isSet for Grammars, Monoidal Category of grammars, finish Dyck Trace Equivalence #28
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stschaef
requested changes
Oct 28, 2024
| variable ℓ ℓG ℓG' ℓH ℓK ℓL : Level | ||
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| module _ where | ||
| isLang : Grammar ℓG → Type ℓG |
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With this interface, the external notion of unambiguity would then be isLang→unambiguous.
The existing definition is in String.Properties and broken at the moment. I still need to fix that, but it's probably not a high priority thing to fix, as its external reasoning that we seemingly don't need because of * continuity
| open NatTrans | ||
| open NatIso | ||
| open isIso | ||
| |GRAMMAR| : Category (ℓ-suc ℓ) ℓ |
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We've talked about how it would be less universe polymorphic to do so, but defining this as a category could now let us replace unambiguous and StrongEquivalence with the definition of mono and iso from the categories library
stschaef
approved these changes
Oct 28, 2024
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Looks good assuming CI goes through |
This was referenced Oct 29, 2024
nvarner
pushed a commit
that referenced
this pull request
Nov 2, 2024
…Equivalence (#28) * HLevels for grammars, instances for epsilon, tensor * triangle and pentagon laws * define monoidal category of grammars * naturality proofs for some combinators * finish the Dyck Trace proof using coherence for monoidal categories * update to CI to use latest cubical-categorical-logic
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This requires maxsnew/cubical-categorical-logic#115 upstream