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On page 44, there are rules for addition/subtraction/multiplication on odd/even/unknown values. However, the rules for "-" only give a precise answer for E - E, whereas it could use the same rules as "+" (i.e., giving precise answers for all of {E,O} x {E,O}).
The omission doesn't compromise the soundness of the abstraction, but it is at odds with the previous page describing the abstracted operators as "push[ing] abstraction through arithmetic operators, calculating their most precise abstractions."
It seems like either (1) the rules for "+" and "-" should match, or (2) the text could take the opportunity to point out that while "-" is less precise, it doesn't compromise its soundness.
The text was updated successfully, but these errors were encountered:
Oops, I wasn't reading closely enough there. I suppose because of the introduction of -, I just assumed we were in Z. No, I do not think my characterization holds in N with Coq's subtraction rules---I withdraw that point. Sorry about that!
For what it's worth, it seems like § 7 introduces e - e, but doesn't define ⟦e - e⟧v.
This case is implemented by parity_subtract in
AbstractInterpretation.v and is necessary to calculate the "most
precise abstraction."
See also achlipala#28, achlipala#37.
On page 44, there are rules for addition/subtraction/multiplication on odd/even/unknown values. However, the rules for "-" only give a precise answer for E - E, whereas it could use the same rules as "+" (i.e., giving precise answers for all of {E,O} x {E,O}).
The omission doesn't compromise the soundness of the abstraction, but it is at odds with the previous page describing the abstracted operators as "push[ing] abstraction through arithmetic operators, calculating their most precise abstractions."
It seems like either (1) the rules for "+" and "-" should match, or (2) the text could take the opportunity to point out that while "-" is less precise, it doesn't compromise its soundness.
The text was updated successfully, but these errors were encountered: