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Implications of the new reduction algorithm
Here are a couple of things that are worth noting:
(1) Name space adoption.
If you have key k1, and you issue a certificate of the form
{k1} ==> {k2}
then you have essentially augmented your name space by all of k2's.
That is, if k2 has defined alice to mean k3, then
{k1,alice}
reduces to
{k2,alice} (by your certificate {k1}==>{k2})
and this then reduces to
{k3} (by k2's certificate {k2,alice}==>{k3}.
This has some potential benefits, and risks. A certificate of the
form {k1}==>{k2} is very powerful, and should be used carefully.
(2) Products of relations
Note that a name of the form {k,friends,friends} does the appropriate
thing: it can evaluate to any key of a friend of a friend of k's.