Functional vector module #1945
Functional vector module #1945
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I like this addition. There's a lot of algebraic structures that you could define but don't, especially:
IsCommutativeMagmaIsCommutativeSemigroupIsGroupIsAbelianGroupIsPrerightSemimoduleIsRightSemimoduleIsBisemimoduleIsRightModuleIsBimoduleIsModule
And with element-wise multiplication:
IsNearSemiringIsSemiringWithoutOneIsCommutativeSemiringWithoutOneIsSemiringWithoutAnnihilatingZeroIsSemiringIsCommutativeSemiringIsRingWithoutOneIsRingIsCommutativeRing
Plus the corresponding bundles.
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I added all of them. |
| @@ -3027,3 +3027,113 @@ This is a full list of proofs that have changed form to use irrelevant instance | |||
| ```agda | |||
| <-weakInduction-startingFrom : P i → (∀ j → P (inject₁ j) → P (suc j)) → ∀ {j} → j ≥ i → P j | |||
| ``` | |||
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In these cases we typically only mention we have added entirely new modules rather than listing their content.
Cf. https://github.com/agda/agda-stdlib/blob/master/CHANGELOG.md#new-modules
| import Algebra.Structures as AS | ||
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| module Data.Vec.Functional.Algebra.Base | ||
| {c ℓ} (cring : CommutativeRing c ℓ) where |
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I'm not happy about this whole module being parameterized on CommutativeRing, as many of the definitions work with smaller algebraic structures, but I'm not sure what to do about it. Maybe other people have some ideas?
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I haven't (yet) looked at this too closely, but it seems as though we might more generally want d isX implies (Vector n d) isX and then if d is suitable as X scalars for the right notion of IsYModule over X then (Vector n d) isYModule over d...?
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I have changed most of my code and it is not done yet. It is still with a lot of comments. I tried to make the code work with more cases, but I don't know if it is helpful in that way. |
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I can remove the code that is commented on if they are not necessary. I also would like some suggestions if something is not in the right way. |
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Sorry not to have had time for a thorough review of this draft PR yet! |
Added structures and bundles about functional vectors and modules.