Weaker interface for neutral conversion #61
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kyoDralliam
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Jan 23, 2024
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| Lemma ne_conv_conv : forall (Γ : context) (A m n : term), | ||
| [Γ |-[de] A] -> | ||
| [Γ |-[de] m : A] -> | ||
| [Γ |-[al] m ~ n ▹ A] -> | ||
| [Γ |-[al] m ≅ n : A]. |
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What's happening with this lemma ? Is it not derivable anymore ? Or just not useful ?
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It is still derivable, but not useful any more, as we only need it when A is a positive type, in which case it is trivial by using the relevant constructor of algorithmic conversion. As explained above, I feel it is more "moral" that this consequence of normalisation is directly handled in the logrel, rather than after the fact.
kyoDralliam
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Jan 23, 2024
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This backports a change we had already on the branch with lists, which makes the generic interface for conversion weaker, by only demanding inclusion of neutral conversion in conversion at positive types. We pay the price in
Neutral, because the proof for negative types is a bit more involved – we need to use η expansion –, but more "moral". It allows to remove a nasty proof that algorithmic neutral conversion in included in algorithmic conversion, which was using normalisation to basically do what is now done in the logical relation