This combines Forest with the new coffins to create a tree style
delimit tree={<left delimiter>}{<right delimiter>}
It tries to keep the baselines correct, although I am not certain that I've got this quite right, so it may need tweaking. (It worked with minimal testing, but I don't really trust it.)
Given the definition of the new style, this allows us to write
\begin{forest}
for tree={
font=\bfseries,
},
delimit tree={\left\llbracket}{\right\rrbracket}
[S
[S
[
[NP
[N
[Ann]
]
]
[VP
[V
[smokes]
]
]
]
]
[and]
[S
[
[NP
[N
[John]
]
]
[VP
[V
[drinks]
]
]
]
]
]
\end{forest}
\begin{forest}
delimit tree={\left\langle\left(}{\right)\right\rangle}
[S
[NP
[N
[Ann]
]
]
[VP
[V
[smokes]
]
]
]
\end{forest}
Note that this maintains (I think!) the corrected alignment of the trees on the baseline.

Complete code:
\documentclass[border=10pt]{standalone}
\usepackage{stmaryrd,xcoffins}
\usepackage[linguistics]{forest}
\NewCoffin\OuterForestCoffin
\NewCoffin\InnerForestCoffin
\forestset{%
delimit tree/.code n args=2{%
\forestset{%
draw tree stage/.style={
for root'={
draw tree box=0,
draw tree,
TeX={%
\SetHorizontalCoffin\InnerForestCoffin{\box0}%
\SetHorizontalCoffin\OuterForestCoffin{%
$#1 \TypesetCoffin\InnerForestCoffin[vc,l]#2$%
}%
\TypesetCoffin\OuterForestCoffin[t,l](0pt,(\CoffinTotalHeight{\OuterForestCoffin}-\CoffinTotalHeight{\InnerForestCoffin})+\CoffinHeight{\InnerForestCoffin})%
},
},
},
}%
},
}
\begin{document}
\begin{forest}
for tree={
font=\bfseries,
},
delimit tree={\left\llbracket}{\right\rrbracket}
[S
[S
[
[NP
[N
[Ann]
]
]
[VP
[V
[smokes]
]
]
]
]
[and]
[S
[
[NP
[N
[John]
]
]
[VP
[V
[drinks]
]
]
]
]
]
\end{forest}
\begin{forest}
delimit tree={\left\langle\left(}{\right)\right\rangle}
[S
[NP
[N
[Ann]
]
]
[VP
[V
[smokes]
]
]
]
\end{forest}
\end{document}
qtreeandtikz-qtree. You should stick to the latter. – Alan Munn Sep 15 '13 at 17:34