Contravariant hierarchy #10

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1. subttle

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   idea

   on Nov 4, 2019
2. subttle commented on Nov 17, 2019

   

   subttle

   on Nov 17, 2019

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   Experiment:

   class Alternative f ⇒ Combines f where
     one ∷ f (These a b) → f (a → c) → f (b → c) → f c
   class Applicative f ⇒ Composes f where
     two ∷ f (These a b) → f (a → b) → f (b → c) → f c

   class Alternative f ⇒ Selective' f where
     select' ∷ f (Either a b) → f (a → c) → f (b → c) → f c
3. subttle commented on Dec 23, 2019

   

   subttle

   on Dec 23, 2019

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   Another experiment:

   class (Contravariant f) ⇒ MaybeH f where
     maybeh ∷ (a → Maybe b) → f b → f a
   

   instance MaybeH Predicate where
     -- FIXME not sure `False` is the correct default value here
     -- TODO compare with `Either () b` instance?
     -- TODO could also just require `Monoid b` and use `mempty` in place of `False`
     maybeh ∷ ∀ a b . (a → Maybe b) → Predicate b → Predicate a
   {-
     maybeh h (Predicate pᵇ) = Predicate pᵃ
       where
         pᵃ ∷ a → Bool
         pᵃ = maybe False pᵇ . h
   -}
     -- maybeh h (Predicate pᵇ) = Predicate (maybe False pᵇ . h)
     maybeh h (Predicate pᵇ) = h >$< Predicate (maybe False pᵇ)
   
4. subttle commented on Dec 23, 2019

   

   subttle

   on Dec 23, 2019

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   And if that works, why stop there? See if something like the following makes sense.

   data List a = Nil | Cons a (List a)
   class (Contravariant f) ⇒ ListH f where
     listh ∷ (a → List b) → f b → f a
   

   But should probably consider both foldr and unfoldr destructors.
   And then would need to consider how that might play out:

   instance ListH Predicate where
     listh ∷ ∀ a b . (a → List b) → Predicate b → Predicate a
     listh h (Predicate pᵇ) = Predicate pᵃ
       where
         pᵃ ∷ Predicate a
         -- pᵃ = Predicate (\a → null (filter pᵇ (h a))) -- not (any pᵇ (h a))
         pᵃ = Predicate (null . filter pᵇ . h) -- not . any pᵇ . h
   

   listh ∷ ∀ a b . (a → List b) → Equivalence b → Equivalence a
   

   implying something like ∷ List b → List b → Bool so maybe equivalence of lists by length? So then I would imagine ∷ List b → List b → Ordering would then be comparing lists by length?
5. subttle

   added

   experimental

   on Dec 23, 2019