How do I multiply labeled vectors of numbers?

I'm an R newbie trying to do an operation that seems like it should be very
simple, but after much playing around with the interface and reading "An
Introduction to R" I can figure out how to do it.

I have two text files.  File1 contains:

type    n
dog        2
cat        4
horse    6

File2 contains:

type    n
horse    1
dog        3
cat        9
mouse 11

I want to read both files into R and multiply corresponding values of n so
that I end up with:

dog       2*3 = 6
cat        4*9 = 36
horse    6*1 = 6
mouse  0*11 = 0

Note that the type rows are not necessarily in the same order in the two
files, and that a missing type gets a default n = 0 value.

I figure the way to do this is use read.table and do the appropriate
manipulation of the factors, but I can't figure out what those manipulations
would be.  Basically I want to use a factor table as a hash table, but I
haven't been able to figure out how to do this, which makes me think I'm not
conceptualizing this is the correct R-ish way.

Thanks.

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