[Haskell-cafe] Trying to test natural transformations, in Haskell.

[David Banas]

Got it:

{-# LANGUAGE Rank2Types
             AllowAmbiguousTypes
             FlexibleContexts
  #-}

type NatTran f f' a = (Functor f, Functor f') => f a -> f' a

to_assert :: (Functor f, Functor f', Eq (f' b)) => (a -> b) -> NatTran f f' a -> NatTran f f' b -> f a -> Bool
to_assert g h h' f = (fmap g . h) f == (h' . fmap g) f

maybe_to_list :: NatTran Maybe [] a
maybe_to_list Nothing  = []
maybe_to_list (Just x) = [x]

test_func :: Num a => a -> (a, a)
test_func x = (x, x + 1)

success = all (to_assert test_func maybe_to_list maybe_to_list) [Nothing, Just 1]

main :: IO ()
main = do
    if success then print "Success!" else print "Failure."

main

Running this code produces:

"Success!"

=================================================

Hi all,

In doing the challenge problems at the end of chapter 10 (Natural Transformations) in Bartosz Milewski’s “Category Theory for Programmers”, I’m trying to write a generic naturality checker:

{-# LANGUAGE Rank2Types
             AllowAmbiguousTypes
  #-}

type NatTran a = (Functor f, Functor f') => f a -> f' a

to_assert :: (Functor f, Eq b) => (a -> b) -> NatTran a -> NatTran b -> f a -> Bool
to_assert g h h' f = (fmap g . h) f == (h' . fmap g) f

which is later made specific to a particular natural transformation:

maybe_to_list :: Maybe a -> [a]
maybe_to_list Nothing  = []
maybe_to_list (Just x) = [x]

test_func :: Num a => a -> (a, a)
test_func x = (x, x + 1)

assertions = map (to_assert test_func maybe_to_list) [Nothing, Just 1]

but I’m getting this from ghc:

Could not deduce (Functor f0) arising from a use of ‘fmap’
from the context (Functor f, Eq b)
  bound by the type signature for interactive:IHaskell465.to_assert :: (Functor f, Eq b) => (a -> b) -> interactive:IHaskell465.NatTran a -> interactive:IHaskell465.NatTran b -> f a -> Bool at :2:14-83
The type variable ‘f0’ is ambiguous
Note: there are several potential instances:
  instance Monad m => Functor (Data.Vector.Fusion.Bundle.Monadic.Bundle m v) -- Defined in ‘Data.Vector.Fusion.Bundle.Monadic’
  instance Functor Data.Vector.Fusion.Util.Box -- Defined in ‘Data.Vector.Fusion.Util’
  instance Functor Data.Vector.Fusion.Util.Id -- Defined in ‘Data.Vector.Fusion.Util’
  ...plus 27 others
In the first argument of ‘(.)’, namely ‘fmap g’
In the expression: fmap g . h
In the first argument of ‘(==)’, namely ‘(fmap g . h) f’

Can anyone offer some advice?

Thanks,
-db


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