On Dec 21, 2011, at 2:24 PM, Alexander Solla wrote:
> I would rather have an incomplete semantic, and have all the incomplete parts
> collapsed into something we call "bottom". We can then be smart and stay
> within a total fragment of the language (where bottom is guaranteed to not
> occur).
But part of the whole point of including bottom in our semantics in the first
place is *exactly* to *enable* us to be smart enough to know when we are
staying within a total fragment of the language. For example, including bottom
in our semantics allows us to make and prove statements like
fst (42,_|_) = 42
and
fst _|_ = _|_
That is, as long a you know that the pair is total and that the first element
is total, calling fst on it is also total regardless of whether the second
value is total.
Refusing to use bottom in our semantics doesn't make life better by forcing us
to stay within a total fragment of the language, it actually makes life harder
by removing from us a useful tool for knowing *how* to stay within a total
fragment of the language.
Cheers,
Greg_______________________________________________
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