Question 268

[Kevin Jacoby]

I'm having trouble understanding the question, specifically "What is
the equivalence relation..." Because variable v is already a bound
variable in (* p v) can it even be replaced?

[A.J. Gardner]

I was similarly confounded: I know what an equivalence relation is,
but we've never defined them in this course.

We've talked about propositional equivalence and maintained
equivalences, and formulae admitting or not admitting propositional
replacement... But what does it mean for an address of a formula to
admit an equivalence relation? The paragraph above the question is of
no help ("We need to update our notion what equivalence relation must
hold..."---but we've never had any formal notion of equivalence
relation...).

[J Strother Moore]

Even if (* p v) cannot be rewritten, it still has an address pi and associated
with pi is the equivalence relation it admits.

J

[A.J. Gardner]

So we're using "maintained equivalence" and "equivalence relation"
interchangeably?

[J Strother Moore]

I should have phrased the question differently:
does pi admit propositional replacement? (Any
subterm that may be replaced may be replaced by an
equivalent (EQUAL) subterm. So the only question
is whether a given occurrence can be replaced by
something that is not EQUAL but merely
propositionally equivalence.)

Sorry for the confusion.

J