Re: [isabelle] Non-idempotence of datatype constructors



> Firstly, I don't think these theorem is especially useful. You might
> have planned to add this to the simplifier, but its term net doesn't do
> any magic here. It will end up checking every term that matches "Cons x
> xs = ys" for whether "xs" can match "ys". I'm not sure if that matching
> is equality, alpha-equivalent or unifiable.

I honestly never think /that/ much about the performance implications of
simp rules (as long as they're unconditional). At least for lists, by
the way, this is already a simp rule by default though, and lists are
probably by far the most prevalent data type in the Isabelle universe.

But you're certainly right that it would make sense to keep a look at
this performance impact if one wanted to add these to the simp set for
all datatypes by default, and I agree that the rules are probably not
helpful /that/ often. Still, it might be nice to have them available
nonetheless.

> Secondly, you can prove these theorems by using this handy trivial
> theorem : "size x ~= size y ==> x ~= y". Apparently that theorem has the
> name  Sledgehammer.size_ne_size_imp_ne - presumably the sledgehammer
> uses it to prove such inequalities.

It's even easier to prove it by induction. Plus, in fact, the "size"
thing only works if the data type even has a sensible size function.
That is not always the case, e.g. when you nest the datatype through a
function.

My main point however is that when you have a datatype with a dozen
binary constructors, there's quite a bit of copying & pasting involved
before you've proven all those theorems. Since it can (probably) be
automated very easily, why not do that? Whether or not these should be
simp lemmas by default is another question.

Manuel




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