definition of lexical closure

[PGS%MIT-OZ@MIT-MC.ARPA]

    Date: Sunday, 27 January 1985  19:57-EST
    From: PGS
    To:   common-lisp at SU-AI.ARPA
    Re:   definition of lexical closure

    I was talking to someone today about the Common Lisp notion of a closure,
    and I noticed that the definition of a lexical closure on page 87 of the
    CL manual is sort of vague and unsatisfactory.  It says that a lexical
    closure is the object returned by FUNCTION, that is, a function which,
    when invoked, obeys the rules for lexical scoping.

    The problem with this definition is that it makes it difficult to explain
    why the thing referred to is called a closure.  It's hard to relate the
    definition even vaguely to the set-theoretic notion of a closure, because
    it doesn't describe a set, so one can't explain the term as coming from
    the notion of `closing over' a set of bindings...

Oops, I take it all back.  I dug out my copy of Kleene and found that I
really wanted the predicate calculus notion of closure, not the set-theoretic
notion of closure.