% The ebproof package - Formal proofs in the style of sequent calculus

%% ebproof.sty
%% Copyright 2017 Emmanuel Beffara <manu@beffara.org>

% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% of this license or (at your option) any later version.
% The latest version of this license is in
%   http://www.latex-project.org/lppl.txt
% and version 1.3 or later is part of all distributions of LaTeX
% version 2005/12/01 or later.

% This work has the LPPL maintenance status `maintained'.

% The Current Maintainer of this work is Emmanuel Beffara.

% This work consists of the files ebproof.sty and ebproof.tex.

\NeedsTeXFormat{LaTeX2e}
\RequirePackage{expl3}
\RequirePackage{xparse}
\ProvidesExplPackage{ebproof}{2017/05/17}{2.0}{EB's proof trees}


%% Parameters

%%% Declaration of the parameters

\keys_define:nn { ebproof } {

% general shape

center .bool_set:N = \l_ebproof_center_bool,

proof~style .choice: ,
proof~style / upwards .code:n = \bool_set_false:N \l_ebproof_updown_bool,
proof~style / downwards .code:n = \bool_set_true:N \l_ebproof_updown_bool,

% spacing

separation .dim_set:N = \l_ebproof_separation_dim,
rule~margin .dim_set:N = \l_ebproof_rule_margin_dim,

% shape of inference lines

rule~thickness .dim_set:N = \l_ebproof_rule_thickness_dim,
rule~separation .dim_set:N = \l_ebproof_rule_separation_dim,
rule~dash~length .dim_set:N = \l_ebproof_rule_dash_length_dim,
rule~dash~space .dim_set:N = \l_ebproof_rule_dash_space_dim,
rule~code .tl_set:N = \l_ebproof_rule_code_tl,

rule~style .choice:,

% templates

template .tl_set:N = \l_ebproof_template_tl,
left~template .tl_set:N = \l_ebproof_left_template_tl,
right~template .tl_set:N = \l_ebproof_right_template_tl,

% labels

left~label .tl_set:N = \l_ebproof_left_label_tl,
right~label .tl_set:N = \l_ebproof_right_label_tl,
left~label~template .tl_set:N = \l_ebproof_left_label_template_tl,
right~label~template .tl_set:N = \l_ebproof_right_label_template_tl,
label~separation .dim_set:N = \l_ebproof_label_separation_dim,
label~axis .dim_set:N = \l_ebproof_label_axis_dim,

}

%%% Rule styles

\NewDocumentCommand \ebproofnewrulestyle { mm } {
  \keys_define:nn { ebproof } {
    rule~style / #1 .meta:nn = { ebproof } { #2 }
  }
}

\ebproofnewrulestyle { simple } {
  rule~code = { \tex_hrule:D height \l_ebproof_rule_thickness_dim }
}

\ebproofnewrulestyle { no~rule } {
  rule~code =
}

\ebproofnewrulestyle { double } {
  rule~code = {
    \tex_hrule:D height \l_ebproof_rule_thickness_dim
    \skip_vertical:N \l_ebproof_rule_separation_dim
    \tex_hrule:D height \l_ebproof_rule_thickness_dim
  }
}

\ebproofnewrulestyle { dashed } {
  rule~code = {
    \hbox_to_wd:nn { \tex_hsize:D } {
      \dim_set:Nn \l_tmpa_dim { \l_ebproof_rule_dash_space_dim / 2 }
      \skip_horizontal:n { -\l_tmpa_dim }
      \tex_cleaders:D \hbox:n {
        \skip_horizontal:N \l_tmpa_dim
        \tex_vrule:D
          height \l_ebproof_rule_thickness_dim
          width \l_ebproof_rule_dash_length_dim
        \skip_horizontal:N \l_tmpa_dim
      }\tex_hfill:D
      \skip_horizontal:n { -\l_tmpa_dim }
    }
  }
}

%%% Default values

\keys_set:nn { ebproof } {
  center = true,
  proof~style = upwards,
  separation = 1.5em,
  rule~margin = .7ex,
  rule~thickness = .4pt,
  rule~separation = 2pt,
  rule~dash~length = .2em,
  rule~dash~space = .3em,
  rule~style = simple,
  template = $\inserttext$,
  left~template = $\inserttext\mathrel{}$,
  right~template = $\mathrel{}\inserttext$,
  left~label = ,
  right~label = ,
  left~label~template = \inserttext,
  right~label~template = \inserttext,
  label~separation = 0.5em,
  label~axis = 0.5ex
}

%%% Defining style macros

\NewDocumentCommand \ebproofnewstyle { mm } {
  \keys_define:nn { ebproof } { #1 .meta:n = { #2 } }
}


%% Proof trees

% Proof trees are represented as a data structure that consists of a box and a
% set of marks, which are vertical positions in the box (as distances from the
% left edge). Arbitrary marks can be defined, the folowing are used for
% alignment:
% - left :  the left of the conclusion
% - right : the right of the conclusion
% - axis :  the vertical axis of the conclusion


%%% Registers

% TeX does not actually provide data structures, so we have to encode things.
% We provide an allocator for "registers" holding boxes with attributes. Such
% a register consists in a box register and a property list for marks, which
% maps mark names to values as explicit dimensions with units.

% Create a new register.

\cs_new:Nn \ebproof_new:N {
  \box_new:N #1
  \prop_new:c { l_ebproof_marks_ \__int_value:w #1 _prop }
}

% Clear a register.

\cs_new:Nn \ebproof_clear:N {
  \hbox_set:Nn #1 {}
  % Using \box_clear:N instead would not work because trying to push this box
  % on the stack would not actually append any box.
  \prop_clear:c { l_ebproof_marks_ \__int_value:w #1 _prop }
  \ebproof_set_mark:Nnn #1 { left } { 0pt }
  \ebproof_set_mark:Nnn #1 { right } { 0pt }
  \ebproof_set_mark:Nnn #1 { axis } { 0pt }
}


%%% Mark operations

% Set the value of a mark. The third argument is a dimension expression.

\dim_new:N \l_ebproof_transit_dim

\cs_new:Nn \ebproof_set_mark:Nnn {
  \dim_set:Nn \l_ebproof_transit_dim { #3 }
  \prop_put:cnV { l_ebproof_marks_ \__int_value:w #1 _prop } { #2 }
    \l_ebproof_transit_dim
}

% Get the value of a mark. This is expandable and can be used in expressions.

\cs_new:Nn \ebproof_mark:Nn {
  \prop_item:cn { l_ebproof_marks_ \__int_value:w #1 _prop } { #2 }
}

% Shift the marks by a specified amount, without modifying the box.

\cs_new:Nn \ebproof_shift_x:Nn {
  \prop_map_inline:cn { l_ebproof_marks_ \__int_value:w #1 _prop } {
    \ebproof_set_mark:Nnn #1 { ##1 } { ##2 + #2 }
  }
}

% Move the left and right marks of the first tree so that they are at least as
% far from the axis as they are in the second tree. For instance if the marks
% are set as
%    1:      L---A-------R
%    2:  L-------A---R
% then the marks of the first tree are then set as
%    1:  L-------A-------R
% The contents of the tree are unchanged.

\cs_new:Nn \ebproof_enlarge_conclusion:NN {
  \dim_set:Nn \l_tmpa_dim { \ebproof_mark:Nn #1 {axis}
    + \ebproof_mark:Nn #2 {left} - \ebproof_mark:Nn #2 {axis} }
  \dim_compare:nNnT { \l_tmpa_dim } < { \ebproof_mark:Nn #1 {left} } {
    \ebproof_set_mark:Nnn #1 {left} { \l_tmpa_dim } }
  \dim_set:Nn \l_tmpa_dim { \ebproof_mark:Nn #1 {axis}
    + \ebproof_mark:Nn #2 {right} - \ebproof_mark:Nn #2 {axis} }
  \dim_compare:nNnT { \l_tmpa_dim } > { \ebproof_mark:Nn #1 {right} } {
    \ebproof_set_mark:Nnn #1 {right} { \l_tmpa_dim } }
}


%%% Building blocks

% Make a tree with explicit material in horizontal mode. Set the left and
% right marks to extremal positions and set the axis in the middle.

\cs_new:Nn \ebproof_make_simple:Nn {
  \hbox_set:Nn #1 { #2 }
  \ebproof_set_mark:Nnn #1 { left } { 0pt }
  \ebproof_set_mark:Nnn #1 { axis } { \box_wd:N #1 / 2 }
  \ebproof_set_mark:Nnn #1 { right } { \box_wd:N #1 }
}

% Make a tree with explicit material in horizontal mode, split in two parts.
% Set the left and right marks to extremal positions and set the axis between
% the two parts.

\cs_new:Nn \ebproof_make_split:Nnn {
  \ebproof_set_mark:Nnn #1 { left } { 0pt }
  \hbox_set:Nn #1 { #2 }
  \ebproof_set_mark:Nnn #1 { axis } { \box_wd:N #1 }
  \hbox_set:Nn #1 { \hbox_unpack:N #1 #3 }
  \ebproof_set_mark:Nnn #1 { right } { \box_wd:N #1 }
}

% Make a tree with explicit material in vertical mode, using an explicit width
% and axis.

\cs_new:Nn \ebproof_make_vertical:Nnnn {
  \ebproof_set_mark:Nnn #1 { left } { 0pt }
  \ebproof_set_mark:Nnn #1 { axis } { #2 }
  \ebproof_set_mark:Nnn #1 { right } { #3 }
  \vbox_set:Nn #1 {
    \dim_set:Nn \tex_hsize:D { \ebproof_mark:Nn #1 {right} }
    #4
  }
  \box_set_wd:Nn #1 { \ebproof_mark:Nn #1 {right} }
}

%%% Assembling boxes

% Extend a tree box. The marks are shifted so that alignment is preserved. The
% arguments are dimensions for the left, top, right and bottom sides
% respectively.

\cs_new:Nn \ebproof_extend:Nnnnn {
  \dim_compare:nNnF { #2 } = { 0pt } {
    \hbox_set:Nn #1 {
      \skip_horizontal:n { #2 }
      \box_use:N #1
    }
    \ebproof_shift_x:Nn #1 { #2 }
  }
  \box_set_ht:Nn #1 { \box_ht:N #1 + #3 }
  \box_set_wd:Nn #1 { \box_wd:N #1 + #4 }
  \box_set_dp:Nn #1 { \box_dp:N #1 + #5 }
}

% Append the contents of the second tree to the first one on the right, with
% matching baselines. The marks of both trees are preserved. The middle
% argument specifies the space to insert between boxes.

\cs_new:Nn \ebproof_append_right:NnN {
  \hbox_set:Nn #1 {
    \box_use:N #1
    \dim_compare:nNnF { #2 } = { 0pt } { \skip_horizontal:n { #2 } }
    \box_use:N #3
  }
}

% Append the contents of the second tree to the first one on the left, with
% matching baselines. The marks of the first tree are shifted accordingly. The
% middle argument specifies the space to insert between boxes.

\cs_new:Nn \ebproof_append_left:NnN {
  \ebproof_shift_x:Nn #1 { \box_wd:N #3 + #2 }
  \hbox_set:Nn #1 {
    \box_use:N #3
    \dim_compare:nNnF { #2 } = { 0pt } { \skip_horizontal:n { #2 } }
    \box_use:N #1
  }
}

% Shift of two trees to the right so that the axes match. The marks of the one
% that is shifted are updated accordingly.

\cs_new:Nn \ebproof_align:NN {
  \dim_set:Nn \l_tmpa_dim
    { \ebproof_mark:Nn #2 {axis} - \ebproof_mark:Nn #1 {axis} }
  \dim_compare:nNnTF \l_tmpa_dim < { 0pt } {
    \ebproof_extend:Nnnnn #2 { -\l_tmpa_dim } { 0pt } { 0pt } { 0pt }
  } {
    \ebproof_extend:Nnnnn #1 { \l_tmpa_dim } { 0pt } { 0pt } { 0pt }
  }
}

% Append the contents of the second tree above the first one, with matching
% axes. The marks of the first tree are preserved.

\cs_new:Nn \ebproof_append_above:NN {
  \ebproof_align:NN #1 #2
  \vbox_set:Nn #1 {
    \box_use:N #2
    \tex_prevdepth:D -1000pt
    \box_use:N #1
  }
}

% Append the contents of the second tree below the first one, with matching
% axes. The marks of the first tree are preserved.

\cs_new:Nn \ebproof_append_below:NN {
  \ebproof_align:NN #1 #2
  \vbox_set_top:Nn #1 {
    \box_use:N #1
    \tex_prevdepth:D -1000pt
    \box_use:N #2
  }
}

% Shift the material in a tree vertically so that the height and depth are
% equal (like TeX's \vcenter but around the baseline).

\cs_new:Nn \ebproof_vcenter:N {
  \dim_set:Nn \l_tmpa_dim { ( \box_ht:N #1 - \box_dp:N #1 ) / 2 }
  \box_set_eq:NN \l_tmpa_box #1
  \hbox_set:Nn #1
    { \box_move_down:nn { \l_tmpa_dim } { \box_use:N \l_tmpa_box } }
}


%% Making inferences
%
% The following commands use the parameters defined at the beginning of the
% package for actually building proof trees using the commands defined above.

% Append the contents of the second tree above or below the first one,
% depending on current settings. Axes are aligned and the marks of the first
% tree are preserved.

\cs_new:Nn \ebproof_append_vertical:NN {
  \bool_if:NTF \l_ebproof_updown_bool
    { \ebproof_append_below:NN #1 #2 }
    { \ebproof_append_above:NN #1 #2 }
}

% Make a box containing an inference rule with labels, using the current
% settings. The width and axis position are taken as those of the conclusion
% of another tree box. The third argument is used as a temporary register for
% building labels.

\cs_new:Nn \ebproof_make_rule_for:NNN {

  % Build the rule.

  \ebproof_make_vertical:Nnnn #1
    { \ebproof_mark:Nn #2 {axis} - \ebproof_mark:Nn #2 {left} }
    { \ebproof_mark:Nn #2 {right} - \ebproof_mark:Nn #2 {left} }
    {
      \skip_vertical:N \l_ebproof_rule_margin_dim
      \tl_if_empty:NF { \l_ebproof_rule_code_tl } {
        \tl_use:N \l_ebproof_rule_code_tl
        \skip_vertical:N \l_ebproof_rule_margin_dim
      }
    }
  \ebproof_vcenter:N #1

  % Append the left label

  \tl_if_blank:VF \l_ebproof_left_label_tl {
    \ebproof_make_simple:Nn #3 {
      \box_move_down:nn { \l_ebproof_label_axis_dim } { \hbox:n {
        \cs_set_eq:NN \inserttext \l_ebproof_left_label_tl
        \tl_use:N \l_ebproof_left_label_template_tl
      } }
    }
    \box_set_ht:Nn #3 { 0pt }
    \box_set_dp:Nn #3 { 0pt }
    \ebproof_append_left:NnN
      \l_ebproof_c_box \l_ebproof_label_separation_dim \l_ebproof_d_box
  }

  % Append the right label

  \tl_if_blank:VF \l_ebproof_right_label_tl {
    \ebproof_make_simple:Nn #3 {
      \box_move_down:nn { \l_ebproof_label_axis_dim } { \hbox:n {
        \cs_set_eq:NN \inserttext \l_ebproof_right_label_tl
        \tl_use:N \l_ebproof_right_label_template_tl
      } }
    }
    \box_set_ht:Nn #3 { 0pt }
    \box_set_dp:Nn #3 { 0pt }
    \ebproof_append_right:NnN
      \l_ebproof_c_box \l_ebproof_label_separation_dim \l_ebproof_d_box
  }

}


%% Stack-based interface

%%% The stack

% Logically, box structures are stored on a stack. However, TeX does not
% provide data structures for that and the grouping mechanism is not flexible
% enough, so we encode them using what we actually have. A stack for boxes is
% implemented using a global hbox |\g_ebproof_stack_box| that contains all the
% boxes successively. A sequence |\g_ebproof_stack_seq| is used to store the
% dimensions property lists textually. We maintain a counter
% |\g_ebproof_level_int| with the number of elements on the stack, for
% consistency checks.

\int_new:N \g_ebproof_level_int
\box_new:N \g_ebproof_stack_box
\seq_new:N \g_ebproof_stack_seq

% Clear the stack.

\cs_new:Nn \ebproof_clear_stack: {
  \int_gset:Nn \g_ebproof_level_int { 0 }
  \hbox_gset:Nn \g_ebproof_stack_box { }
  \seq_gclear:N \g_ebproof_stack_seq
}

% Push the contents of a register on the stack.

\cs_new:Nn \ebproof_push:N {
  \int_gincr:N \g_ebproof_level_int
  \hbox_gset:Nn \g_ebproof_stack_box
    { \hbox_unpack:N \g_ebproof_stack_box \box_use:N #1 }
  \seq_gput_left:Nv \g_ebproof_stack_seq
    { l_ebproof_marks_ \__int_value:w #1 _prop }
}

% Pop the value from the top of the stack into a register.

\cs_new:Nn \ebproof_pop:N {
  \int_compare:nNnTF { \g_ebproof_level_int } > { 0 } {
    \int_gdecr:N \g_ebproof_level_int
    \hbox_gset:Nn \g_ebproof_stack_box {
      \hbox_unpack:N \g_ebproof_stack_box
      \box_gset_to_last:N \g_tmpa_box
    }
    \box_set_eq_clear:NN #1 \g_tmpa_box
    \seq_gpop_left:NN \g_ebproof_stack_seq \l_tmpa_tl
    \tl_set_eq:cN { l_ebproof_marks_ \__int_value:w #1 _prop } \l_tmpa_tl
  } {
    \PackageError{ebproof}{Missing~premiss~in~a~proof~tree}{}
    \ebproof_clear:N #1
  }
}

%%% Assembling trees

\ebproof_new:N \l_ebproof_a_box
\ebproof_new:N \l_ebproof_b_box
\ebproof_new:N \l_ebproof_c_box
\ebproof_new:N \l_ebproof_d_box

% Join horizontally a number of elements at the top of the stack. If several
% trees are joined, use the left mark of the left tree, the right mark of the
% right tree and set the axis in the middle of these marks.

\cs_new:Nn \ebproof_join_horizontal:n {
  \int_case:nnF { #1 } {
  { 0 } {
    \group_begin:
    \ebproof_clear:N \l_ebproof_a_box
    \ebproof_push:N \l_ebproof_a_box
    \group_end:
  }
  { 1 } { }
  } {
    \group_begin:
    \ebproof_pop:N \l_ebproof_a_box
    \prg_replicate:nn { #1 - 1 } {
      \ebproof_pop:N \l_ebproof_b_box
      \ebproof_append_left:NnN
        \l_ebproof_a_box \l_ebproof_separation_dim \l_ebproof_b_box
    }
    \ebproof_set_mark:Nnn \l_ebproof_a_box { left }
      { \ebproof_mark:Nn \l_ebproof_b_box { left } }
    \ebproof_set_mark:Nnn \l_ebproof_a_box { axis }
      { ( \ebproof_mark:Nn \l_ebproof_a_box { left }
        + \ebproof_mark:Nn \l_ebproof_a_box { right } ) / 2 }
    \ebproof_push:N \l_ebproof_a_box
    \group_end:
  }
}

% Join vertically the two elements at the top of the stack, with a horizontal
% rule of the appropriate size.

\cs_new:Nn \ebproof_join_vertical: {
  \group_begin:
  \ebproof_pop:N \l_ebproof_a_box
  \ebproof_pop:N \l_ebproof_b_box
  \ebproof_enlarge_conclusion:NN \l_ebproof_b_box \l_ebproof_a_box
  \ebproof_make_rule_for:NNN \l_ebproof_c_box \l_ebproof_b_box
    \l_ebproof_d_box
  \ebproof_append_vertical:NN \l_ebproof_a_box \l_ebproof_c_box
  \ebproof_append_vertical:NN \l_ebproof_a_box \l_ebproof_b_box
  \ebproof_push:N \l_ebproof_a_box
  \group_end:
}

%%% High-level commands

% Push a box with default formatting, using explicit alignment if the code
% contains a |&| character

\cs_new:Npn \ebproof_statement_parse:w #1&#2&#3\ebproof_statement_stop: {
  \tl_if_empty:nTF { #3 } {
    \ebproof_make_simple:Nn \l_ebproof_a_box
      { \cs_set:Npn \inserttext { #1 } \tl_use:N \l_ebproof_template_tl }
  } {
    \ebproof_make_split:Nnn \l_ebproof_a_box
      { \cs_set:Npn \inserttext { #1 } \tl_use:N \l_ebproof_left_template_tl }
      { \cs_set:Npn \inserttext { #2 } \tl_use:N \l_ebproof_right_template_tl }
  }
  \ebproof_push:N \l_ebproof_a_box
}

\cs_new:Nn \ebproof_push_statement:n {
  \ebproof_statement_parse:w #1&& \ebproof_statement_stop:
}


%% Document interface

%%% Functions to define statements

% The |\g_ebproof_stack_seq| variable contains the list of all defined
% statements. For each statement |X|, there is a document command |\ebproofX|
% and the alias |\X| is defined when entering a |prooftree| environment.

\seq_new:N \g_ebproof_statements_seq

% Install the aliases for statements, saving the original value of the control
% sequences.

\cs_new:Nn \ebproof_setup_statements: {
  \seq_map_inline:Nn \g_ebproof_statements_seq {
    \cs_set_eq:cc { ebproof_saved_ ##1 } { ##1 }
    \cs_set_eq:cc { ##1 } { ebproof ##1 }
  }
}

% Restore the saved meanings of the control sequences. This is useful when
% interpreting user-provided code in statement arguments. The meanings are
% automatically restored when leaving a |prooftree| environment because of
% grouping.

\cs_new:Nn \ebproof_restore_statements: {
  \seq_map_inline:Nn \g_ebproof_statements_seq {
    \cs_set_eq:cc { ##1 } { ebproof_saved_ ##1 }
  }
}

% Define a new statement. The first argument is the name, the second one is an
% argument specifier as used by |xparse| and the third one is the body of the
% command.

\cs_new:Nn \ebproof_new_statement:nnn {
  \exp_args:Nc \NewDocumentCommand { ebproof#1 }{ #2 } { #3 }
  \seq_put_right:Nn \g_ebproof_statements_seq { #1 }
}

% Define a deprecated statement. The syntax is the same as above except that
% an extra argument in third position indicates what should be used instead.
% The effect is the same except that a warning message is issued the first
% time the statement is used.

\cs_new:Nn \ebproof_new_deprecated_statement:nnnn {
  \cs_new:cpn { ebproof_#1_warning: } {
    \PackageWarning { ebproof } { \token_to_str:c{#1}~is~deprecated,~#3 }
    \cs_gset:cn { ebproof_#1_warning: } { }
  }
  \ebproof_new_statement:nnn { #1 } { #2 }
    { \use:c { ebproof_#1_warning: } #4 }
}


%%% Basic commands

\ebproof_new_statement:nnn { set } { m } {
  \keys_set:nn { ebproof } { #1 }
}

\ebproof_new_statement:nnn { hypo } { O{} m } {
  \group_begin:
  \ebproof_restore_statements:
  \keys_set:nn { ebproof } { #1 }
  \ebproof_push_statement:n { #2 }
  \group_end:
}

\ebproof_new_statement:nnn { infer } { O{} m O{} m } {
  \group_begin:
  \ebproof_restore_statements:
  \keys_set_known:nnN { ebproof / rule~style } { #1 } \l_tmpa_tl
  \keys_set:nV { ebproof } \l_tmpa_tl
  \tl_set:Nn \l_ebproof_right_label_tl { #3 }
  \ebproof_join_horizontal:n { #2 }
  \ebproof_push_statement:n { #4 }
  \ebproof_join_vertical:
  \group_end:
}

\ebproof_new_statement:nnn { ellipsis } { m m } {
  \group_begin:
  \ebproof_restore_statements:
  \tl_clear:N \l_ebproof_rule_code_tl
  \ebproof_make_split:Nnn \l_ebproof_a_box { } {
    \vbox_set:Nn \l_tmpa_box {
      \skip_vertical:n { 1.2ex }
      \hbox:n { \tex_ignorespaces:D #1 }
      \skip_vertical:n { 1.2ex }
    }
    \vbox_to_ht:nn { \box_ht:N \l_tmpa_box } {
      \tex_xleaders:D \vbox_to_ht:nn { .8ex }
        { \tex_vss:D \hbox:n { . } \tex_vss:D }
      \tex_vfill:D
    }
    \hbox_overlap_right:n { ~ \box_use:N \l_tmpa_box }
  }
  \ebproof_push:N \l_ebproof_a_box
  \ebproof_join_vertical:
  \ebproof_push_statement:n {#2}
  \ebproof_join_vertical:
  \group_end:
}


%%% Modifying trees

% Rewrite the box at the top of the stack while preserving its dimensions an
% marks. The code is typeset in horizontal mode, with control sequences to
% access the original box and its marks:
%  - \treebox is a box register with the original material
%  - \treemark{NAME} provides the value of a given mark

\ebproof_new_statement:nnn { rewrite } { m } {
  \group_begin:
  \ebproof_restore_statements:
  \ebproof_pop:N \l_ebproof_a_box
  \box_set_eq:NN \l_tmpa_box \l_ebproof_a_box
  \hbox_set:Nn \l_tmpb_box {
    \cs_set_eq:NN \treebox \l_tmpa_box
    \cs_set:Npn \treemark { \ebproof_mark:Nn \l_ebproof_a_box }
    { #1 }
  }
  \box_set_wd:Nn \l_tmpb_box { \box_wd:N \l_ebproof_a_box }
  \box_set_ht:Nn \l_tmpb_box { \box_ht:N \l_ebproof_a_box }
  \box_set_dp:Nn \l_tmpb_box { \box_dp:N \l_ebproof_a_box }
  \box_set_eq:NN \l_ebproof_a_box \l_tmpb_box
  \ebproof_push:N \l_ebproof_a_box
  \group_end:
}

% Insert |\left| and |\right| delimiters without changing the alignment

\ebproof_new_statement:nnn { delims } { m m } {
  \group_begin:
  \ebproof_restore_statements:
  \ebproof_pop:N \l_ebproof_a_box
  \hbox_set:Nn \l_tmpa_box
    { $ \tex_vcenter:D { \box_use:N \l_ebproof_a_box } $ }
  \dim_set:Nn \l_tmpa_dim
    { \box_ht:N \l_tmpa_box - \box_ht:N \l_ebproof_a_box }
  \hbox_set:Nn \l_ebproof_a_box {
    $ #1 \tex_vrule:D
      height \box_ht:N \l_tmpa_box depth \box_dp:N \l_tmpa_box width 0pt
    \tex_right:D . $
  }
  \ebproof_shift_x:Nn \l_ebproof_a_box { \box_wd:N \l_ebproof_a_box }
  \hbox_set:Nn \l_ebproof_a_box {
    \hbox_unpack:N \l_ebproof_a_box
    $ \tex_left:D . \box_use:N \l_tmpa_box #2 $
  }
  \hbox_set:Nn \l_ebproof_a_box
    { \box_move_down:nn { \l_tmpa_dim } { \box_use:N \l_ebproof_a_box } }
  \ebproof_push:N \l_ebproof_a_box
  \group_end:
}


%%% Deprecated statements

% These statements were defined in versions 1.x of the package, they are
% preserved for temporary upwards compatibility and will be removed in a
% future version.

\ebproof_new_deprecated_statement:nnnn { Alter } { m }
  { use~\token_to_str:c{rewrite}~instead } { \ebproofrewrite{ #1 \box\treebox } }
\ebproof_new_deprecated_statement:nnnn { Delims } { }
  { use~\token_to_str:c{delims}~instead } { \ebproofdelims }
\ebproof_new_deprecated_statement:nnnn { Ellipsis } { }
  { use~\token_to_str:c{ellipsis}~instead } { \ebproofellipsis }
\ebproof_new_deprecated_statement:nnnn { Hypo } { }
  { use~\token_to_str:c{hypo}~instead } { \ebproofhypo }
\ebproof_new_deprecated_statement:nnnn { Infer } { }
  { use~\token_to_str:c{infer}~instead } { \ebproofinfer }


%%% Environment interface

\ebproof_clear_stack:

\tl_new:N \l_ebproof_start_level_tl

\NewDocumentEnvironment { prooftree } { s O{} } {
  \keys_set_known:nnN { ebproof / proof~style } { #2 } \l_tmpa_tl
  \keys_set:nV { ebproof } \l_tmpa_tl
  \tl_set:Nx \l_ebproof_start_level_tl { \int_use:N \g_ebproof_level_int }
  \vbox_set:Nw \l_tmpa_box
  \ebproof_setup_statements:
} {
  \vbox_set_end:
  \ebproof_pop:N \l_ebproof_a_box
  \int_compare:nNnF { \g_ebproof_level_int } = { \tl_use:N \l_ebproof_start_level_tl } {
    \PackageError{ebproof}{Malformed~proof~tree}{
      Some~hypotheses~were~declared~but~not~used~in~this~tree.}
  }
  \IfBooleanTF { #1 } {
    \[ \box_use:N \l_ebproof_a_box \]
    \ignorespacesafterend
  } {
    \hbox_unpack:N \c_empty_box
    \bool_if:NTF \l_ebproof_center_bool {
      \hbox:n { $ \tex_vcenter:D { \box_use:N \l_ebproof_a_box } $ }
    } {
      \box_use:N \l_ebproof_a_box
    }
  }
}

% A trick for the starred version:
\cs_new:cpn { prooftree* } { \prooftree* }
\cs_new:cpn { endprooftree* } { \endprooftree }
