Chris,
I'm not sure what exactly your question is as you are mixing up several
concepts. However, you start with:
In haskell, we can transform:
g x + f x
into:
f x + g x
Here you assume that the function + is commutative. Although this is
probably true for all numeric types in all Haskell implementations,
neither functional languages in general nor the Haskell report guarantee
commutativity of +. So this assumption is dangerous.
0 + _|_ /= _|_ + 0
Or, does this just become:
_|_ = _|_ ?
The Haskell report probably does not say so explicitly, but in general
primitive functions like + are strict in all arguments and hence 0 + _|_
= _|_ = _|_ + 0.
Ciao,
Olaf
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