Syntactic trees within denotation brackets in LaTeX (mwe)

treeden-mwe.tex

\documentclass{article}

% this is necessary for the denotation brackets [[.]]
\usepackage{stmaryrd}

% this is necessary for syntactic trees. There are other packages too,
% this is just the one I prefer.
\usepackage[linguistics]{forest}

\begin{document}

% enclosing the forest environment within an `array' environment seems
% ensures that the alignment is as desired.

\[
  \left\llbracket\begin{array}{c}
    \begin{forest}
      [{XP}
        [{X}]
        [{Y}]
      ]
    \end{forest}
    \end{array}\right\rrbracket^{w} = \ldots
\]

\end{document}