Define instances for GenTambara
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module Data.Profunctor.Strong
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import Data.Tensor
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import Data.Profunctor.Functor
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import Data.Profunctor.Types
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@ -33,10 +34,41 @@ uncurry' = rmap (uncurry id) . first
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-- Tambara
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public export
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record GenTambara (ten, p : Type -> Type -> Type) where
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record GenTambara (ten, p : Type -> Type -> Type) a b where
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constructor MkTambara
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getTambara : {0 c : Type} -> p (a `ten` c) (b `ten` c)
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export
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Bifunctor ten => Profunctor p => Profunctor (GenTambara ten p) where
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dimap f g (MkTambara p) = MkTambara $ dimap (mapFst f) (mapFst g) p
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export
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ProfunctorFunctor (GenTambara ten) where
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promap f (MkTambara p) = MkTambara (f p)
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export
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Tensor ten i => ProfunctorComonad (GenTambara ten) where
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proextract (MkTambara p) = dimap unitr.bwd unitr.fwd p
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produplicate (MkTambara p) = MkTambara $ MkTambara $ dimap assoc.bwd assoc.fwd p
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export
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Associative ten => Symmetric ten => Profunctor p => GenStrong ten (GenTambara ten p) where
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strongl (MkTambara p) = MkTambara $ dimap assoc.bwd assoc.fwd p
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strongr = dimap swap swap . strongl {ten,p=GenTambara ten p}
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export
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Bifunctor ten => Profunctor p => Functor (GenTambara ten p a) where
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map = rmap
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export
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gentambara : GenStrong ten p => p :-> q -> p :-> GenTambara ten q
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gentambara @{gs} f x = MkTambara $ f $ strongl @{gs} x
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export
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ungentambara : Tensor ten i => Profunctor q => p :-> GenTambara ten q -> p :-> q
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ungentambara f x = dimap unitr.bwd unitr.fwd $ getTambara $ f x
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public export
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Tambara : (p : Type -> Type -> Type) -> Type
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Tambara = GenTambara Pair
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