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This is the first definition has come to my mind. It works at least for ADT < CCC intuitively.
I expect `2CC < CCC` so `ADT < CCC` should follow using transitivity.
As ≤Size is not total, <Size is not transitive without requiring ≤Size. Moreover, ≱Size is not antisymmetric. Note that ≱Size is ¬ ≤Size with the arguments flipped and the negation moved inside.
This makes it easier to use because the artifact type doesn't need to be applied when invoking `≤Size`. Furthermore, this enables proofs of `≱Size` to fix a single artifact type, for example the natural numbers, and automatically have the inhabitants it needs. The order between the quantifier over `n` and `A` doesn't have a big impact. On the one hand, the chosen order allows `≱Size` to use different artifact types for each `n`. However, it doesn't change the relation inhabitants if they are swapped because there exists a type with enough elements (i.e., union of all `A` ranging all `n`s) that can be fixed and then only a subset of the artifacts can be used for a specific `n`. On the other hand, `≤Size` is a `Set` and, thus, can't be inspected if the order is changed. This specific order is chosen purely as it's more convenient for pattern matching (e.g., one less `with` clause in case of `≤Size`).
Previously, these where not inferred correctly, but now it works™.
This reduces duplication and allows refactoring of 𝔸.
This allows to easily add more fields.
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Hi @ibbem
thank you for the PR. As always, it would be great to have some documentation here and there. I leave it up to you to decide how much time you want to invest. I have some comments below but would be willing to merge in any case.
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I added all the requested documentation and added my thesis in the README. |
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Thank you a lot for the documentation! I have a few last questions on the new documentation, and then we can merge. :)
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The name was misleading as every variant has a root artifact (although it doesn't have any children). The new name also incorporates existing software product line terminology.
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This is the formalization of succinctness as advertised in my master thesis "On the Succinctness of
Languages for Static Variability".
Note that there are merge conflicts between
thesis_bmandmain. Hence, this branch already includes the merge tomainand should be merged using a fast-forward merge.