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TOTBWF
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Sep 22, 2025
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This is a really great change! Part-ext has always annoyed me.
We should also be able to use this trick for Inductive instances as well, though I'm not sure how this would play out in practice. Definitely warrants an experiment!
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| part-map-id x = part-ext id id λ _ _ → | ||
| ↯-indep x | ||
| part-map-id x = part-ext id id λ _ _ → ↯-indep x | ||
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| part-map-∘ | ||
| : ∀ (f : B → C) (g : A → B) | ||
| → ∀ (x : ↯ A) → part-map (f ∘ g) x ≡ part-map f (part-map g x) | ||
| part-map-∘ f g x = part-ext id id λ _ _ → | ||
| ap (f ∘ g) (↯-indep x) | ||
| part-map-∘ f g x = part-ext id id λ _ _ → ap (f ∘ g) (↯-indep x) |
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While we are at it, the type of part-ext should probably be changed to be ∀ xd → x .elt xs ≡ x .elt (to xd): this would let us avoid a lot of uses of ↯-indep
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Just an idea for how extensionality could work for some types of record. Unfortunately the nice syntax where you use an extended lambda like below needs a workaround for agda/agda#8112 (which we can do somewhat generically, by just blocking checking the extended lambda ourselves).