arrows

[Wolfgang Jeltsch]

Hello,
in his paper "Generalising monads to arrows" John Hughes introduces an
Arrow class with the members arr and (>>>) and extends this with a
member first. The Arrow module by Ross Paterson adopts the practice of
including first in the Arrow class.
Now, I have a type which would fit wonderfully into the Arrow concept if
arrows wouldn't be expected to have a first operator. To be precise, I
have a type Parser of kind * -> * -> * with Parser a b being a parser
which reads from a list of tokens of type a and produces a value of type
b. Parser a is an instance of Monad and MonadPlus, thus providing
sequencing, handling of alternatives and the like.
Now I want to implement scanners via my parser type. A scanner shall
simply be described by a parser which parses one higher-level token from
a stream of lower-level tokens. I want to provide a function of type
Parser a b -> Parser b c -> Parser a c which constructs a parser which
reads a value of type c from a stream of type a tokens by repeatedly
invoking the first argument parser to produce higher-level tokens which
are then consumed by the second argument parser in order to produce the
final output.
Of course this function looks like a candidate for being (>>>) in a
Parser arrow. And there is also a meaningful definition for pure (arr).
pure f just has to be a parser which reads exactly one token, applies f
to it and outputs the resulting value.
The problem is that there seems to be no appropriate definition for
first. That's why, in my opinion, it would be very good to have only the
members pure (arr) and (>>>) in Arrow and to define a subclass which
adds first, similar to ArrowChoice which adds left. This would have also
the advantage that the handling of first, second, (***) and (&&&) on the
one hand, and the handling of left, right, (+++) and (|||) on the other
would be totally analogous.
What do you think of this approach? Are there any of you who think that
modifying the Arrow module this way would be a good idea? I'm waiting
for your comments.

Wolfgang