Multidominance tree with forest

Question

I am curious as to whether a multidominance tree such as the one below may be drawn with \Forest:

I have found evidence of this using qtree (Adding trees or terminal words to multi-dominance structures), but I would like to be able to do this in Forest if possible.

I have ascertained how to get a syntactic terminal higher in the tree to attach to a lower constituent such as the following:

\documentclass{article}
\usepackage[linguistics]{forest}
\forestset{
  nice nodes/.style={
    for tree={
      inner sep=0pt,
      fit=band,
    },
  },
  default preamble=nice nodes,
}
\begin{document}
\begin{forest}
sn edges
[L,name=L 
    [,name=D] 
        [ 
            [$\beta$] 
            [K 
                [$\gamma$,name=G] 
                [$\alpha$]
            ]
        ]
]
\begin{pgfinterruptboundingbox}
\draw[-,looseness=1] (G) to [out=west,in=south] (D);
\end{pgfinterruptboundingbox}
\end{forest}
\end{document}

... which gives the following:

However, these trees are clearly very different. I am fairly new to LaTeX, so I'm unsure even where to begin as far as trying this out.

Answer 1

I don't think anyone has spent any time to figure out a way to make generalized multidominance structures. So they're always going to require some sort of manual intervention, unless they are very restricted, as in the examples of phonological multidominance described here. But forest does make things a bit easier to do, since it makes every node in the tree a TikZ node, and so connecting arbitrary bits together isn't that hard. Here's an example of a typical multidominance structure from the coordination literature. I've chosen to use straight line connections between the nodes, but that can be adjusted using curves as you prefer.

The main trick here is that the multidominant node(s) ideally should be connected to the tree itself (in this case I've connected it to the \& node) because you can't embed a tree inside a tree. So all the nodes you want to connect have to be part of the same tree if possible.

\documentclass{article}
\usepackage[linguistics]{forest}
\newcommand*\1{$'$}
\begin{document}
\begin{forest}
[\&P 
    [TP [DP\\Sam ] [T\1 [T ] [VP,name=VP1 [V\\caught ] [DP,phantom] ]]]
    [\&\1
        [\&\\and, [DP,no edge,l=1.25in,name=shared [D\\a ][NP\\fish ]]]
        [TP [DP\\Alex ] [T\1 [T] [VP,name=VP2 [V\\cooked ] ][DP,phantom ] ]]
    ]
]
\draw (VP1.south) -- (shared.north);
\draw (VP2.south) -- (shared.north);
\end{forest}
\end{document}

For curved lines, the idea is the same, just use the to[...] syntax:

\documentclass{article}
\usepackage[linguistics]{forest}
\newcommand*\1{$'$}
\begin{document}
\begin{forest}
[TP,name=TP [DP,phantom] 
    [T\1 [T [DP\\Alex,name=shared,l=.5in,no edge  ][XP,phantom]]
        [VP,name=VP [DP,phantom] [V\1  [V\\smokes ]  ]]]]
\draw (shared.north) to[out=80] (TP.south);
\draw (shared.north) to[out=-40] (VP.south);
\end{forest}
\end{document}

Adapting cfr's code to something that is a bit more flexible, we can define a multidom style which takes 6 arguments:

multidom={<x-shift>}{<y-shift}{<out1>}{<node1>}{<out2>}{<node2>}

This makes a node of this style shifted in the x and y directions, and sets the out-locations of the lines connecting the node to its parent nodes. This style reduces the number of hacks needed in the previous examples. In particular, the multidominated node itself is actually a daughter of one of its parents rather than being attached to some arbitrary node in the tree. You still need to add a phantom node in the position of the second parent, so that the parent's branch angle looks right.

Here's a full example:

\documentclass{article}
\usepackage[linguistics]{forest}
\forestset{multidom/.style n args=6{%
    no edge,
    before drawing tree={%
      for tree={x'+=#1,y'+=#2},
      tikz+={%
        \draw [-] (.#3) to [out=#3,looseness=.5] (#4.south);
        \draw [-] (.#5) to [out=#5,looseness=.5] (#6.south);
      }
    },
  }
}
\newcommand*\1{$'$}
\begin{document}
\begin{forest}
[TP,name=TP [DP,multidom={-.5cm}{-2cm}{north}{TP}{east}{VP} [D\\the ][NP\\chimney ]] 
    [T\1 [T ]
        [VP,name=VP [DP,phantom] [V\1  [V\\smokes ]  ]]]]
\end{forest}
\end{document}

Answer 2

Updated Updated answer

This version supports append and 3+ parents. However, if the shift is negative and would be a fraction of a centimetre, you must specify millimetres instead. (Even with the direct '+ assignment.) If anybody knows why, please let me know.

\documentclass{article}
\usepackage[linguistics]{forest}
\forestset{% addaswyd o ateb Alan Munn: https://tex.stackexchange.com/a/695600/ (addaswyd o fy ateb gwreiddiol)
  declare keylist={other parents}{},
  declare boolean register={inc multidom},
  not inc multidom,
  declare toks register={multidom toksa},
  multidom toksa={},
  declare toks register={multidom toksb},
  multidom toksb={},
  declare toks register={multidom toksc},
  multidom toksc={},
  declare toks register={multidom toksd},
  multidom toksd={},
  declare dimen register={multidom dimx},
  multidom dimx'=0pt,
  declare dimen register={multidom dimy},
  multidom dimy'=0pt,
  includes multidom/.style={%
    where={>{O_=!}{other parents}{}}{%
      split option={other parents}{,}{multidom aux},
    }{},
  },
  multidom aux/.style={%
    multidom toksa={},
    multidom toksb={},
    multidom toksc={},
    multidom toksd={},
    multidom dimx'=0pt,
    multidom dimy'=0pt,
    split={#1}{:}{multidom toksa,temptoksa,temptoksb,multidom toksb,multidom toksc,multidom toksd},
    if={>{R_=}{multidom toksd}{}}{% no sixth arg -> resplit -> multidoms
      split={#1}{:}{multidom toksa,multidom toksb,multidom toksc},
      multidoms/.process={RRR{multidom toksa}{multidom toksb}{multidom toksc}},      
    }{% sixth arg -> (first) multicom
      split={#1}{:}{multidom toksa,multidom dimx,multidom dimy,multidom toksb,multidom toksc,multidom toksd},
      typeout/.register=multidom dimx,
      multidom/.process={RRRRRR{multidom toksa}{multidom dimx}{multidom dimy}{multidom toksb}{multidom toksc}{multidom toksd}},
    },
  },
  multidoms/.style n args=3{%
    before typesetting nodes={%
      temptoksa/.option=content,
      for nodewalk={fake=current,name=#3}{#1/.expanded={[\foresteregister{temptoksa},phantom]}},
    },
    before drawing tree={% parametised from https://tex.stackexchange.com/a/249615/
      tikz+={%
        \draw [-] (.#2) to [out=#2,looseness=.5] (#3.south);
      },
    },
  },
  multidom/.style n args=6{%
    no edge,
    before typesetting nodes={%
      temptoksa/.option=content,
      for nodewalk={fake=current,name=#6}{#1/.expanded={[\foresteregister{temptoksa},phantom]}},
    },
    before drawing tree={% parametised from https://tex.stackexchange.com/a/249615/
      for tree={x'+=#2,y'+=#3},
      tikz+={%
        \draw [-] (.#4) to [out=#4,looseness=.5] (!u.south);
        \draw [-] (.#5) to [out=#5,looseness=.5] (#6.south);
      },
    },
  },
  multidom prepend/.style n args=5{multidom={prepend}{#1}{#2}{#3}{#4}{#5}},
  multidom append/.style n args=5{multidom={append}{#1}{#2}{#3}{#4}{#5}},
  default preamble+={%
    delay={%
      for tree={%
        if={>{O_=!}{other parents}{}}{inc multidom}{},
      },
    },
    before typesetting nodes={if inc multidom={includes multidom}{}},
  },
}
\newcommand*\1{$'$}
\begin{document}
\begin{forest}
  [TP,name=TP 
  [DP,multidom prepend={-.5cm}{-2cm}{north}{east}{VP} 
    [D\\the ]
    [NP\\chimney ]
    ] 
    [T\1
      [T ]
      [VP,name=VP  
        [V\1  
          [V\\smokes ] 
        ]
      ]
    ]
  ]
\end{forest}
\begin{forest}
  [TP,name=TP 
  [DP,other parents={prepend:-5mm:-2cm:north:east:VP,prepend:south east:V}
    [D\the ]
    [NP\chimney ]
    ] 
    [T\1
      [T ]
      [VP,name=VP

        [V\1,name=V
          [V\smokes ] 
        ]
      ]
    ]
  ]
\end{forest}
\end{document}

Updated answer

This is a modification of Alan's modification of my original answer below. This version eliminates one of the arguments and the need to add a phantom node to the other parent. Currently, the code assumes the phantom should always be prepended to the other parent. If that's not the case, appending could be enabled either with a sixth argument or a second style. I haven't done that here because I don't know if it is required or, if it is, what approach might be most convenient.

\documentclass{article}
\usepackage[linguistics]{forest}
\forestset{% addaswyd o ateb Alan Munn: https://tex.stackexchange.com/a/695600/ (addaswyd o fy ateb gwreiddiol)
  multidom/.style n args=5{%
    no edge,
    before typesetting nodes={%
      temptoksa/.option=content,
      for nodewalk={fake=current,name=#5}{prepend/.expanded={[\foresteregister{temptoksa},phantom]}},
    },
    before drawing tree={% parametised from https://tex.stackexchange.com/a/249615/
      for tree={x'+=#1,y'+=#2},
      tikz+={%
        \draw [-] (.#3) to [out=#3,looseness=.5] (!u.south);
        \draw [-] (.#4) to [out=#4,looseness=.5] (#5.south);
      },
    },
  }
}
\newcommand*\1{$'$}
\begin{document}
\begin{forest}
  [TP,name=TP 
  [DP,multidom={-.5cm}{-2cm}{north}{east}{VP} 
    [D\\the ]
    [NP\\chimney ]
    ] 
    [T\1
      [T ]
      [VP,name=VP  
        [V\1  
          [V\\smokes ] 
        ]
      ]
    ]
  ]
\end{forest}
\end{document}

The output is (should be) no different from Alan's.

Original proof-of-concept

Here's a quickish proof-of-concept which needs improvement but gets the general structure right. I may fiddle with this later if anybody is interested. I use relative node names (!r) but you can use names (G) if preferred.

\documentclass{standalone}
\usepackage[linguistics]{forest}
\forestset{
  nice nodes/.style={
    for tree={
      inner sep=0pt,
      fit=band,
    },
  },
  default preamble=nice nodes,
  dominated/.style n args=4{%
    no edge,
    before drawing tree={% parametised from https://tex.stackexchange.com/a/249615/
      for tree={x+=#1},
      tikz+={%
        \draw [-,looseness=1] (.#2) to [out=#2] (#3);
        \draw [-,looseness=1] (.#2) to [out=#2] (#4);
      }
    },
  },
}
\begin{document}
\begin{forest}
sn edges
[L,name=L 
    [,name=D,no edge] 
        [ 
            [$\beta$] 
            [K 
            [$\gamma$,name=G,dominated={-20mm}{east}{!r.south west}{!u.south},no edge[smoke]] 
                [$\alpha$[smoke]]
            ]
        ] 
]
\end{forest}
\end{document}