Imagine a mapping (abstraction mapping) from the integer … -3, -2, -1, 0, 1, 2, 3, … to the set {-, 0, +}. This is the abstract domain. Negatives to {-}, positives to {+} and 0 to {0}.
Yes, it would. If you want to write a program that only operates on the ideas of positive, negative, and zero, then representing a positive state by any positive number is a terrible way to do it. Like checking for a non-zero exit code.
I suspect that counts as mapping from the “Real World to abstract state.” I believe that because, in the quoted paragraphs, “this is the abstract domain” seems to refer to the {-, 0, +} set.
My interpretation might be wrong! It’s weird to say integers are any more or less abstract concept than sign.
I think the author says “abstract” because it’s the part that’s usually in our head; whereas the “concrete” part is usually in our code.
I don’t see any difference in the ways of potentially mismapping from abstract to concrete than I do in the potential ways of potentially mismapping from the real world to abstract. Only that we explicitly choose to have missing states— that’s the point of simplifying abstractions!
This has an interesting correspondence to one of my favorite software design talks of all time, by Daniel Jackson - Rethinking Software Design
The main premise of the talk is that each concept in a codebase should be in 1:1 correspondence with a purpose, and he identifies the same mismatches between the two (“4 bad smells”, timestamped link).
The purposes/concepts split is very similar to the abstract/concrete state split defined in the post, but it’s more general in that it doesn’t refer only to state.
Does this count as a redundant mapping?
Nope.
Sorry, I meant this one:
Oh.
Yes, it would. If you want to write a program that only operates on the ideas of positive, negative, and zero, then representing a positive state by any positive number is a terrible way to do it. Like checking for a non-zero exit code.
I suspect that counts as mapping from the “Real World to abstract state.” I believe that because, in the quoted paragraphs, “this is the abstract domain” seems to refer to the
{-, 0, +}set.My interpretation might be wrong! It’s weird to say integers are any more or less abstract concept than sign.
I think the author says “abstract” because it’s the part that’s usually in our head; whereas the “concrete” part is usually in our code.
I don’t see any difference in the ways of potentially mismapping from abstract to concrete than I do in the potential ways of potentially mismapping from the real world to abstract. Only that we explicitly choose to have missing states— that’s the point of simplifying abstractions!
This has an interesting correspondence to one of my favorite software design talks of all time, by Daniel Jackson - Rethinking Software Design
The main premise of the talk is that each concept in a codebase should be in 1:1 correspondence with a purpose, and he identifies the same mismatches between the two (“4 bad smells”, timestamped link).
The purposes/concepts split is very similar to the abstract/concrete state split defined in the post, but it’s more general in that it doesn’t refer only to state.
That’s a great talk, I’m watching it now. Thanks for the link!