\section{Related and Future Research}
\label{related}

Many proposals have been put forth for programming languages targeted
for computer music composition
\cite{canon,pla,moxie,formula,fugue,scoresynth,formes,grame94},
% common-music
so many in fact that it would be difficult to describe them all here.
None of them (perhaps surprisingly) are based on a {\em pure}
functional language, with one exception: the recent work done by
Orlarey et al.\ at GRAME \cite{grame94}, which uses a pure lambda
calculus approach to music description, and bears some resemblance to
our effort.  There are some other related approaches based on variants
of Lisp, most notably Dannenberg's {\em Fugue} language \cite{fugue},
in which operators similar to ours can be found but where the emphasis
is more on instrument synthesis rather than note-oriented composition.
Fugue also highlights the utility of lazy evaluation in certain
contexts, but extra effort is needed to make this work in Lisp,
whereas in a non-strict language such as Haskell it essentially comes
``for free.''  Other efforts based on Lisp utilize Lisp primarily as a
convenient vehicle for ``embedded language design,'' and the
applicative nature of Lisp is not exploited well (for example, in
Common Music the user will find a large number of macros which are
difficult if not impossible to use in a functional style).

We are not aware of any computer music language that has been shown to
exhibit the kinds of algebraic properties that we have demonstrated
for Haskore.  Indeed, none of the languages that we have investigated
make a useful distinction between music and performance, a property
that we find especially attractive about the Haskore design.  On the
other hand, Balaban describes an abstract notion (apparently not yet a
programming language) of ``music structure,'' and provides various
operators that look similar to ours \cite{balaban92}.  In addition,
she describes an operation called {\em flatten} that resembles our
literal interpretation {\tt perform}.  It would be interesting to
translate her ideas into Haskell; the match would likely be good.

Perhaps surprisingly, the work that we find most closely related to
ours is not about music at all: it is Henderson's {\em functional
geometry}, a functional language approach to generating computer
graphics \cite{henderson82}.  There we find a structure that is in
spirit very similar to ours: most importantly, a clear distinction
between object {\em description} and {\em interpretation} (which in
this paper we have been calling musical objects and their
performance).  A similar structure can be found in Arya's {\em
functional animation} work \cite{arya94}.

There are many interesting avenues to pursue with this research.  On
the theoretical side, we need a deeper investigation of the algebraic
structure of music, and would like to express certain modern theories
of music in Haskore.  The possibility of expressing other scale types
instead of the thus far unstated assumption of standard equal
temperament scales is another area of investigation.  On the practical
side, the potential of a graphical interface to Haskore is appealing.
We are also interested in extending the methodology to sound
synthesis.  Our primary goal currently, however, is to continue using
Haskore as a vehicle for interesting algorithmic composition (for
example, see \cite{hudakberger95}).