 pt } { 0 pt } }
-\prop_put:Nnn \c_coffin_corners_prop { tr } { { 0 pt } { 0 pt } }
-\prop_put:Nnn \c_coffin_corners_prop { bl } { { 0 pt } { 0 pt } }
-\prop_put:Nnn \c_coffin_corners_prop { br } { { 0 pt } { 0 pt } }
+\prop_new:N \c_@@_corners_prop
+\prop_put:Nnn \c_@@_corners_prop { tl } { { 0 pt } { 0 pt } }
+\prop_put:Nnn \c_@@_corners_prop { tr } { { 0 pt } { 0 pt } }
+\prop_put:Nnn \c_@@_corners_prop { bl } { { 0 pt } { 0 pt } }
+\prop_put:Nnn \c_@@_corners_prop { br } { { 0 pt } { 0 pt } }
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\c_coffin_poles_prop}
+% \begin{variable}{\c_@@_poles_prop}
 %   Pole positions are given for horizontal, vertical and reference-point
 %   based values.
 %    \begin{macrocode}
-\prop_new:N \c_coffin_poles_prop
-\tl_set:Nn \l_coffin_internal_tl { { 0 pt } { 0 pt } { 0 pt } { 1000 pt } }
-\prop_put:Nno \c_coffin_poles_prop { l }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { hc } { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { r }  { \l_coffin_internal_tl }
-\tl_set:Nn \l_coffin_internal_tl { { 0 pt } { 0 pt } { 1000 pt } { 0 pt } }
-\prop_put:Nno \c_coffin_poles_prop { b }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { vc } { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { t }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { B }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { H }  { \l_coffin_internal_tl }
-\prop_put:Nno \c_coffin_poles_prop { T }  { \l_coffin_internal_tl }
+\prop_new:N \c_@@_poles_prop
+\tl_set:Nn \l_@@_internal_tl { { 0 pt } { 0 pt } { 0 pt } { 1000 pt } }
+\prop_put:Nno \c_@@_poles_prop { l }  { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { hc } { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { r }  { \l_@@_internal_tl }
+\tl_set:Nn \l_@@_internal_tl { { 0 pt } { 0 pt } { 1000 pt } { 0 pt } }
+\prop_put:Nno \c_@@_poles_prop { b }  { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { vc } { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { t }  { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { B }  { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { H }  { \l_@@_internal_tl }
+\prop_put:Nno \c_@@_poles_prop { T }  { \l_@@_internal_tl }
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_calc_a_fp}
-% \begin{variable}{\l_coffin_calc_b_fp}
-% \begin{variable}{\l_coffin_calc_c_fp}
-% \begin{variable}{\l_coffin_calc_d_fp}
-% \begin{variable}{\l_coffin_calc_result_fp}
-%   Used for calculations of intersections and in other internal places.
+% \begin{variable}{\l_@@_slope_x_fp}
+% \begin{variable}{\l_@@_slope_y_fp}
+%   Used for calculations of intersections.
 %    \begin{macrocode}
-\fp_new:N \l_coffin_calc_a_fp
-\fp_new:N \l_coffin_calc_b_fp
-\fp_new:N \l_coffin_calc_c_fp
-\fp_new:N \l_coffin_calc_d_fp
-\fp_new:N \l_coffin_calc_result_fp
+\fp_new:N \l_@@_slope_x_fp
+\fp_new:N \l_@@_slope_y_fp
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
 %
-% \begin{variable}{\l_coffin_error_bool}
+% \begin{variable}{\l_@@_error_bool}
 %   For propagating errors so that parts of the code can work around them.
 %    \begin{macrocode}
-\bool_new:N \l_coffin_error_bool
+\bool_new:N \l_@@_error_bool
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_offset_x_dim}
-% \begin{variable}{\l_coffin_offset_y_dim}
+% \begin{variable}{\l_@@_offset_x_dim}
+% \begin{variable}{\l_@@_offset_y_dim}
 %   The offset between two sets of coffin handles when typesetting. These
 %   values are corrected from those requested in an alignment for the
 %   positions of the handles.
 %    \begin{macrocode}
-\dim_new:N \l_coffin_offset_x_dim
-\dim_new:N \l_coffin_offset_y_dim
+\dim_new:N \l_@@_offset_x_dim
+\dim_new:N \l_@@_offset_y_dim
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_pole_a_tl}
-% \begin{variable}{\l_coffin_pole_b_tl}
+% \begin{variable}{\l_@@_pole_a_tl}
+% \begin{variable}{\l_@@_pole_b_tl}
 %   Needed for finding the intersection of two poles.
 %    \begin{macrocode}
-\tl_new:N \l_coffin_pole_a_tl
-\tl_new:N \l_coffin_pole_b_tl
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_coffin_sin_fp}
-% \begin{variable}{\l_coffin_cos_fp}
-%   Used for rotations to get the sine and cosine values.
-%    \begin{macrocode}
-\fp_new:N \l_coffin_sin_fp
-\fp_new:N \l_coffin_cos_fp
+\tl_new:N \l_@@_pole_a_tl
+\tl_new:N \l_@@_pole_b_tl
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_x_dim}
-% \begin{variable}{\l_coffin_y_dim}
-% \begin{variable}{\l_coffin_x_prime_dim}
-% \begin{variable}{\l_coffin_y_prime_dim}
+% \begin{variable}{\l_@@_x_dim}
+% \begin{variable}{\l_@@_y_dim}
+% \begin{variable}{\l_@@_x_prime_dim}
+% \begin{variable}{\l_@@_y_prime_dim}
 %   For calculating intersections and so forth.
 %    \begin{macrocode}
-\dim_new:N \l_coffin_x_dim
-\dim_new:N \l_coffin_y_dim
-\dim_new:N \l_coffin_x_prime_dim
-\dim_new:N \l_coffin_y_prime_dim
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_coffin_x_fp}
-% \begin{variable}{\l_coffin_y_fp}
-% \begin{variable}{\l_coffin_x_prime_fp}
-% \begin{variable}{\l_coffin_y_prime_fp}
-%   Used for calculations where there are clear $x$- and
-%   $y$-components, for example during vector rotation.
-%    \begin{macrocode}
-\fp_new:N \l_coffin_x_fp
-\fp_new:N \l_coffin_y_fp
-\fp_new:N \l_coffin_x_prime_fp
-\fp_new:N \l_coffin_y_prime_fp
+\dim_new:N \l_@@_x_dim
+\dim_new:N \l_@@_y_dim
+\dim_new:N \l_@@_x_prime_dim
+\dim_new:N \l_@@_y_prime_dim
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 % \end{variable}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_Depth_dim}
-% \begin{variable}{\l_coffin_Height_dim}
-% \begin{variable}{\l_coffin_TotalHeight_dim}
-% \begin{variable}{\l_coffin_Width_dim}
+% \begin{variable}{\l_@@_Depth_dim}
+% \begin{variable}{\l_@@_Height_dim}
+% \begin{variable}{\l_@@_TotalHeight_dim}
+% \begin{variable}{\l_@@_Width_dim}
 %   Dimensions for the various parts of a coffin.
 %    \begin{macrocode}
-\dim_new:N \l_coffin_Depth_dim
-\dim_new:N \l_coffin_Height_dim
-\dim_new:N \l_coffin_TotalHeight_dim
-\dim_new:N \l_coffin_Width_dim
+\dim_new:N \l_@@_Depth_dim
+\dim_new:N \l_@@_Height_dim
+\dim_new:N \l_@@_TotalHeight_dim
+\dim_new:N \l_@@_Width_dim
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 % \end{variable}
 % \end{variable}
 %
-% \begin{macro}{\coffin_saved_Depth:}
-% \begin{macro}{\coffin_saved_Height:}
-% \begin{macro}{\coffin_saved_TotalHeight:}
-% \begin{macro}{\coffin_saved_Width:}
+% \begin{macro}{\@@_saved_Depth:}
+% \begin{macro}{\@@_saved_Height:}
+% \begin{macro}{\@@_saved_TotalHeight:}
+% \begin{macro}{\@@_saved_Width:}
 %   Used to save the meaning of \cs{Depth}, \cs{Height}, \cs{TotalHeight}
 %   and \cs{Width}.
 %    \begin{macrocode}
-\cs_new_nopar:Npn \coffin_saved_Depth:       { }
-\cs_new_nopar:Npn \coffin_saved_Height:      { }
-\cs_new_nopar:Npn \coffin_saved_TotalHeight: { }
-\cs_new_nopar:Npn \coffin_saved_Width:       { }
+\cs_new_nopar:Npn \@@_saved_Depth:       { }
+\cs_new_nopar:Npn \@@_saved_Height:      { }
+\cs_new_nopar:Npn \@@_saved_TotalHeight: { }
+\cs_new_nopar:Npn \@@_saved_Width:       { }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
@@ -552,25 +503,40 @@
 % placing material in them. This all relies on the following data
 % structures.
 %
-% \begin{macro}{\coffin_if_exist:NT}
+% \begin{macro}[EXP, pTF]{\coffin_if_exist:N, \coffin_if_exist:c}
 %   Several of the higher-level coffin functions will give multiple
 %   errors if the coffin does not exist. A cleaner way to handle this
 %   is provided here: both the box and the coffin structure are
 %   checked.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_if_exist:NT #1#2
+\prg_new_conditional:Npnn \coffin_if_exist:N #1 { p , T , F , TF }
   {
     \cs_if_exist:NTF #1
       {
-        \cs_if_exist:cTF { l_coffin_poles_ \int_value:w #1 _prop }
-          { #2 }
-          {
-            \msg_kernel_error:nnx { coffins } { unknown-coffin }
-              { \token_to_str:N #1 }
-          }
+        \cs_if_exist:cTF { l_@@_poles_ \__int_value:w #1 _prop }
+          { \prg_return_true: }
+          { \prg_return_false: }
       }
+      { \prg_return_false: }
+  }
+\cs_generate_variant:Nn \coffin_if_exist_p:N { c }
+\cs_generate_variant:Nn \coffin_if_exist:NT  { c }
+\cs_generate_variant:Nn \coffin_if_exist:NF  { c }
+\cs_generate_variant:Nn \coffin_if_exist:NTF { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\@@_if_exist:NT}
+%   Several of the higher-level coffin functions will give multiple
+%   errors if the coffin does not exist. So a wrapper is provided to deal
+%   with this correctly, issuing an error on erroneous use.
+%    \begin{macrocode}
+\cs_new_protected:Npn \@@_if_exist:NT #1#2
+  {
+    \coffin_if_exist:NTF #1
+      { #2 }
       {
-        \msg_kernel_error:nnx { coffins } { unknown-coffin }
+        \__msg_kernel_error:nnx { kernel } { unknown-coffin }
           { \token_to_str:N #1 }
       }
   }
@@ -583,10 +549,10 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_clear:N #1
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
         \box_clear:N #1
-        \coffin_reset_structure:N #1
+        \@@_reset_structure:N #1
       }
   }
 \cs_generate_variant:Nn \coffin_clear:N { c }
@@ -603,12 +569,12 @@
 \cs_new_protected:Npn \coffin_new:N #1
   {
     \box_new:N #1
-    \prop_clear_new:c { l_coffin_corners_ \int_value:w #1 _prop }
-    \prop_clear_new:c { l_coffin_poles_   \int_value:w #1 _prop }
-    \prop_gset_eq:cN { l_coffin_corners_ \int_value:w #1 _prop }
-      \c_coffin_corners_prop
-    \prop_gset_eq:cN { l_coffin_poles_ \int_value:w #1 _prop }
-      \c_coffin_poles_prop
+    \prop_clear_new:c { l_@@_corners_ \__int_value:w #1 _prop }
+    \prop_clear_new:c { l_@@_poles_   \__int_value:w #1 _prop }
+    \prop_gset_eq:cN { l_@@_corners_ \__int_value:w #1 _prop }
+      \c_@@_corners_prop
+    \prop_gset_eq:cN { l_@@_poles_ \__int_value:w #1 _prop }
+      \c_@@_poles_prop
   }
 \cs_generate_variant:Nn \coffin_new:N { c }
 %    \end{macrocode}
@@ -620,7 +586,7 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \hcoffin_set:Nn #1#2
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
         \hbox_set:Nn #1
           {
@@ -629,9 +595,9 @@
               #2
             \color_group_end:
           }
-        \coffin_reset_structure:N #1
-        \coffin_update_poles:N #1
-        \coffin_update_corners:N #1
+        \@@_reset_structure:N #1
+        \@@_update_poles:N #1
+        \@@_update_corners:N #1
       }
   }
 \cs_generate_variant:Nn \hcoffin_set:Nn { c }
@@ -642,32 +608,38 @@
 %   Setting vertical coffins is more complex. First, the material is
 %   typeset with a given width. The default handles and poles are set as
 %   for a horizontal coffin, before finding the top baseline using a
-%   temporary box.
+%   temporary box. No \cs{color_ensure_current:} here as that would add a
+%   whatsit to the start of the vertical box and mess up the location of the
+%   \texttt{T}~pole (see \emph{\TeX{} by Topic} for discussion of the
+%   \tn{vtop} primitive, used to do the measuring).
 %    \begin{macrocode}
 \cs_new_protected:Npn \vcoffin_set:Nnn #1#2#3
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
         \vbox_set:Nn #1
           {
             \dim_set:Nn \tex_hsize:D {#2}
+%<*package>
+            \dim_set_eq:NN \linewidth   \tex_hsize:D
+            \dim_set_eq:NN \columnwidth \tex_hsize:D
+%</package>
             \color_group_begin:
-              \color_ensure_current:
               #3
             \color_group_end:
           }
-        \coffin_reset_structure:N #1
-        \coffin_update_poles:N #1
-        \coffin_update_corners:N #1
-        \vbox_set_top:Nn \l_coffin_internal_box { \vbox_unpack:N #1 }
-        \coffin_set_pole:Nnx #1 { T }
+        \@@_reset_structure:N #1
+        \@@_update_poles:N #1
+        \@@_update_corners:N #1
+        \vbox_set_top:Nn \l_@@_internal_box { \vbox_unpack:N #1 }
+        \@@_set_pole:Nnx #1 { T }
           {
             { 0 pt }
-            { \dim_eval:n { \box_ht:N #1 - \box_ht:N \l_coffin_internal_box } }
+            { \dim_eval:n { \box_ht:N #1 - \box_ht:N \l_@@_internal_box } }
             { 1000 pt }
             { 0 pt }
           }
-        \box_clear:N \l_coffin_internal_box
+        \box_clear:N \l_@@_internal_box
       }
   }
 \cs_generate_variant:Nn \vcoffin_set:Nnn { c }
@@ -681,16 +653,16 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \hcoffin_set:Nw #1
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
         \hbox_set:Nw #1 \color_group_begin: \color_ensure_current:
           \cs_set_protected_nopar:Npn \hcoffin_set_end:
             {
                 \color_group_end:
               \hbox_set_end:
-              \coffin_reset_structure:N #1
-              \coffin_update_poles:N #1
-              \coffin_update_corners:N #1
+              \@@_reset_structure:N #1
+              \@@_update_poles:N #1
+              \@@_update_corners:N #1
             }
       }
   }
@@ -706,29 +678,33 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \vcoffin_set:Nnw #1#2
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
         \vbox_set:Nw #1
           \dim_set:Nn \tex_hsize:D {#2}
+%<*package>
+            \dim_set_eq:NN \linewidth   \tex_hsize:D
+            \dim_set_eq:NN \columnwidth \tex_hsize:D
+%</package>
           \color_group_begin: \color_ensure_current:
           \cs_set_protected:Npn \vcoffin_set_end:
             {
                 \color_group_end:
               \vbox_set_end:
-              \coffin_reset_structure:N #1
-              \coffin_update_poles:N #1
-              \coffin_update_corners:N #1
-              \vbox_set_top:Nn \l_coffin_internal_box { \vbox_unpack:N #1 }
-              \coffin_set_pole:Nnx #1 { T }
+              \@@_reset_structure:N #1
+              \@@_update_poles:N #1
+              \@@_update_corners:N #1
+              \vbox_set_top:Nn \l_@@_internal_box { \vbox_unpack:N #1 }
+              \@@_set_pole:Nnx #1 { T }
                 {
                   { 0 pt }
                   {
-                    \dim_eval:n { \box_ht:N #1 - \box_ht:N \l_coffin_internal_box }
+                    \dim_eval:n { \box_ht:N #1 - \box_ht:N \l_@@_internal_box }
                   }
                   { 1000 pt }
                   { 0 pt }
                 }
-              \box_clear:N \l_coffin_internal_box
+              \box_clear:N \l_@@_internal_box
             }
       }
   }
@@ -747,10 +723,10 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_set_eq:NN #1#2
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
         \box_set_eq:NN #1 #2
-        \coffin_set_eq_structure:NN #1 #2
+        \@@_set_eq_structure:NN #1 #2
       }
   }
 \cs_generate_variant:Nn \coffin_set_eq:NN { c , Nc , cc }
@@ -758,20 +734,28 @@
 % \end{macro}
 %
 % \begin{variable}{\c_empty_coffin}
-% \begin{variable}{\l_coffin_aligned_coffin}
-% \begin{variable}{\l_coffin_aligned_internal_coffin}
+% \begin{variable}{\l_@@_aligned_coffin}
+% \begin{variable}{\l_@@_aligned_internal_coffin}
 %   Special coffins: these cannot be set up earlier as they need
 %   \cs{coffin_new:N}. The empty coffin is set as a box as the full
 %   coffin-setting system needs some material which is not yet available.
 %    \begin{macrocode}
 \coffin_new:N \c_empty_coffin
 \hbox_set:Nn  \c_empty_coffin { }
-\coffin_new:N \l_coffin_aligned_coffin
-\coffin_new:N \l_coffin_aligned_internal_coffin
+\coffin_new:N \l_@@_aligned_coffin
+\coffin_new:N \l_@@_aligned_internal_coffin
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 % \end{variable}
+% 
+% \begin{variable}{\l_tmpa_coffin, \l_tmpb_coffin}
+%   The usual scratch space.
+%    \begin{macrocode}
+\coffin_new:N \l_tmpa_coffin
+\coffin_new:N \l_tmpb_coffin
+%    \end{macrocode}
+% \end{variable}
 %
 % \subsection{Measuring coffins}
 %
@@ -794,16 +778,16 @@
 %
 % \subsection{Coffins: handle and pole management}
 %
-% \begin{macro}{\coffin_get_pole:NnN}
+% \begin{macro}{\@@_get_pole:NnN}
 %   A simple wrapper around the recovery of a coffin pole, with some
 %   error checking and recovery built-in.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_get_pole:NnN #1#2#3
+\cs_new_protected:Npn \@@_get_pole:NnN #1#2#3
   {
     \prop_get:cnNF
-      { l_coffin_poles_ \int_value:w #1 _prop } {#2} #3
+      { l_@@_poles_ \__int_value:w #1 _prop } {#2} #3
       {
-        \msg_kernel_error:nnxx { coffins } { unknown-coffin-pole }
+        \__msg_kernel_error:nnxx { kernel } { unknown-coffin-pole }
           {#2} { \token_to_str:N #1 }
         \tl_set:Nn #3 { { 0 pt } { 0 pt } { 0 pt } { 0 pt } }
       }
@@ -811,42 +795,42 @@
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\coffin_reset_structure:N}
+% \begin{macro}{\@@_reset_structure:N}
 %   Resetting the structure is a simple copy job.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_reset_structure:N #1
+\cs_new_protected:Npn \@@_reset_structure:N #1
   {
-    \prop_set_eq:cN { l_coffin_corners_ \int_value:w #1 _prop }
-      \c_coffin_corners_prop
-    \prop_set_eq:cN { l_coffin_poles_ \int_value:w #1 _prop }
-      \c_coffin_poles_prop
+    \prop_set_eq:cN { l_@@_corners_ \__int_value:w #1 _prop }
+      \c_@@_corners_prop
+    \prop_set_eq:cN { l_@@_poles_ \__int_value:w #1 _prop }
+      \c_@@_poles_prop
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\coffin_set_eq_structure:NN,\coffin_gset_eq_structure:NN}
+% \begin{macro}{\@@_set_eq_structure:NN,\@@_gset_eq_structure:NN}
 % Setting coffin structures equal simply means copying the property
 % list.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_set_eq_structure:NN #1#2
+\cs_new_protected:Npn \@@_set_eq_structure:NN #1#2
   {
-    \prop_set_eq:cc { l_coffin_corners_ \int_value:w #1 _prop }
-      { l_coffin_corners_ \int_value:w #2 _prop }
-    \prop_set_eq:cc { l_coffin_poles_ \int_value:w #1 _prop }
-      { l_coffin_poles_ \int_value:w #2 _prop }
+    \prop_set_eq:cc { l_@@_corners_ \__int_value:w #1 _prop }
+      { l_@@_corners_ \__int_value:w #2 _prop }
+    \prop_set_eq:cc { l_@@_poles_ \__int_value:w #1 _prop }
+      { l_@@_poles_ \__int_value:w #2 _prop }
   }
-\cs_new_protected:Npn \coffin_gset_eq_structure:NN #1#2
+\cs_new_protected:Npn \@@_gset_eq_structure:NN #1#2
   {
-    \prop_gset_eq:cc { l_coffin_corners_ \int_value:w #1 _prop }
-      { l_coffin_corners_ \int_value:w #2 _prop }
-    \prop_gset_eq:cc { l_coffin_poles_ \int_value:w #1 _prop }
-      { l_coffin_poles_ \int_value:w #2 _prop }
+    \prop_gset_eq:cc { l_@@_corners_ \__int_value:w #1 _prop }
+      { l_@@_corners_ \__int_value:w #2 _prop }
+    \prop_gset_eq:cc { l_@@_poles_ \__int_value:w #1 _prop }
+      { l_@@_poles_ \__int_value:w #2 _prop }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\coffin_set_user_dimensions:N}
-% \begin{macro}{\coffin_end_user_dimensions:}
+% \begin{macro}{\@@_set_user_dimensions:N}
+% \begin{macro}{\@@_end_user_dimensions:}
 % \begin{macro}{\Depth}
 % \begin{macro}{\Height}
 % \begin{macro}{\TotalHeight}
@@ -854,27 +838,27 @@
 %   These make design-level names for the dimensions of a coffin easy to
 %   get at.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_set_user_dimensions:N #1
+\cs_new_protected:Npn \@@_set_user_dimensions:N #1
   {
-    \cs_set_eq:NN \coffin_saved_Height:      \Height
-    \cs_set_eq:NN \coffin_saved_Depth:       \Depth
-    \cs_set_eq:NN \coffin_saved_TotalHeight: \TotalHeight
-    \cs_set_eq:NN \coffin_saved_Width:       \Width
-    \cs_set_eq:NN \Height      \l_coffin_Height_dim
-    \cs_set_eq:NN \Depth       \l_coffin_Depth_dim
-    \cs_set_eq:NN \TotalHeight \l_coffin_TotalHeight_dim
-    \cs_set_eq:NN \Width       \l_coffin_Width_dim
+    \cs_set_eq:NN \@@_saved_Height:      \Height
+    \cs_set_eq:NN \@@_saved_Depth:       \Depth
+    \cs_set_eq:NN \@@_saved_TotalHeight: \TotalHeight
+    \cs_set_eq:NN \@@_saved_Width:       \Width
+    \cs_set_eq:NN \Height      \l_@@_Height_dim
+    \cs_set_eq:NN \Depth       \l_@@_Depth_dim
+    \cs_set_eq:NN \TotalHeight \l_@@_TotalHeight_dim
+    \cs_set_eq:NN \Width       \l_@@_Width_dim
     \dim_set:Nn \Height      { \box_ht:N #1 }
     \dim_set:Nn \Depth       { \box_dp:N #1 }
     \dim_set:Nn \TotalHeight { \box_ht:N #1 + \box_dp:N #1 }
     \dim_set:Nn \Width       { \box_wd:N #1 }
   }
-\cs_new_protected_nopar:Npn \coffin_end_user_dimensions:
+\cs_new_protected_nopar:Npn \@@_end_user_dimensions:
   {
-    \cs_set_eq:NN \Height      \coffin_saved_Height:
-    \cs_set_eq:NN \Depth       \coffin_saved_Depth:
-    \cs_set_eq:NN \TotalHeight \coffin_saved_TotalHeight:
-    \cs_set_eq:NN \Width       \coffin_saved_Width:
+    \cs_set_eq:NN \Height      \@@_saved_Height:
+    \cs_set_eq:NN \Depth       \@@_saved_Depth:
+    \cs_set_eq:NN \TotalHeight \@@_saved_TotalHeight:
+    \cs_set_eq:NN \Width       \@@_saved_Width:
   }
 %    \end{macrocode}
 % \end{macro}
@@ -887,7 +871,7 @@
 % \begin{macro}
 %   {\coffin_set_horizontal_pole:Nnn, \coffin_set_horizontal_pole:cnn}
 % \begin{macro}{\coffin_set_vertical_pole:Nnn,\coffin_set_vertical_pole:cnn}
-% \begin{macro}{\coffin_set_pole:Nnn, \coffin_set_pole:Nnx}
+% \begin{macro}{\@@_set_pole:Nnn, \@@_set_pole:Nnx}
 %   Setting the pole of a coffin at the user/designer level requires a
 %   bit more care. The idea here is to provide a reasonable interface to
 %   the system, then to do the setting with full expansion. The
@@ -895,93 +879,93 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_set_horizontal_pole:Nnn #1#2#3
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
-        \coffin_set_user_dimensions:N #1
-        \coffin_set_pole:Nnx #1 {#2}
+        \@@_set_user_dimensions:N #1
+        \@@_set_pole:Nnx #1 {#2}
           {
             { 0 pt } { \dim_eval:n {#3} }
             { 1000 pt } { 0 pt }
           }
-        \coffin_end_user_dimensions:
+        \@@_end_user_dimensions:
       }
   }
 \cs_new_protected:Npn \coffin_set_vertical_pole:Nnn #1#2#3
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
-        \coffin_set_user_dimensions:N #1
-        \coffin_set_pole:Nnx #1 {#2}
+        \@@_set_user_dimensions:N #1
+        \@@_set_pole:Nnx #1 {#2}
           {
             { \dim_eval:n {#3} } { 0 pt }
             { 0 pt } { 1000 pt }
           }
-        \coffin_end_user_dimensions:
+        \@@_end_user_dimensions:
       }
   }
-\cs_new_protected:Npn \coffin_set_pole:Nnn #1#2#3
-  { \prop_put:cnn { l_coffin_poles_ \int_value:w #1 _prop } {#2} {#3} }
+\cs_new_protected:Npn \@@_set_pole:Nnn #1#2#3
+  { \prop_put:cnn { l_@@_poles_ \__int_value:w #1 _prop } {#2} {#3} }
 \cs_generate_variant:Nn \coffin_set_horizontal_pole:Nnn { c }
 \cs_generate_variant:Nn \coffin_set_vertical_pole:Nnn { c }
-\cs_generate_variant:Nn \coffin_set_pole:Nnn { Nnx }
+\cs_generate_variant:Nn \@@_set_pole:Nnn { Nnx }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\coffin_update_corners:N}
+% \begin{macro}{\@@_update_corners:N}
 %   Updating the corners of a coffin is straight-forward as at this stage
 %   there can be no rotation. So the corners of the content are just those
 %   of the underlying \TeX{} box.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_update_corners:N #1
+\cs_new_protected:Npn \@@_update_corners:N #1
   {
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { tl }
+    \prop_put:cnx { l_@@_corners_ \__int_value:w #1 _prop } { tl }
       { { 0 pt } { \dim_use:N \box_ht:N #1 } }
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { tr }
+    \prop_put:cnx { l_@@_corners_ \__int_value:w #1 _prop } { tr }
       { { \dim_use:N \box_wd:N #1 } { \dim_use:N \box_ht:N #1 } }
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { bl }
+    \prop_put:cnx { l_@@_corners_ \__int_value:w #1 _prop } { bl }
       { { 0 pt } { \dim_eval:n { - \box_dp:N #1 } } }
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { br }
+    \prop_put:cnx { l_@@_corners_ \__int_value:w #1 _prop } { br }
       { { \dim_use:N \box_wd:N #1 } { \dim_eval:n { - \box_dp:N #1 } } }
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\coffin_update_poles:N}
+% \begin{macro}{\@@_update_poles:N}
 %   This function is called when a coffin is set, and updates the poles to
 %   reflect the nature of size of the box. Thus this function only alters
 %   poles where the default position is dependent on the size of the box.
 %   It also does not set poles which are relevant only to vertical
 %   coffins.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_update_poles:N #1
+\cs_new_protected:Npn \@@_update_poles:N #1
   {
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { hc }
+    \prop_put:cnx { l_@@_poles_ \__int_value:w #1 _prop } { hc }
       {
         { \dim_eval:n { 0.5 \box_wd:N #1 } }
         { 0 pt } { 0 pt } { 1000 pt }
       }
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { r }
+    \prop_put:cnx { l_@@_poles_ \__int_value:w #1 _prop } { r }
       {
         { \dim_use:N \box_wd:N #1 }
         { 0 pt } { 0 pt } { 1000 pt }
       }
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { vc }
+    \prop_put:cnx { l_@@_poles_ \__int_value:w #1 _prop } { vc }
       {
         { 0 pt }
         { \dim_eval:n { ( \box_ht:N #1 - \box_dp:N #1 ) / 2 } }
         { 1000 pt }
         { 0 pt }
       }
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { t }
+    \prop_put:cnx { l_@@_poles_ \__int_value:w #1 _prop } { t }
       {
         { 0 pt }
         { \dim_use:N \box_ht:N #1 }
         { 1000 pt }
         { 0 pt }
       }
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { b }
+    \prop_put:cnx { l_@@_poles_ \__int_value:w #1 _prop } { b }
       {
         { 0 pt }
         { \dim_eval:n { - \box_dp:N #1 } }
@@ -994,27 +978,27 @@
 %
 % \subsection{Coffins: calculation of pole intersections}
 %
-% \begin{macro}{\coffin_calculate_intersection:Nnn}
-% \begin{macro}[aux]{\coffin_calculate_intersection:nnnnnnnn}
-% \begin{macro}[aux]{\coffin_calculate_intersection_aux:nnnnnN}
+% \begin{macro}{\@@_calculate_intersection:Nnn}
+% \begin{macro}[aux]{\@@_calculate_intersection:nnnnnnnn}
+% \begin{macro}[aux]{\@@_calculate_intersection_aux:nnnnnN}
 %   The lead off in finding intersections is to recover the two poles
 %   and then hand off to the auxiliary for the actual calculation. There
 %   may of course not be an intersection, for which an error trap is
 %   needed.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_calculate_intersection:Nnn #1#2#3
+\cs_new_protected:Npn \@@_calculate_intersection:Nnn #1#2#3
   {
-    \coffin_get_pole:NnN #1 {#2} \l_coffin_pole_a_tl
-    \coffin_get_pole:NnN #1 {#3} \l_coffin_pole_b_tl
-    \bool_set_false:N \l_coffin_error_bool
+    \@@_get_pole:NnN #1 {#2} \l_@@_pole_a_tl
+    \@@_get_pole:NnN #1 {#3} \l_@@_pole_b_tl
+    \bool_set_false:N \l_@@_error_bool
     \exp_last_two_unbraced:Noo
-      \coffin_calculate_intersection:nnnnnnnn
-        \l_coffin_pole_a_tl \l_coffin_pole_b_tl
-    \bool_if:NT \l_coffin_error_bool
+      \@@_calculate_intersection:nnnnnnnn
+        \l_@@_pole_a_tl \l_@@_pole_b_tl
+    \bool_if:NT \l_@@_error_bool
       {
-        \msg_kernel_error:nn { coffins } { no-pole-intersection }
-        \dim_zero:N \l_coffin_x_dim
-        \dim_zero:N \l_coffin_y_dim
+        \__msg_kernel_error:nn { kernel } { no-pole-intersection }
+        \dim_zero:N \l_@@_x_dim
+        \dim_zero:N \l_@@_y_dim
       }
   }
 %    \end{macrocode}
@@ -1029,7 +1013,7 @@
 %   is either horizontal or vertical then one or more of $c$, $d$,
 %   $c'$ and $d'$ will be zero and a special case is needed.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_calculate_intersection:nnnnnnnn
+\cs_new_protected:Npn \@@_calculate_intersection:nnnnnnnn
   #1#2#3#4#5#6#7#8
   {
     \dim_compare:nNnTF {#3} = { \c_zero_dim }
@@ -1039,9 +1023,9 @@
 %   second pole: if it is also vertical then there is an error.
 %    \begin{macrocode}
       {
-        \dim_set:Nn \l_coffin_x_dim {#1}
+        \dim_set:Nn \l_@@_x_dim {#1}
         \dim_compare:nNnTF {#7} = \c_zero_dim
-          { \bool_set_true:N \l_coffin_error_bool }
+          { \bool_set_true:N \l_@@_error_bool }
 %    \end{macrocode}
 %   The second pole may still be horizontal, in which case the
 %   $y$-component of the intersection will be $b'$. If not,
@@ -1053,10 +1037,10 @@
 %    \begin{macrocode}
           {
             \dim_compare:nNnTF {#8} = \c_zero_dim
-              { \dim_set:Nn \l_coffin_y_dim {#6} }
+              { \dim_set:Nn \l_@@_y_dim {#6} }
               {
-                \coffin_calculate_intersection_aux:nnnnnN
-                  {#1} {#5} {#6} {#7} {#8} \l_coffin_y_dim
+                \@@_calculate_intersection_aux:nnnnnN
+                  {#1} {#5} {#6} {#7} {#8} \l_@@_y_dim
               }
           }
       }
@@ -1068,12 +1052,12 @@
       {
         \dim_compare:nNnTF {#4} = \c_zero_dim
           {
-            \dim_set:Nn \l_coffin_y_dim {#2}
+            \dim_set:Nn \l_@@_y_dim {#2}
             \dim_compare:nNnTF {#8} = { \c_zero_dim }
-              { \bool_set_true:N \l_coffin_error_bool }
+              { \bool_set_true:N \l_@@_error_bool }
               {
                 \dim_compare:nNnTF {#7} = \c_zero_dim
-                  { \dim_set:Nn \l_coffin_x_dim {#5} }
+                  { \dim_set:Nn \l_@@_x_dim {#5} }
 %    \end{macrocode}
 %   The formula for the case where the second pole is neither horizontal
 %   nor vertical is
@@ -1083,8 +1067,8 @@
 %   which is again handled by the same auxiliary.
 %    \begin{macrocode}
                   {
-                    \coffin_calculate_intersection_aux:nnnnnN
-                      {#2} {#6} {#5} {#8} {#7} \l_coffin_x_dim
+                    \@@_calculate_intersection_aux:nnnnnN
+                      {#2} {#6} {#5} {#8} {#7} \l_@@_x_dim
                   }
               }
           }
@@ -1097,32 +1081,30 @@
           {
             \dim_compare:nNnTF {#7} = \c_zero_dim
               {
-                \dim_set:Nn \l_coffin_x_dim {#5}
-                \coffin_calculate_intersection_aux:nnnnnN
-                  {#5} {#1} {#2} {#3} {#4} \l_coffin_y_dim
+                \dim_set:Nn \l_@@_x_dim {#5}
+                \@@_calculate_intersection_aux:nnnnnN
+                  {#5} {#1} {#2} {#3} {#4} \l_@@_y_dim
               }
               {
                 \dim_compare:nNnTF {#8} = \c_zero_dim
                   {
-                    \dim_set:Nn \l_coffin_x_dim {#6}
-                    \coffin_calculate_intersection_aux:nnnnnN
-                      {#6} {#2} {#1} {#4} {#3} \l_coffin_x_dim
+                    \dim_set:Nn \l_@@_x_dim {#6}
+                    \@@_calculate_intersection_aux:nnnnnN
+                      {#6} {#2} {#1} {#4} {#3} \l_@@_x_dim
                   }
 %    \end{macrocode}
 %   If none of the special cases apply then there is still a need to
 %   check that there is a unique intersection between the two pole. This
 %   is the case if they have different slopes.
 %    \begin{macrocode}
-                {
-                    \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#3}
-                    \fp_set_from_dim:Nn \l_coffin_calc_b_fp {#4}
-                    \fp_set_from_dim:Nn \l_coffin_calc_c_fp {#7}
-                    \fp_set_from_dim:Nn \l_coffin_calc_d_fp {#8}
-                    \fp_div:Nn \l_coffin_calc_b_fp \l_coffin_calc_a_fp
-                    \fp_div:Nn \l_coffin_calc_d_fp \l_coffin_calc_c_fp
+                  {
+                    \fp_set:Nn \l_@@_slope_x_fp
+                      { \dim_to_fp:n {#4} / \dim_to_fp:n {#3} }
+                    \fp_set:Nn \l_@@_slope_y_fp
+                      { \dim_to_fp:n {#8} / \dim_to_fp:n {#7} }
                     \fp_compare:nNnTF
-                      \l_coffin_calc_b_fp = \l_coffin_calc_d_fp
-                      { \bool_set_true:N \l_coffin_error_bool }
+                      \l_@@_slope_x_fp = \l_@@_slope_y_fp
+                      { \bool_set_true:N \l_@@_error_bool }
 %    \end{macrocode}
 %   All of the tests pass, so there is the full complexity of the
 %   calculation:
@@ -1137,29 +1119,23 @@
 %   $x$-position.
 %    \begin{macrocode}
                       {
-                        \fp_set_from_dim:Nn \l_coffin_calc_result_fp {#6}
-                        \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#2}
-                        \fp_sub:Nn \l_coffin_calc_result_fp
-                          { \l_coffin_calc_a_fp }
-                        \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#1}
-                        \fp_mul:Nn \l_coffin_calc_a_fp
-                          { \l_coffin_calc_b_fp }
-                        \fp_add:Nn \l_coffin_calc_result_fp
-                          { \l_coffin_calc_a_fp }
-                        \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#5}
-                        \fp_mul:Nn \l_coffin_calc_a_fp
-                          { \l_coffin_calc_d_fp }
-                        \fp_sub:Nn \l_coffin_calc_result_fp
-                          { \l_coffin_calc_a_fp }
-                        \fp_sub:Nn \l_coffin_calc_b_fp
-                          { \l_coffin_calc_d_fp }
-                        \fp_div:Nn \l_coffin_calc_result_fp
-                          { \l_coffin_calc_b_fp }
-                        \dim_set:Nn \l_coffin_x_dim
-                          { \fp_to_dim:N \l_coffin_calc_result_fp }
-                        \coffin_calculate_intersection_aux:nnnnnN
-                          { \l_coffin_x_dim }
-                          {#5} {#6} {#8} {#7} \l_coffin_y_dim
+                        \dim_set:Nn \l_@@_x_dim
+                          {
+                            \fp_to_dim:n
+                              {
+                                (
+                                      \dim_to_fp:n {#1} * \l_@@_slope_x_fp
+                                  - ( \dim_to_fp:n {#5} * \l_@@_slope_y_fp )
+                                  -   \dim_to_fp:n {#2}
+                                  +   \dim_to_fp:n {#6}
+                                )
+                                /
+                                ( \l_@@_slope_x_fp - \l_@@_slope_y_fp )
+                            }
+                          }
+                        \@@_calculate_intersection_aux:nnnnnN
+                          { \l_@@_x_dim }
+                          {#5} {#6} {#8} {#7} \l_@@_y_dim
                       }
                   }
               }
@@ -1170,24 +1146,23 @@
 %   The formula for finding the intersection point is in most cases the
 %   same. The formula here is
 %   \[
-%     \#6 = \frac{\#5}{\#4} \left ( \#1 - \#2 \right ) + \#3
+%     \#6 = \#4 \cdot \left( \frac { \#1 - \#2 } { \#5 } \right)\#3
 %   \]
 %   Thus |#4| and |#5| should be the directions of the pole while
 %   |#2| and |#3| are co-ordinates.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_calculate_intersection_aux:nnnnnN
-  #1#2#3#4#5#6
+\cs_new_protected:Npn \@@_calculate_intersection_aux:nnnnnN #1#2#3#4#5#6
   {
-    \fp_set_from_dim:Nn \l_coffin_calc_result_fp {#1}
-    \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#2}
-    \fp_set_from_dim:Nn \l_coffin_calc_b_fp {#3}
-    \fp_set_from_dim:Nn \l_coffin_calc_c_fp {#4}
-    \fp_set_from_dim:Nn \l_coffin_calc_d_fp {#5}
-    \fp_sub:Nn \l_coffin_calc_result_fp { \l_coffin_calc_a_fp }
-    \fp_div:Nn \l_coffin_calc_result_fp { \l_coffin_calc_d_fp }
-    \fp_mul:Nn \l_coffin_calc_result_fp { \l_coffin_calc_c_fp }
-    \fp_add:Nn \l_coffin_calc_result_fp { \l_coffin_calc_b_fp }
-    \dim_set:Nn #6 { \fp_to_dim:N \l_coffin_calc_result_fp }
+    \dim_set:Nn #6
+      {
+        \fp_to_dim:n
+          {
+            \dim_to_fp:n {#4} *
+            ( \dim_to_fp:n {#1} - \dim_to_fp:n {#2} ) /
+            \dim_to_fp:n {#5}
+            + \dim_to_fp:n {#3}
+          }
+      }
   }
 %    \end{macrocode}
 % \end{macro}
@@ -1209,8 +1184,8 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_join:NnnNnnnn #1#2#3#4#5#6#7#8
   {
-    \coffin_align:NnnNnnnnN
-      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_coffin_aligned_coffin
+    \@@_align:NnnNnnnnN
+      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_@@_aligned_coffin
 %    \end{macrocode}
 %   Correct the placement of the reference point. If the $x$-offset
 %   is negative then the reference point of the second box is to the left
@@ -1219,46 +1194,46 @@
 %   than the sum of the $x$-offset and the width of the second box.
 %   So a second kern may be needed.
 %    \begin{macrocode}
-    \hbox_set:Nn \l_coffin_aligned_coffin
+    \hbox_set:Nn \l_@@_aligned_coffin
       {
-        \dim_compare:nNnT { \l_coffin_offset_x_dim } < \c_zero_dim
-          { \tex_kern:D -\l_coffin_offset_x_dim }
-        \hbox_unpack:N \l_coffin_aligned_coffin
-        \dim_set:Nn \l_coffin_internal_dim
-          { \l_coffin_offset_x_dim - \box_wd:N #1 + \box_wd:N #4 }
-        \dim_compare:nNnT \l_coffin_internal_dim < \c_zero_dim
-          { \tex_kern:D -\l_coffin_internal_dim }
+        \dim_compare:nNnT { \l_@@_offset_x_dim } < \c_zero_dim
+          { \tex_kern:D -\l_@@_offset_x_dim }
+        \hbox_unpack:N \l_@@_aligned_coffin
+        \dim_set:Nn \l_@@_internal_dim
+          { \l_@@_offset_x_dim - \box_wd:N #1 + \box_wd:N #4 }
+        \dim_compare:nNnT \l_@@_internal_dim < \c_zero_dim
+          { \tex_kern:D -\l_@@_internal_dim }
       }
 %    \end{macrocode}
 %   The coffin structure is reset, and the corners are cleared: only
 %   those from the two parent coffins are needed.
 %    \begin{macrocode}
-   \coffin_reset_structure:N \l_coffin_aligned_coffin
+   \@@_reset_structure:N \l_@@_aligned_coffin
     \prop_clear:c
-      {  l_coffin_corners_ \int_value:w \l_coffin_aligned_coffin _ prop }
-    \coffin_update_poles:N \l_coffin_aligned_coffin
+      {  l_@@_corners_ \__int_value:w \l_@@_aligned_coffin _ prop }
+    \@@_update_poles:N \l_@@_aligned_coffin
 %    \end{macrocode}
 %   The structures of the parent coffins are now transferred to the new
 %   coffin, which requires that the appropriate offsets are applied. That
 %   will then depend on whether any shift was needed.
 %    \begin{macrocode}
-    \dim_compare:nNnTF \l_coffin_offset_x_dim < \c_zero_dim
+    \dim_compare:nNnTF \l_@@_offset_x_dim < \c_zero_dim
       {
-        \coffin_offset_poles:Nnn #1 { -\l_coffin_offset_x_dim } { 0 pt }
-        \coffin_offset_poles:Nnn #4 { 0 pt } { \l_coffin_offset_y_dim }
-        \coffin_offset_corners:Nnn #1 { -\l_coffin_offset_x_dim } { 0 pt }
-        \coffin_offset_corners:Nnn #4 { 0 pt } { \l_coffin_offset_y_dim }
+        \@@_offset_poles:Nnn #1 { -\l_@@_offset_x_dim } { 0 pt }
+        \@@_offset_poles:Nnn #4 { 0 pt } { \l_@@_offset_y_dim }
+        \@@_offset_corners:Nnn #1 { -\l_@@_offset_x_dim } { 0 pt }
+        \@@_offset_corners:Nnn #4 { 0 pt } { \l_@@_offset_y_dim }
       }
       {
-        \coffin_offset_poles:Nnn #1 { 0 pt } { 0 pt }
-        \coffin_offset_poles:Nnn #4
-          { \l_coffin_offset_x_dim } { \l_coffin_offset_y_dim }
-        \coffin_offset_corners:Nnn #1 { 0 pt } { 0 pt }
-        \coffin_offset_corners:Nnn #4
-          { \l_coffin_offset_x_dim } { \l_coffin_offset_y_dim }
+        \@@_offset_poles:Nnn #1 { 0 pt } { 0 pt }
+        \@@_offset_poles:Nnn #4
+          { \l_@@_offset_x_dim } { \l_@@_offset_y_dim }
+        \@@_offset_corners:Nnn #1 { 0 pt } { 0 pt }
+        \@@_offset_corners:Nnn #4
+          { \l_@@_offset_x_dim } { \l_@@_offset_y_dim }
       }
-    \coffin_update_vertical_poles:NNN #1 #4 \l_coffin_aligned_coffin
-    \coffin_set_eq:NN #1 \l_coffin_aligned_coffin
+    \@@_update_vertical_poles:NNN #1 #4 \l_@@_aligned_coffin
+    \coffin_set_eq:NN #1 \l_@@_aligned_coffin
   }
 \cs_generate_variant:Nn \coffin_join:NnnNnnnn { c , Nnnc , cnnc }
 %    \end{macrocode}
@@ -1278,37 +1253,37 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_attach:NnnNnnnn #1#2#3#4#5#6#7#8
   {
-    \coffin_align:NnnNnnnnN
-      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_coffin_aligned_coffin
-    \box_set_ht:Nn \l_coffin_aligned_coffin { \box_ht:N #1 }
-    \box_set_dp:Nn \l_coffin_aligned_coffin { \box_dp:N #1 }
-    \box_set_wd:Nn \l_coffin_aligned_coffin { \box_wd:N #1 }
-    \coffin_reset_structure:N \l_coffin_aligned_coffin
+    \@@_align:NnnNnnnnN
+      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_@@_aligned_coffin
+    \box_set_ht:Nn \l_@@_aligned_coffin { \box_ht:N #1 }
+    \box_set_dp:Nn \l_@@_aligned_coffin { \box_dp:N #1 }
+    \box_set_wd:Nn \l_@@_aligned_coffin { \box_wd:N #1 }
+    \@@_reset_structure:N \l_@@_aligned_coffin
     \prop_set_eq:cc
-      { l_coffin_corners_ \int_value:w \l_coffin_aligned_coffin _prop }
-      { l_coffin_corners_ \int_value:w #1 _prop }
-    \coffin_update_poles:N  \l_coffin_aligned_coffin
-    \coffin_offset_poles:Nnn #1 { 0 pt } { 0 pt }
-    \coffin_offset_poles:Nnn #4
-      { \l_coffin_offset_x_dim } { \l_coffin_offset_y_dim }
-    \coffin_update_vertical_poles:NNN #1 #4 \l_coffin_aligned_coffin
-    \coffin_set_eq:NN #1 \l_coffin_aligned_coffin
+      { l_@@_corners_ \__int_value:w \l_@@_aligned_coffin _prop }
+      { l_@@_corners_ \__int_value:w #1 _prop }
+    \@@_update_poles:N  \l_@@_aligned_coffin
+    \@@_offset_poles:Nnn #1 { 0 pt } { 0 pt }
+    \@@_offset_poles:Nnn #4
+      { \l_@@_offset_x_dim } { \l_@@_offset_y_dim }
+    \@@_update_vertical_poles:NNN #1 #4 \l_@@_aligned_coffin
+    \coffin_set_eq:NN #1 \l_@@_aligned_coffin
   }
 \cs_new_protected:Npn \coffin_attach_mark:NnnNnnnn #1#2#3#4#5#6#7#8
   {
-    \coffin_align:NnnNnnnnN
-      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_coffin_aligned_coffin
-    \box_set_ht:Nn \l_coffin_aligned_coffin { \box_ht:N #1 }
-    \box_set_dp:Nn \l_coffin_aligned_coffin { \box_dp:N #1 }
-    \box_set_wd:Nn \l_coffin_aligned_coffin { \box_wd:N #1 }
-    \box_set_eq:NN #1 \l_coffin_aligned_coffin
+    \@@_align:NnnNnnnnN
+      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_@@_aligned_coffin
+    \box_set_ht:Nn \l_@@_aligned_coffin { \box_ht:N #1 }
+    \box_set_dp:Nn \l_@@_aligned_coffin { \box_dp:N #1 }
+    \box_set_wd:Nn \l_@@_aligned_coffin { \box_wd:N #1 }
+    \box_set_eq:NN #1 \l_@@_aligned_coffin
   }
 \cs_generate_variant:Nn \coffin_attach:NnnNnnnn { c , Nnnc , cnnc }
 %    \end{macrocode}
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\coffin_align:NnnNnnnnN}
+% \begin{macro}{\@@_align:NnnNnnnnN}
 %   The internal function aligns the two coffins into a third one, but
 %   performs no corrections on the resulting coffin poles. The process
 %   begins by finding the points of intersection for the poles for each
@@ -1319,30 +1294,30 @@
 %   input coffins. The default poles are then set up, but the final result
 %   will depend on how the bounding box is being handled.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_align:NnnNnnnnN #1#2#3#4#5#6#7#8#9
+\cs_new_protected:Npn \@@_align:NnnNnnnnN #1#2#3#4#5#6#7#8#9
   {
-    \coffin_calculate_intersection:Nnn #4 {#5} {#6}
-    \dim_set:Nn \l_coffin_x_prime_dim { \l_coffin_x_dim }
-    \dim_set:Nn \l_coffin_y_prime_dim { \l_coffin_y_dim }
-    \coffin_calculate_intersection:Nnn #1 {#2} {#3}
-    \dim_set:Nn \l_coffin_offset_x_dim
-      { \l_coffin_x_dim - \l_coffin_x_prime_dim + #7 }
-    \dim_set:Nn \l_coffin_offset_y_dim
-      { \l_coffin_y_dim - \l_coffin_y_prime_dim + #8 }
-    \hbox_set:Nn \l_coffin_aligned_internal_coffin
+    \@@_calculate_intersection:Nnn #4 {#5} {#6}
+    \dim_set:Nn \l_@@_x_prime_dim { \l_@@_x_dim }
+    \dim_set:Nn \l_@@_y_prime_dim { \l_@@_y_dim }
+    \@@_calculate_intersection:Nnn #1 {#2} {#3}
+    \dim_set:Nn \l_@@_offset_x_dim
+      { \l_@@_x_dim - \l_@@_x_prime_dim + #7 }
+    \dim_set:Nn \l_@@_offset_y_dim
+      { \l_@@_y_dim - \l_@@_y_prime_dim + #8 }
+    \hbox_set:Nn \l_@@_aligned_internal_coffin
       {
         \box_use:N #1
         \tex_kern:D -\box_wd:N #1
-        \tex_kern:D \l_coffin_offset_x_dim
-        \box_move_up:nn { \l_coffin_offset_y_dim } { \box_use:N #4 }
+        \tex_kern:D \l_@@_offset_x_dim
+        \box_move_up:nn { \l_@@_offset_y_dim } { \box_use:N #4 }
       }
-    \coffin_set_eq:NN #9 \l_coffin_aligned_internal_coffin
+    \coffin_set_eq:NN #9 \l_@@_aligned_internal_coffin
   }
 %    \end{macrocode}
 % \end{macro}
 %
-% \begin{macro}{\coffin_offset_poles:Nnn}
-% \begin{macro}[aux]{\coffin_offset_pole:Nnnnnnn}
+% \begin{macro}{\@@_offset_poles:Nnn}
+% \begin{macro}[aux]{\@@_offset_pole:Nnnnnnn}
 %   Transferring structures from one coffin to another requires that the
 %   positions are updated by the offset between the two coffins. This is
 %   done by mapping to the property list of the source coffins, moving
@@ -1353,22 +1328,22 @@
 %   or handle names, and that multiple alignments do not result in a
 %   whole set of values.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_offset_poles:Nnn #1#2#3
+\cs_new_protected:Npn \@@_offset_poles:Nnn #1#2#3
   {
-    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-      { \coffin_offset_pole:Nnnnnnn #1 {##1} ##2 {#2} {#3} }
+    \prop_map_inline:cn { l_@@_poles_ \__int_value:w #1 _prop }
+      { \@@_offset_pole:Nnnnnnn #1 {##1} ##2 {#2} {#3} }
   }
-\cs_new_protected:Npn \coffin_offset_pole:Nnnnnnn #1#2#3#4#5#6#7#8
+\cs_new_protected:Npn \@@_offset_pole:Nnnnnnn #1#2#3#4#5#6#7#8
   {
-    \dim_set:Nn \l_coffin_x_dim { #3 + #7 }
-    \dim_set:Nn \l_coffin_y_dim { #4 + #8 }
+    \dim_set:Nn \l_@@_x_dim { #3 + #7 }
+    \dim_set:Nn \l_@@_y_dim { #4 + #8 }
     \tl_if_in:nnTF {#2} { - }
-      { \tl_set:Nn \l_coffin_internal_tl { {#2} } }
-      { \tl_set:Nn \l_coffin_internal_tl { { #1 - #2 } } }
-    \exp_last_unbraced:NNo \coffin_set_pole:Nnx \l_coffin_aligned_coffin
-      { \l_coffin_internal_tl }
+      { \tl_set:Nn \l_@@_internal_tl { {#2} } }
+      { \tl_set:Nn \l_@@_internal_tl { { #1 - #2 } } }
+    \exp_last_unbraced:NNo \@@_set_pole:Nnx \l_@@_aligned_coffin
+      { \l_@@_internal_tl }
       {
-        { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim }
+        { \dim_use:N \l_@@_x_dim } { \dim_use:N \l_@@_y_dim }
         {#5} {#6}
       }
   }
@@ -1376,21 +1351,21 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\coffin_offset_corners:Nnn}
-% \begin{macro}[aux]{\coffin_offset_corners:Nnnnn}
+% \begin{macro}{\@@_offset_corners:Nnn}
+% \begin{macro}[aux]{\@@_offset_corner:Nnnnn}
 %   Saving the offset corners of a coffin is very similar, except that
 %   there is no need to worry about naming: every corner can be saved
 %   here as order is unimportant.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_offset_corners:Nnn #1#2#3
+\cs_new_protected:Npn \@@_offset_corners:Nnn #1#2#3
   {
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_offset_corner:Nnnnn #1 {##1} ##2 {#2} {#3} }
+    \prop_map_inline:cn { l_@@_corners_ \__int_value:w #1 _prop }
+      { \@@_offset_corner:Nnnnn #1 {##1} ##2 {#2} {#3} }
   }
-\cs_new_protected:Npn \coffin_offset_corner:Nnnnn #1#2#3#4#5#6
+\cs_new_protected:Npn \@@_offset_corner:Nnnnn #1#2#3#4#5#6
   {
     \prop_put:cnx
-      { l_coffin_corners_ \int_value:w \l_coffin_aligned_coffin _prop }
+      { l_@@_corners_ \__int_value:w \l_@@_aligned_coffin _prop }
       { #1 - #2 }
       {
         { \dim_eval:n { #3 + #5 } }
@@ -1401,46 +1376,46 @@
 % \end{macro}
 % \end{macro}
 %
-% \begin{macro}{\coffin_update_vertical_poles:NNN}
-% \begin{macro}[aux]{\coffin_update_T:nnnnnnnnN}
-% \begin{macro}[aux]{\coffin_update_B:nnnnnnnnN}
+% \begin{macro}{\@@_update_vertical_poles:NNN}
+% \begin{macro}[aux]{\@@_update_T:nnnnnnnnN}
+% \begin{macro}[aux]{\@@_update_B:nnnnnnnnN}
 %   The \texttt{T} and \texttt{B} poles will need to be recalculated
 %   after alignment. These functions find the larger absolute value for
 %   the poles, but this is of course only logical when the poles are
 %   horizontal.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_update_vertical_poles:NNN #1#2#3
+\cs_new_protected:Npn \@@_update_vertical_poles:NNN #1#2#3
   {
-    \coffin_get_pole:NnN #3 { #1 -T } \l_coffin_pole_a_tl
-    \coffin_get_pole:NnN #3 { #2 -T } \l_coffin_pole_b_tl
-    \exp_last_two_unbraced:Noo \coffin_update_T:nnnnnnnnN
-      \l_coffin_pole_a_tl \l_coffin_pole_b_tl #3
-    \coffin_get_pole:NnN #3 { #1 -B } \l_coffin_pole_a_tl
-    \coffin_get_pole:NnN #3 { #2 -B } \l_coffin_pole_b_tl
-    \exp_last_two_unbraced:Noo \coffin_update_B:nnnnnnnnN
-      \l_coffin_pole_a_tl \l_coffin_pole_b_tl #3
+    \@@_get_pole:NnN #3 { #1 -T } \l_@@_pole_a_tl
+    \@@_get_pole:NnN #3 { #2 -T } \l_@@_pole_b_tl
+    \exp_last_two_unbraced:Noo \@@_update_T:nnnnnnnnN
+      \l_@@_pole_a_tl \l_@@_pole_b_tl #3
+    \@@_get_pole:NnN #3 { #1 -B } \l_@@_pole_a_tl
+    \@@_get_pole:NnN #3 { #2 -B } \l_@@_pole_b_tl
+    \exp_last_two_unbraced:Noo \@@_update_B:nnnnnnnnN
+      \l_@@_pole_a_tl \l_@@_pole_b_tl #3
   }
-\cs_new_protected:Npn \coffin_update_T:nnnnnnnnN #1#2#3#4#5#6#7#8#9
+\cs_new_protected:Npn \@@_update_T:nnnnnnnnN #1#2#3#4#5#6#7#8#9
   {
     \dim_compare:nNnTF {#2} < {#6}
       {
-        \coffin_set_pole:Nnx #9 { T }
+        \@@_set_pole:Nnx #9 { T }
           { { 0 pt } {#6} { 1000 pt } { 0 pt } }
       }
       {
-        \coffin_set_pole:Nnx #9 { T }
+        \@@_set_pole:Nnx #9 { T }
           { { 0 pt } {#2} { 1000 pt } { 0 pt } }
       }
   }
-\cs_new_protected:Npn \coffin_update_B:nnnnnnnnN #1#2#3#4#5#6#7#8#9
+\cs_new_protected:Npn \@@_update_B:nnnnnnnnN #1#2#3#4#5#6#7#8#9
   {
     \dim_compare:nNnTF {#2} < {#6}
       {
-        \coffin_set_pole:Nnx #9 { B }
+        \@@_set_pole:Nnx #9 { B }
           { { 0 pt } {#2}  { 1000 pt } { 0 pt } }
       }
       {
-        \coffin_set_pole:Nnx #9 { B }
+        \@@_set_pole:Nnx #9 { B }
           { { 0 pt } {#6} { 1000 pt } { 0 pt } }
       }
   }
@@ -1456,556 +1431,120 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_typeset:Nnnnn #1#2#3#4#5
   {
-    \coffin_align:NnnNnnnnN \c_empty_coffin { H } { l }
-      #1 {#2} {#3} {#4} {#5} \l_coffin_aligned_coffin
+    \@@_align:NnnNnnnnN \c_empty_coffin { H } { l }
+      #1 {#2} {#3} {#4} {#5} \l_@@_aligned_coffin
     \hbox_unpack:N \c_empty_box
-    \box_use:N \l_coffin_aligned_coffin
+    \box_use:N \l_@@_aligned_coffin
   }
 \cs_generate_variant:Nn \coffin_typeset:Nnnnn { c }
 %    \end{macrocode}
 % \end{macro}
 %
-% \subsection{Rotating coffins}
-%
-% \begin{variable}{\l_coffin_bounding_prop}
-%   A property list for the bounding box of a coffin. This is only needed
-%   during the rotation, so there is just the one.
-%    \begin{macrocode}
-\prop_new:N \l_coffin_bounding_prop
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_coffin_bounding_shift_dim}
-%   The shift of the bounding box of a coffin from the real content.
-%    \begin{macrocode}
-\dim_new:N \l_coffin_bounding_shift_dim
-%    \end{macrocode}
-% \end{variable}
-%
-% \begin{variable}{\l_coffin_left_corner_dim}
-% \begin{variable}{\l_coffin_right_corner_dim}
-% \begin{variable}{\l_coffin_bottom_corner_dim}
-% \begin{variable}{\l_coffin_top_corner_dim}
-%   These are used to hold maxima for the various corner values: these
-%   thus define the minimum size of the bounding box after rotation.
-%    \begin{macrocode}
-\dim_new:N \l_coffin_left_corner_dim
-\dim_new:N \l_coffin_right_corner_dim
-\dim_new:N \l_coffin_bottom_corner_dim
-\dim_new:N \l_coffin_top_corner_dim
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-% \end{variable}
-%
-% \begin{macro}{\coffin_rotate:Nn, \coffin_rotate:cn}
-%   Rotating a coffin requires several steps which can be conveniently
-%   run together. The first step is to convert the angle given in degrees
-%   to one in radians. This is then used to set \cs{l_coffin_sin_fp} and
-%   \cs{l_coffin_cos_fp}, which are carried through unchanged for the rest
-%   of the procedure.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_rotate:Nn #1#2
-  {
-    \fp_set:Nn \l_coffin_internal_fp {#2}
-    \fp_div:Nn \l_coffin_internal_fp { 180 }
-    \fp_mul:Nn \l_coffin_internal_fp { \c_pi_fp }
-    \fp_sin:Nn \l_coffin_sin_fp { \l_coffin_internal_fp }
-    \fp_cos:Nn \l_coffin_cos_fp { \l_coffin_internal_fp }
-%    \end{macrocode}
-%   The corners and poles of the coffin can now be rotated around the
-%    origin. This is best achieved using mapping functions.
-%    \begin{macrocode}
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_rotate_corner:Nnnn #1 {##1} ##2 }
-    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-      { \coffin_rotate_pole:Nnnnnn #1 {##1} ##2 }
-%    \end{macrocode}
-%   The bounding box of the coffin needs to be rotated, and to do this
-%   the corners have to be found first. They are then rotated in the same
-%   way as the corners of the coffin material itself.
-%    \begin{macrocode}
-    \coffin_set_bounding:N #1
-    \prop_map_inline:Nn \l_coffin_bounding_prop
-      { \coffin_rotate_bounding:nnn {##1} ##2 }
-%    \end{macrocode}
-%   At this stage, there needs to be a calculation to find where the
-%   corners of the content and the box itself will end up.
-%    \begin{macrocode}
-    \coffin_find_corner_maxima:N #1
-    \coffin_find_bounding_shift:
-    \box_rotate:Nn #1 {#2}
-%    \end{macrocode}
-%   The correction of the box position itself takes place here. The idea
-%   is that the bounding box for a coffin is tight up to the content, and
-%   has the reference point at the bottom-left. The $x$-direction is
-%   handled by moving the content by the difference in the positions of
-%   the bounding box and the content left edge. The $y$-direction is
-%   dealt with by moving the box down by any depth it has acquired.
-%    \begin{macrocode}
-    \hbox_set:Nn #1
-      {
-        \tex_kern:D \l_coffin_bounding_shift_dim
-        \tex_kern:D -\l_coffin_left_corner_dim
-        \box_move_down:nn { \l_coffin_bottom_corner_dim }
-          { \box_use:N #1 }
-      }
-%    \end{macrocode}
-%   If there have been any previous rotations then the size of the
-%   bounding box will be bigger than the contents. This can be corrected
-%   easily by setting the size of the box to the height and width of the
-%   content.
-%    \begin{macrocode}
-    \box_set_ht:Nn #1
-      { \l_coffin_top_corner_dim - \l_coffin_bottom_corner_dim }
-    \box_set_dp:Nn #1 { 0 pt }
-    \box_set_wd:Nn #1
-      { \l_coffin_right_corner_dim - \l_coffin_left_corner_dim }
-%    \end{macrocode}
-%   The final task is to move the poles and corners such that they are
-%   back in alignment with the box reference point.
-%    \begin{macrocode}
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_shift_corner:Nnnn #1 {##1} ##2 }
-    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-      { \coffin_shift_pole:Nnnnnn #1 {##1} ##2 }
-  }
-\cs_generate_variant:Nn \coffin_rotate:Nn { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_set_bounding:N}
-%   The bounding box corners for a coffin are easy enough to find: this
-%   is the same code as for the corners of the material itself, but
-%   using a dedicated property list.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_set_bounding:N #1
-  {
-   \prop_put:Nnx \l_coffin_bounding_prop { tl }
-      { { 0 pt } { \dim_use:N \box_ht:N #1 } }
-    \prop_put:Nnx \l_coffin_bounding_prop { tr }
-      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \box_ht:N #1 } }
-    \dim_set:Nn \l_coffin_internal_dim { - \box_dp:N #1 }
-    \prop_put:Nnx \l_coffin_bounding_prop { bl }
-      { { 0 pt } { \dim_use:N \l_coffin_internal_dim } }
-    \prop_put:Nnx \l_coffin_bounding_prop { br }
-      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \l_coffin_internal_dim } }
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_rotate_bounding:nnn}
-% \begin{macro}{\coffin_rotate_corner:Nnnn}
-%   Rotating the position of the corner of the coffin is just a case
-%   of treating this as a vector from the reference point. The same
-%   treatment is used for the corners of the material itself and the
-%   bounding box.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_rotate_bounding:nnn #1#2#3
-  {
-    \coffin_rotate_vector:nnNN {#2} {#3} \l_coffin_x_dim \l_coffin_y_dim
-    \prop_put:Nnx \l_coffin_bounding_prop {#1}
-      { { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim } }
-  }
-\cs_new_protected:Npn \coffin_rotate_corner:Nnnn #1#2#3#4
-  {
-    \coffin_rotate_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } {#2}
-      { { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim } }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\coffin_rotate_pole:Nnnnnn}
-%   Rotating a single pole simply means shifting the co-ordinate of
-%   the pole and its direction. The rotation here is about the bottom-left
-%   corner of the coffin.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_rotate_pole:Nnnnnn #1#2#3#4#5#6
-  {
-    \coffin_rotate_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
-    \coffin_rotate_vector:nnNN {#5} {#6}
-      \l_coffin_x_prime_dim \l_coffin_y_prime_dim
-    \coffin_set_pole:Nnx #1 {#2}
-      {
-        { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim }
-        { \dim_use:N \l_coffin_x_prime_dim }
-        { \dim_use:N \l_coffin_y_prime_dim }
-      }
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_rotate_vector:nnNN}
-%   A rotation function, which needs only an input vector (as dimensions)
-%   and an output space. The values \cs{l_coffin_cos_fp} and
-%   \cs{l_coffin_sin_fp} should previously have been set up correctly.
-%   Working this way means that the floating point work is kept to a
-%   minimum: for any given rotation the sin and cosine values do no
-%   change, after all.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_rotate_vector:nnNN #1#2#3#4
-  {
-    \fp_set_from_dim:Nn \l_coffin_x_fp {#1}
-    \fp_set_from_dim:Nn \l_coffin_y_fp {#2}
-    \fp_set_eq:NN \l_coffin_x_prime_fp \l_coffin_x_fp
-    \fp_set_eq:NN \l_coffin_internal_fp     \l_coffin_y_fp
-    \fp_mul:Nn \l_coffin_x_prime_fp { \l_coffin_cos_fp }
-    \fp_mul:Nn \l_coffin_internal_fp     { \l_coffin_sin_fp }
-    \fp_sub:Nn \l_coffin_x_prime_fp { \l_coffin_internal_fp }
-    \fp_set_eq:NN \l_coffin_y_prime_fp \l_coffin_y_fp
-    \fp_set_eq:NN \l_coffin_internal_fp     \l_coffin_x_fp
-    \fp_mul:Nn \l_coffin_y_prime_fp { \l_coffin_cos_fp }
-    \fp_mul:Nn \l_coffin_internal_fp     { \l_coffin_sin_fp }
-    \fp_add:Nn \l_coffin_y_prime_fp { \l_coffin_internal_fp }
-    \dim_set:Nn #3 { \fp_to_dim:N \l_coffin_x_prime_fp }
-    \dim_set:Nn #4 { \fp_to_dim:N \l_coffin_y_prime_fp }
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_find_corner_maxima:N}
-% \begin{macro}[aux]{\coffin_find_corner_maxima_aux:nn}
-%   The idea here is to find the extremities of the content of the
-%   coffin. This is done by looking for the smallest values for the bottom
-%   and left corners, and the largest values for the top and right
-%   corners. The values start at the maximum dimensions so that the
-%   case where all are positive or all are negative works out correctly.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_find_corner_maxima:N #1
-  {
-    \dim_set:Nn \l_coffin_top_corner_dim   { -\c_max_dim }
-    \dim_set:Nn \l_coffin_right_corner_dim { -\c_max_dim }
-    \dim_set:Nn \l_coffin_bottom_corner_dim { \c_max_dim }
-    \dim_set:Nn \l_coffin_left_corner_dim   { \c_max_dim }
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_find_corner_maxima_aux:nn ##2 }
-  }
-\cs_new_protected:Npn \coffin_find_corner_maxima_aux:nn #1#2
-  {
-    \dim_set_min:Nn \l_coffin_left_corner_dim   {#1}
-    \dim_set_max:Nn \l_coffin_right_corner_dim  {#1}
-    \dim_set_min:Nn \l_coffin_bottom_corner_dim {#2}
-    \dim_set_max:Nn \l_coffin_top_corner_dim    {#2}
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\coffin_find_bounding_shift:}
-% \begin{macro}[aux]{\coffin_find_bounding_shift_aux:nn}
-%   The approach to finding the shift for the bounding box is similar to
-%   that for the corners. However, there is only one value needed here and
-%   a fixed input property list, so things are a bit clearer.
-%    \begin{macrocode}
-\cs_new_protected_nopar:Npn \coffin_find_bounding_shift:
-  {
-    \dim_set:Nn \l_coffin_bounding_shift_dim { \c_max_dim }
-    \prop_map_inline:Nn \l_coffin_bounding_prop
-      { \coffin_find_bounding_shift_aux:nn ##2 }
-  }
-\cs_new_protected:Npn \coffin_find_bounding_shift_aux:nn #1#2
-  { \dim_set_min:Nn \l_coffin_bounding_shift_dim {#1} }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\coffin_shift_corner:Nnnn}
-% \begin{macro}{\coffin_shift_pole:Nnnnnn}
-%   Shifting the corners and poles of a coffin means subtracting the
-%   appropriate values from the $x$- and $y$-components. For
-%   the poles, this means that the direction vector is unchanged.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_shift_corner:Nnnn #1#2#3#4
-  {
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _ prop } {#2}
-      {
-        { \dim_eval:n { #3 - \l_coffin_left_corner_dim } }
-        { \dim_eval:n { #4 - \l_coffin_bottom_corner_dim } }
-      }
-  }
-\cs_new_protected:Npn \coffin_shift_pole:Nnnnnn #1#2#3#4#5#6
-  {
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _ prop } {#2}
-      {
-        { \dim_eval:n { #3 - \l_coffin_left_corner_dim } }
-        { \dim_eval:n { #4 - \l_coffin_bottom_corner_dim } }
-        {#5} {#6}
-      }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \subsection{Resizing coffins}
-%
-% \begin{variable}{\l_coffin_scale_x_fp}
-% \begin{variable}{\l_coffin_scale_y_fp}
-%   Storage for the scaling factors in $x$ and $y$, respectively.
-%    \begin{macrocode}
-\fp_new:N \l_coffin_scale_x_fp
-\fp_new:N \l_coffin_scale_y_fp
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \begin{variable}{\l_coffin_scaled_total_height_dim}
-% \begin{variable}{\l_coffin_scaled_width_dim}
-%   When scaling, the values given have to be turned into absolute values.
-%    \begin{macrocode}
-\dim_new:N \l_coffin_scaled_total_height_dim
-\dim_new:N \l_coffin_scaled_width_dim
-%    \end{macrocode}
-% \end{variable}
-% \end{variable}
-%
-% \begin{macro}{\coffin_resize:Nnn, \coffin_resize:cnn}
-%   Resizing a coffin begins by setting up the user-friendly names for
-%   the dimensions of the coffin box. The new sizes are then turned into
-%   scale factor. This is the same operation as takes place for the
-%   underlying box, but that operation is grouped and so the same
-%   calculation is done here.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_resize:Nnn #1#2#3
-  {
-    \coffin_set_user_dimensions:N #1
-    \box_resize:Nnn #1 {#2} {#3}
-    \fp_set_from_dim:Nn \l_coffin_scale_x_fp {#2}
-    \fp_set_from_dim:Nn \l_coffin_internal_fp { \Width }
-    \fp_div:Nn \l_coffin_scale_x_fp { \l_coffin_internal_fp }
-    \fp_set_from_dim:Nn \l_coffin_scale_y_fp {#3}
-    \fp_set_from_dim:Nn \l_coffin_internal_fp { \TotalHeight }
-    \fp_div:Nn \l_coffin_scale_y_fp { \l_coffin_internal_fp }
-    \coffin_resize_common:Nnn #1 {#2} {#3}
-  }
-\cs_generate_variant:Nn \coffin_resize:Nnn { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_resize_common:Nnn}
-%   The poles and corners of the coffin are scaled to the appropriate
-%   places before actually resizing the underlying box.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_resize_common:Nnn #1#2#3
-  {
-    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-      { \coffin_scale_corner:Nnnn #1 {##1} ##2 }
-    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-      { \coffin_scale_pole:Nnnnnn #1 {##1} ##2 }
-%    \end{macrocode}
-%   Negative $x$-scaling values will place the poles in the wrong
-%   location: this is corrected here.
-%    \begin{macrocode}
-    \fp_compare:NNNT \l_coffin_scale_x_fp < \c_zero_fp
-      {
-        \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
-          { \coffin_x_shift_corner:Nnnn #1 {##1} ##2 }
-        \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
-          { \coffin_x_shift_pole:Nnnnnn #1 {##1} ##2 }
-      }
-    \coffin_end_user_dimensions:
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_scale:Nnn, \coffin_scale:cnn}
-%   For scaling, the opposite calculation is done to find the new
-%   dimensions for the coffin. Only the total height is needed, as this
-%   is the shift required for corners and poles. The scaling is done
-%   the \TeX{} way as this works properly with floating point values
-%   without needing to use the \texttt{fp} module.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_scale:Nnn #1#2#3
-  {
-    \box_scale:Nnn #1 {#2} {#3}
-    \coffin_set_user_dimensions:N #1
-    \fp_set:Nn \l_coffin_scale_x_fp {#2}
-    \fp_set:Nn \l_coffin_scale_y_fp {#3}
-    \fp_compare:NNNTF \l_coffin_scale_y_fp > \c_zero_fp
-      { \l_coffin_scaled_total_height_dim #3 \TotalHeight }
-      { \l_coffin_scaled_total_height_dim -#3 \TotalHeight }
-    \fp_compare:NNNTF \l_coffin_scale_x_fp > \c_zero_fp
-      { \l_coffin_scaled_width_dim -#2 \Width }
-      { \l_coffin_scaled_width_dim #2 \Width }
-    \coffin_resize_common:Nnn #1
-      { \l_coffin_scaled_width_dim } { \l_coffin_scaled_total_height_dim }
-  }
-\cs_generate_variant:Nn \coffin_scale:Nnn { c }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_scale_vector:nnNN}
-%   This functions scales a vector from the origin using the pre-set scale
-%   factors in $x$ and $y$. This is a much less complex operation
-%   than rotation, and as a result the code is a lot clearer.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_scale_vector:nnNN #1#2#3#4
-  {
-    \fp_set_from_dim:Nn \l_coffin_internal_fp {#1}
-    \fp_mul:Nn \l_coffin_internal_fp { \l_coffin_scale_x_fp }
-    \dim_set:Nn #3 { \fp_to_dim:N \l_coffin_internal_fp }
-    \fp_set_from_dim:Nn \l_coffin_internal_fp {#2}
-    \fp_mul:Nn \l_coffin_internal_fp { \l_coffin_scale_y_fp }
-    \dim_set:Nn #4 { \fp_to_dim:N \l_coffin_internal_fp }
-  }
-%    \end{macrocode}
-% \end{macro}
-%
-% \begin{macro}{\coffin_scale_corner:Nnnn}
-% \begin{macro}{\coffin_scale_pole:Nnnnnn}
-%   Scaling both corners and poles is a simple calculation using the
-%   preceding vector scaling.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_scale_corner:Nnnn #1#2#3#4
-  {
-    \coffin_scale_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } {#2}
-      { { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim } }
-  }
-\cs_new_protected:Npn \coffin_scale_pole:Nnnnnn #1#2#3#4#5#6
-  {
-    \coffin_scale_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
-    \coffin_set_pole:Nnx #1 {#2}
-      {
-        { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim }
-        {#5} {#6}
-      }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
-% \begin{macro}{\coffin_x_shift_corner:Nnnn}
-% \begin{macro}{\coffin_x_shift_pole:Nnnnnn}
-%   These functions correct for the $x$ displacement that takes
-%   place with a negative horizontal scaling.
-%    \begin{macrocode}
-\cs_new_protected:Npn \coffin_x_shift_corner:Nnnn #1#2#3#4
-  {
-    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } {#2}
-      {
-        { \dim_eval:n { #3 + \box_wd:N #1 } } {#4}
-    }
-  }
-\cs_new_protected:Npn \coffin_x_shift_pole:Nnnnnn #1#2#3#4#5#6
-  {
-    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } {#2}
-      {
-        { \dim_eval:n #3 + \box_wd:N #1 } {#4}
-        {#5} {#6}
-      }
-  }
-%    \end{macrocode}
-% \end{macro}
-% \end{macro}
-%
 % \subsection{Coffin diagnostics}
 %
-% \begin{variable}{\l_coffin_display_coffin}
-% \begin{variable}{\l_coffin_display_coord_coffin}
-% \begin{variable}{\l_coffin_display_pole_coffin}
+% \begin{variable}{\l_@@_display_coffin}
+% \begin{variable}{\l_@@_display_coord_coffin}
+% \begin{variable}{\l_@@_display_pole_coffin}
 %   Used for printing coffins with data structures attached.
 %    \begin{macrocode}
-\coffin_new:N \l_coffin_display_coffin
-\coffin_new:N \l_coffin_display_coord_coffin
-\coffin_new:N \l_coffin_display_pole_coffin
+\coffin_new:N \l_@@_display_coffin
+\coffin_new:N \l_@@_display_coord_coffin
+\coffin_new:N \l_@@_display_pole_coffin
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_display_handles_prop}
+% \begin{variable}{\l_@@_display_handles_prop}
 %   This property list is used to print coffin handles at suitable
 %   positions. The offsets are expressed as multiples of the basic offset
 %   value, which therefore acts as a scale-factor.
 %    \begin{macrocode}
-\prop_new:N \l_coffin_display_handles_prop
-\prop_put:Nnn \l_coffin_display_handles_prop { tl }
+\prop_new:N \l_@@_display_handles_prop
+\prop_put:Nnn \l_@@_display_handles_prop { tl }
   { { b } { r } { -1 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { thc }
+\prop_put:Nnn \l_@@_display_handles_prop { thc }
   { { b } { hc } { 0 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { tr }
+\prop_put:Nnn \l_@@_display_handles_prop { tr }
   { { b } { l } { 1 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { vcl }
+\prop_put:Nnn \l_@@_display_handles_prop { vcl }
   { { vc } { r } { -1 } { 0 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { vchc }
+\prop_put:Nnn \l_@@_display_handles_prop { vchc }
   { { vc } { hc } { 0 } { 0 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { vcr }
+\prop_put:Nnn \l_@@_display_handles_prop { vcr }
   { { vc } { l } { 1 } { 0 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { bl }
+\prop_put:Nnn \l_@@_display_handles_prop { bl }
   { { t } { r } { -1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { bhc }
+\prop_put:Nnn \l_@@_display_handles_prop { bhc }
   { { t } { hc } { 0 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { br }
+\prop_put:Nnn \l_@@_display_handles_prop { br }
   { { t } { l } { 1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Tl }
+\prop_put:Nnn \l_@@_display_handles_prop { Tl }
   { { t } { r } { -1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Thc }
+\prop_put:Nnn \l_@@_display_handles_prop { Thc }
   { { t } { hc } { 0 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Tr }
+\prop_put:Nnn \l_@@_display_handles_prop { Tr }
   { { t } { l } { 1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Hl }
+\prop_put:Nnn \l_@@_display_handles_prop { Hl }
   { { vc } { r } { -1 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Hhc }
+\prop_put:Nnn \l_@@_display_handles_prop { Hhc }
   { { vc } { hc } { 0 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Hr }
+\prop_put:Nnn \l_@@_display_handles_prop { Hr }
   { { vc } { l } { 1 } { 1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Bl }
+\prop_put:Nnn \l_@@_display_handles_prop { Bl }
   { { b } { r } { -1 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Bhc }
+\prop_put:Nnn \l_@@_display_handles_prop { Bhc }
   { { b } { hc } { 0 } { -1 } }
-\prop_put:Nnn \l_coffin_display_handles_prop { Br }
+\prop_put:Nnn \l_@@_display_handles_prop { Br }
   { { b } { l } { 1 } { -1 } }
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_display_offset_dim}
+% \begin{variable}{\l_@@_display_offset_dim}
 %   The standard offset for the label from the handle position when
 %   displaying handles.
 %    \begin{macrocode}
-\dim_new:N  \l_coffin_display_offset_dim
-\dim_set:Nn \l_coffin_display_offset_dim { 2 pt }
+\dim_new:N  \l_@@_display_offset_dim
+\dim_set:Nn \l_@@_display_offset_dim { 2 pt }
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_display_x_dim}
-% \begin{variable}{\l_coffin_display_y_dim}
+% \begin{variable}{\l_@@_display_x_dim}
+% \begin{variable}{\l_@@_display_y_dim}
 %   As the intersections of poles have to be calculated to find which
 %   ones to print, there is a need to avoid repetition. This is done
 %   by saving the intersection into two dedicated values.
 %    \begin{macrocode}
-\dim_new:N \l_coffin_display_x_dim
-\dim_new:N \l_coffin_display_y_dim
+\dim_new:N \l_@@_display_x_dim
+\dim_new:N \l_@@_display_y_dim
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_display_poles_prop}
+% \begin{variable}{\l_@@_display_poles_prop}
 %   A property list for printing poles: various things need to be deleted
 %   from this to get a \enquote{nice} output.
 %    \begin{macrocode}
-\prop_new:N \l_coffin_display_poles_prop
+\prop_new:N \l_@@_display_poles_prop
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_coffin_display_font_tl}
+% \begin{variable}{\l_@@_display_font_tl}
 %   Stores the settings used to print coffin data: this keeps things
 %   flexible.
 %    \begin{macrocode}
-\tl_new:N  \l_coffin_display_font_tl
+\tl_new:N  \l_@@_display_font_tl
 %<*initex>
-\tl_set:Nn \l_coffin_display_font_tl { } % TODO
+\tl_set:Nn \l_@@_display_font_tl { } % TODO
 %</initex>
 %<*package>
-\tl_set:Nn \l_coffin_display_font_tl { \sffamily \tiny }
+\tl_set:Nn \l_@@_display_font_tl { \sffamily \tiny }
 %</package>
 %    \end{macrocode}
 % \end{variable}
 %
 % \begin{macro}{\coffin_mark_handle:Nnnn, \coffin_mark_handle:cnnn}
-% \begin{macro}[aux]{\coffin_mark_handle_aux:nnnnNnn}
+% \begin{macro}[aux]{\@@_mark_handle_aux:nnnnNnn}
 %   Marking a single handle is relatively easy. The standard attachment
 %   function is used, meaning that there are two calculations for the
 %   location. However, this is likely to be okay given the load expected.
@@ -2014,7 +1553,7 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_mark_handle:Nnnn #1#2#3#4
   {
-    \hcoffin_set:Nn \l_coffin_display_pole_coffin
+    \hcoffin_set:Nn \l_@@_display_pole_coffin
       {
 %<*initex>
         \hbox:n { \tex_vrule:D width 1 pt height 1 pt \scan_stop: } % TODO
@@ -2025,8 +1564,8 @@
 %</package>
       }
     \coffin_attach_mark:NnnNnnnn #1 {#2} {#3}
-      \l_coffin_display_pole_coffin { hc } { vc } { 0 pt } { 0 pt }
-    \hcoffin_set:Nn \l_coffin_display_coord_coffin
+      \l_@@_display_pole_coffin { hc } { vc } { 0 pt } { 0 pt }
+    \hcoffin_set:Nn \l_@@_display_coord_coffin
       {
 %<*initex>
         % TODO
@@ -2034,37 +1573,37 @@
 %<*package>
         \color {#4}
 %</package>
-        \l_coffin_display_font_tl
+        \l_@@_display_font_tl
         ( \tl_to_str:n { #2 , #3 } )
       }
-    \prop_get:NnN \l_coffin_display_handles_prop
-      { #2 #3 } \l_coffin_internal_tl
-    \quark_if_no_value:NTF \l_coffin_internal_tl
+    \prop_get:NnN \l_@@_display_handles_prop
+      { #2 #3 } \l_@@_internal_tl
+    \quark_if_no_value:NTF \l_@@_internal_tl
       {
-        \prop_get:NnN \l_coffin_display_handles_prop
-          { #3 #2 } \l_coffin_internal_tl
-        \quark_if_no_value:NTF \l_coffin_internal_tl
+        \prop_get:NnN \l_@@_display_handles_prop
+          { #3 #2 } \l_@@_internal_tl
+        \quark_if_no_value:NTF \l_@@_internal_tl
           {
             \coffin_attach_mark:NnnNnnnn #1 {#2} {#3}
-              \l_coffin_display_coord_coffin { l } { vc }
+              \l_@@_display_coord_coffin { l } { vc }
                 { 1 pt } { 0 pt }
           }
           {
-            \exp_last_unbraced:No \coffin_mark_handle_aux:nnnnNnn
-              \l_coffin_internal_tl #1 {#2} {#3}
+            \exp_last_unbraced:No \@@_mark_handle_aux:nnnnNnn
+              \l_@@_internal_tl #1 {#2} {#3}
           }
       }
       {
-        \exp_last_unbraced:No \coffin_mark_handle_aux:nnnnNnn
-          \l_coffin_internal_tl #1 {#2} {#3}
+        \exp_last_unbraced:No \@@_mark_handle_aux:nnnnNnn
+          \l_@@_internal_tl #1 {#2} {#3}
       }
   }
-\cs_new_protected:Npn \coffin_mark_handle_aux:nnnnNnn #1#2#3#4#5#6#7
+\cs_new_protected:Npn \@@_mark_handle_aux:nnnnNnn #1#2#3#4#5#6#7
   {
     \coffin_attach_mark:NnnNnnnn #5 {#6} {#7}
-      \l_coffin_display_coord_coffin {#1} {#2}
-      { #3 \l_coffin_display_offset_dim }
-      { #4 \l_coffin_display_offset_dim }
+      \l_@@_display_coord_coffin {#1} {#2}
+      { #3 \l_@@_display_offset_dim }
+      { #4 \l_@@_display_offset_dim }
   }
 \cs_generate_variant:Nn \coffin_mark_handle:Nnnn { c }
 %    \end{macrocode}
@@ -2072,9 +1611,9 @@
 % \end{macro}
 %
 % \begin{macro}{\coffin_display_handles:Nn, \coffin_display_handles:cn}
-% \begin{macro}[aux]{\coffin_display_handles_aux:nnnnnn}
-% \begin{macro}[aux]{\coffin_display_handles_aux:nnnn}
-% \begin{macro}[aux]{\coffin_display_attach:Nnnnn}
+% \begin{macro}[aux]{\@@_display_handles_aux:nnnnnn}
+% \begin{macro}[aux]{\@@_display_handles_aux:nnnn}
+% \begin{macro}[aux]{\@@_display_attach:Nnnnn}
 %   Printing the poles starts by removing any duplicates, for which the
 %   \texttt{H} poles is used as the definitive version for the baseline
 %   and bottom. Two loops are then used to find the combinations of
@@ -2083,7 +1622,7 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_display_handles:Nn #1#2
   {
-    \hcoffin_set:Nn \l_coffin_display_pole_coffin
+    \hcoffin_set:Nn \l_@@_display_pole_coffin
       {
 %<*initex>
         \hbox:n { \tex_vrule:D width 1 pt height 1 pt \scan_stop: } % TODO
@@ -2093,22 +1632,22 @@
         \rule { 1 pt } { 1 pt }
 %</package>
       }
-    \prop_set_eq:Nc \l_coffin_display_poles_prop
-      { l_coffin_poles_ \int_value:w #1 _prop }
-    \coffin_get_pole:NnN #1 { H } \l_coffin_pole_a_tl
-    \coffin_get_pole:NnN #1 { T } \l_coffin_pole_b_tl
-    \tl_if_eq:NNT \l_coffin_pole_a_tl \l_coffin_pole_b_tl
-      { \prop_del:Nn \l_coffin_display_poles_prop { T } }
-    \coffin_get_pole:NnN #1 { B } \l_coffin_pole_b_tl
-    \tl_if_eq:NNT \l_coffin_pole_a_tl \l_coffin_pole_b_tl
-      { \prop_del:Nn \l_coffin_display_poles_prop { B } }
-    \coffin_set_eq:NN \l_coffin_display_coffin #1
-    \prop_map_inline:Nn \l_coffin_display_poles_prop
+    \prop_set_eq:Nc \l_@@_display_poles_prop
+      { l_@@_poles_ \__int_value:w #1 _prop }
+    \@@_get_pole:NnN #1 { H } \l_@@_pole_a_tl
+    \@@_get_pole:NnN #1 { T } \l_@@_pole_b_tl
+    \tl_if_eq:NNT \l_@@_pole_a_tl \l_@@_pole_b_tl
+      { \prop_remove:Nn \l_@@_display_poles_prop { T } }
+    \@@_get_pole:NnN #1 { B } \l_@@_pole_b_tl
+    \tl_if_eq:NNT \l_@@_pole_a_tl \l_@@_pole_b_tl
+      { \prop_remove:Nn \l_@@_display_poles_prop { B } }
+    \coffin_set_eq:NN \l_@@_display_coffin #1
+    \prop_map_inline:Nn \l_@@_display_poles_prop
       {
-        \prop_del:Nn \l_coffin_display_poles_prop {##1}
-        \coffin_display_handles_aux:nnnnnn {##1} ##2 {#2}
+        \prop_remove:Nn \l_@@_display_poles_prop {##1}
+        \@@_display_handles_aux:nnnnnn {##1} ##2 {#2}
       }
-    \box_use:N \l_coffin_display_coffin
+    \box_use:N \l_@@_display_coffin
   }
 %    \end{macrocode}
 %   For each pole there is a check for an intersection, which here does
@@ -2116,20 +1655,20 @@
 %   and used to align the pole coffin with the main coffin for output.
 %   The positions are recovered from the preset list if available.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_display_handles_aux:nnnnnn #1#2#3#4#5#6
+\cs_new_protected:Npn \@@_display_handles_aux:nnnnnn #1#2#3#4#5#6
   {
-    \prop_map_inline:Nn \l_coffin_display_poles_prop
+    \prop_map_inline:Nn \l_@@_display_poles_prop
       {
-        \bool_set_false:N \l_coffin_error_bool
-        \coffin_calculate_intersection:nnnnnnnn {#2} {#3} {#4} {#5} ##2
-        \bool_if:NF \l_coffin_error_bool
+        \bool_set_false:N \l_@@_error_bool
+        \@@_calculate_intersection:nnnnnnnn {#2} {#3} {#4} {#5} ##2
+        \bool_if:NF \l_@@_error_bool
           {
-            \dim_set:Nn \l_coffin_display_x_dim { \l_coffin_x_dim }
-            \dim_set:Nn \l_coffin_display_y_dim { \l_coffin_y_dim }
-            \coffin_display_attach:Nnnnn
-              \l_coffin_display_pole_coffin { hc } { vc }
+            \dim_set:Nn \l_@@_display_x_dim { \l_@@_x_dim }
+            \dim_set:Nn \l_@@_display_y_dim { \l_@@_y_dim }
+            \@@_display_attach:Nnnnn
+              \l_@@_display_pole_coffin { hc } { vc }
               { 0 pt } { 0 pt }
-            \hcoffin_set:Nn \l_coffin_display_coord_coffin
+            \hcoffin_set:Nn \l_@@_display_coord_coffin
               {
 %<*initex>
                 % TODO
@@ -2137,40 +1676,40 @@
 %<*package>
                 \color {#6}
 %</package>
-                \l_coffin_display_font_tl
+                \l_@@_display_font_tl
                 ( \tl_to_str:n { #1 , ##1 } )
               }
-            \prop_get:NnN \l_coffin_display_handles_prop
-              { #1 ##1 } \l_coffin_internal_tl
-            \quark_if_no_value:NTF \l_coffin_internal_tl
+            \prop_get:NnN \l_@@_display_handles_prop
+              { #1 ##1 } \l_@@_internal_tl
+            \quark_if_no_value:NTF \l_@@_internal_tl
               {
-                \prop_get:NnN \l_coffin_display_handles_prop
-                  { ##1 #1 } \l_coffin_internal_tl
-                \quark_if_no_value:NTF \l_coffin_internal_tl
+                \prop_get:NnN \l_@@_display_handles_prop
+                  { ##1 #1 } \l_@@_internal_tl
+                \quark_if_no_value:NTF \l_@@_internal_tl
                   {
-                    \coffin_display_attach:Nnnnn
-                      \l_coffin_display_coord_coffin { l } { vc }
+                    \@@_display_attach:Nnnnn
+                      \l_@@_display_coord_coffin { l } { vc }
                       { 1 pt } { 0 pt }
                   }
                   {
                     \exp_last_unbraced:No
-                      \coffin_display_handles_aux:nnnn
-                      \l_coffin_internal_tl
+                      \@@_display_handles_aux:nnnn
+                      \l_@@_internal_tl
                   }
               }
               {
-                \exp_last_unbraced:No \coffin_display_handles_aux:nnnn
-                  \l_coffin_internal_tl
+                \exp_last_unbraced:No \@@_display_handles_aux:nnnn
+                  \l_@@_internal_tl
               }
           }
       }
   }
-\cs_new_protected:Npn \coffin_display_handles_aux:nnnn #1#2#3#4
+\cs_new_protected:Npn \@@_display_handles_aux:nnnn #1#2#3#4
   {
-    \coffin_display_attach:Nnnnn
-      \l_coffin_display_coord_coffin {#1} {#2}
-      { #3 \l_coffin_display_offset_dim }
-      { #4 \l_coffin_display_offset_dim }
+    \@@_display_attach:Nnnnn
+      \l_@@_display_coord_coffin {#1} {#2}
+      { #3 \l_@@_display_offset_dim }
+      { #4 \l_@@_display_offset_dim }
   }
 \cs_generate_variant:Nn \coffin_display_handles:Nn { c }
 %    \end{macrocode}
@@ -2179,29 +1718,29 @@
 %   and stored for the display coffin the code simply uses it directly,
 %   with no calculation.
 %    \begin{macrocode}
-\cs_new_protected:Npn \coffin_display_attach:Nnnnn #1#2#3#4#5
+\cs_new_protected:Npn \@@_display_attach:Nnnnn #1#2#3#4#5
   {
-    \coffin_calculate_intersection:Nnn #1 {#2} {#3}
-    \dim_set:Nn \l_coffin_x_prime_dim { \l_coffin_x_dim }
-    \dim_set:Nn \l_coffin_y_prime_dim { \l_coffin_y_dim }
-    \dim_set:Nn \l_coffin_offset_x_dim
-      { \l_coffin_display_x_dim - \l_coffin_x_prime_dim + #4 }
-    \dim_set:Nn \l_coffin_offset_y_dim
-      { \l_coffin_display_y_dim - \l_coffin_y_prime_dim + #5 }
-    \hbox_set:Nn \l_coffin_aligned_coffin
+    \@@_calculate_intersection:Nnn #1 {#2} {#3}
+    \dim_set:Nn \l_@@_x_prime_dim { \l_@@_x_dim }
+    \dim_set:Nn \l_@@_y_prime_dim { \l_@@_y_dim }
+    \dim_set:Nn \l_@@_offset_x_dim
+      { \l_@@_display_x_dim - \l_@@_x_prime_dim + #4 }
+    \dim_set:Nn \l_@@_offset_y_dim
+      { \l_@@_display_y_dim - \l_@@_y_prime_dim + #5 }
+    \hbox_set:Nn \l_@@_aligned_coffin
       {
-        \box_use:N \l_coffin_display_coffin
-        \tex_kern:D -\box_wd:N \l_coffin_display_coffin
-        \tex_kern:D \l_coffin_offset_x_dim
-        \box_move_up:nn { \l_coffin_offset_y_dim } { \box_use:N #1 }
+        \box_use:N \l_@@_display_coffin
+        \tex_kern:D -\box_wd:N \l_@@_display_coffin
+        \tex_kern:D \l_@@_offset_x_dim
+        \box_move_up:nn { \l_@@_offset_y_dim } { \box_use:N #1 }
       }
-    \box_set_ht:Nn \l_coffin_aligned_coffin
-      { \box_ht:N \l_coffin_display_coffin }
-    \box_set_dp:Nn \l_coffin_aligned_coffin
-      { \box_dp:N \l_coffin_display_coffin }
-    \box_set_wd:Nn \l_coffin_aligned_coffin
-      { \box_wd:N \l_coffin_display_coffin }
-    \box_set_eq:NN \l_coffin_display_coffin \l_coffin_aligned_coffin
+    \box_set_ht:Nn \l_@@_aligned_coffin
+      { \box_ht:N \l_@@_display_coffin }
+    \box_set_dp:Nn \l_@@_aligned_coffin
+      { \box_dp:N \l_@@_display_coffin }
+    \box_set_wd:Nn \l_@@_aligned_coffin
+      { \box_wd:N \l_@@_display_coffin }
+    \box_set_eq:NN \l_@@_display_coffin \l_@@_aligned_coffin
   }
 %    \end{macrocode}
 % \end{macro}
@@ -2216,13 +1755,13 @@
 %    \begin{macrocode}
 \cs_new_protected:Npn \coffin_show_structure:N #1
   {
-    \coffin_if_exist:NT #1
+    \@@_if_exist:NT #1
       {
-        \msg_aux_show:Nnx #1 { coffins }
+        \__msg_show_variable:Nnn #1 { coffins }
           {
             \prop_map_function:cN
-              { l_coffin_poles_ \int_value:w #1 _prop }
-              \msg_aux_show_unbraced:nn
+              { l_@@_poles_ \__int_value:w #1 _prop }
+              \__msg_show_item_unbraced:nn
           }
       }
   }
@@ -2233,7 +1772,7 @@
 % \subsection{Messages}
 %
 %    \begin{macrocode}
-\msg_kernel_new:nnnn { coffins } { no-pole-intersection }
+\__msg_kernel_new:nnnn { kernel } { no-pole-intersection }
   { No~intersection~between~coffin~poles. }
   {
     \c_msg_coding_error_text_tl
@@ -2241,17 +1780,17 @@
     but~they~do~not~have~a~unique~meeting~point:~
     the~value~(0~pt,~0~pt)~will~be~used.
   }
-\msg_kernel_new:nnnn { coffins } { unknown-coffin }
+\__msg_kernel_new:nnnn { kernel } { unknown-coffin }
   { Unknown~coffin~'#1'. }
   { The~coffin~'#1'~was~never~defined. }
-\msg_kernel_new:nnnn { coffins } { unknown-coffin-pole }
+\__msg_kernel_new:nnnn { kernel } { unknown-coffin-pole }
   { Pole~'#1'~unknown~for~coffin~'#2'. }
   {
     \c_msg_coding_error_text_tl
     LaTeX~was~asked~to~find~a~typesetting~pole~for~a~coffin,~
     but~either~the~coffin~does~not~exist~or~the~pole~name~is~wrong.
   }
-\msg_kernel_new:nnn { coffins } { show }
+\__msg_kernel_new:nnn { kernel } { show-coffins }
   {
     Size~of~coffin~\token_to_str:N #1 : \\
     > ~ ht~=~\dim_use:N \box_ht:N #1 \\
-- 
cgit v1.2.3

