After playing with too many permutations to put in here... the closest I came up with is:

perl -e 'sub foo { CORE::log(shift) }; print foo(123),$/;'
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In other words, you need to create &readlines as a sub around CORE::readline. Note a few things:

1. The built-ins have proper prototyping. If you pass in @_ when it's expecting a scalar (such as CORE::log above), you're going to be getting funny results (I kept getting 0 ... because log(1) == 0). I had to change it from CORE::log(@_) to CORE::log(shift) to get it to work. Of course, CORE::log($_[0]) would work as well.
2. It's not quite the same thing as aliasing. We're not mapping $foo to $CORE::log, or %foo to %CORE::log or anything like that.
3. It's probably not as fast ... but it may be close enough.

Hope that helps.