<html><head><meta http-equiv="Content-Type" content="text/html charset=windows-1252"><meta http-equiv="Content-Type" content="text/html charset=windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div>Got it:</div><div><br></div><blockquote style="margin: 0 0 0 40px; border: none; padding: 0px;"><div><div><font face="Menlo">{-# LANGUAGE Rank2Types</font></div></div><div><div><font face="Menlo"> AllowAmbiguousTypes</font></div></div><div><div><font face="Menlo"> FlexibleContexts</font></div></div><div><div><font face="Menlo"> #-}</font></div></div><div><div><font face="Menlo"><br></font></div></div><div><div><font face="Menlo">type NatTran f f' a = (Functor f, Functor f') => f a -> f' a</font></div></div><div><div><font face="Menlo"><br></font></div></div><div><div><font face="Menlo">to_assert :: (Functor f, Functor f', Eq (f' b)) => (a -> b) -> NatTran f f' a -> NatTran f f' b -> f a -> Bool</font></div></div><div><div><font face="Menlo">to_assert g h h' f = (fmap g . h) f == (h' . fmap g) f</font></div></div><div><div><font face="Menlo"><br></font></div></div><div><div><font face="Menlo">maybe_to_list :: NatTran Maybe [] a</font></div></div><div><div><font face="Menlo">maybe_to_list Nothing = []</font></div></div><div><div><font face="Menlo">maybe_to_list (Just x) = [x]</font></div></div><div><div><font face="Menlo"><br></font></div></div><div><div><font face="Menlo">test_func :: Num a => a -> (a, a)</font></div></div><div><div><font face="Menlo">test_func x = (x, x + 1)</font></div></div><div><div><font face="Menlo"><br></font></div></div><div><div><font face="Menlo">success = all (to_assert test_func maybe_to_list maybe_to_list) [Nothing, Just 1]</font></div></div><div><div><font face="Menlo"><br></font></div></div><div><div><font face="Menlo">main :: IO ()</font></div></div><div><div><font face="Menlo">main = do</font></div></div><div><div><font face="Menlo"> if success then print "Success!" else print "Failure."</font></div></div><div><div><font face="Menlo"> </font></div></div><div><div><font face="Menlo">main</font></div></div></blockquote><div><div><br></div></div><div>Running this code produces:</div><div><br></div><div><pre style="box-sizing: border-box; overflow: auto; font-size: 14px; padding: 0px; margin-top: 0px; margin-bottom: 0px; line-height: inherit; word-break: break-all; word-wrap: break-word; border: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; border-bottom-right-radius: 0px; border-bottom-left-radius: 0px; white-space: pre-wrap; vertical-align: baseline;">"Success!"</pre><div><br></div></div><div>=================================================</div><div><br></div>Hi all,<div><br></div><div>In doing the challenge problems at the end of chapter 10 (<i>Natural Transformations</i>) in Bartosz Milewski’s “Category Theory for Programmers”, I’m trying to write a generic naturality checker:</div><div><br></div><blockquote style="margin: 0 0 0 40px; border: none; padding: 0px;"><div><font face="Menlo">{-# LANGUAGE Rank2Types</font></div><div><font face="Menlo"> AllowAmbiguousTypes</font></div><div><font face="Menlo"> #-}</font></div><div><font face="Menlo"><br></font></div><div><font face="Menlo">type NatTran a = (Functor f, Functor f') => f a -> f' a</font></div><div><font face="Menlo"><br></font></div><div><font face="Menlo">to_assert :: (Functor f, Eq b) => (a -> b) -> NatTran a -> NatTran b -> f a -> Bool</font></div><div><font face="Menlo">to_assert g h h' f = (fmap g . h) f == (h' . fmap g) f</font></div></blockquote><div><br></div><div>which is later made specific to a particular natural transformation:</div><div><br></div><blockquote style="margin: 0 0 0 40px; border: none; padding: 0px;"><div><font face="Menlo">maybe_to_list :: Maybe a -> [a]</font></div><div><font face="Menlo">maybe_to_list Nothing = []</font></div><div><font face="Menlo">maybe_to_list (Just x) = [x]</font></div><div><font face="Menlo"><br></font></div><div><font face="Menlo">test_func :: Num a => a -> (a, a)</font></div><div><font face="Menlo">test_func x = (x, x + 1)</font></div><div><font face="Menlo"><br></font></div><div><font face="Menlo">assertions = map (to_assert test_func maybe_to_list) [Nothing, Just 1]</font></div></blockquote><div><br></div><div>but I’m getting this from ghc:</div><div><br></div><div><span style="color: rgb(255, 0, 0); font-family: monospace; font-size: 14px; font-style: italic; white-space: pre; background-color: rgb(255, 255, 255);">Could not deduce (Functor f0) arising from a use of ‘fmap’</span><br style="box-sizing: border-box; color: rgb(255, 0, 0); font-family: monospace; font-size: 14px; font-style: italic; white-space: pre;"><span style="color: rgb(255, 0, 0); font-family: monospace; font-size: 14px; font-style: italic; white-space: pre; background-color: rgb(255, 255, 255);">from the context (Functor f, Eq b)</span><br style="box-sizing: border-box; color: rgb(255, 0, 0); font-family: monospace; font-size: 14px; font-style: italic; white-space: pre;"><span style="color: rgb(255, 0, 0); font-family: monospace; font-size: 14px; font-style: italic; white-space: pre; background-color: rgb(255, 255, 255);"> 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 </span><interactive style="box-sizing: border-box; color: rgb(255, 0, 0); font-family: monospace; font-size: 14px; font-style: italic; white-space: pre;">:2:14-83<br style="box-sizing: border-box;">The type variable ‘f0’ is ambiguous<br style="box-sizing: border-box;">Note: there are several potential instances:<br style="box-sizing: border-box;"> instance Monad m => Functor (Data.Vector.Fusion.Bundle.Monadic.Bundle m v) -- Defined in ‘Data.Vector.Fusion.Bundle.Monadic’<br style="box-sizing: border-box;"> instance Functor Data.Vector.Fusion.Util.Box -- Defined in ‘Data.Vector.Fusion.Util’<br style="box-sizing: border-box;"> instance Functor Data.Vector.Fusion.Util.Id -- Defined in ‘Data.Vector.Fusion.Util’<br style="box-sizing: border-box;"> ...plus 27 others<br style="box-sizing: border-box;">In the first argument of ‘(.)’, namely ‘fmap g’<br style="box-sizing: border-box;">In the expression: fmap g . h<br style="box-sizing: border-box;">In the first argument of ‘(==)’, namely ‘(fmap g . h) f’<br style="box-sizing: border-box;"></interactive></div><div><interactive style="box-sizing: border-box; color: rgb(255, 0, 0); font-family: monospace; font-size: 14px; font-style: italic; white-space: pre;"><br></interactive></div><div>Can anyone offer some advice?</div><div><br></div><div>Thanks,</div><div>-db</div><div><br></div><div><br></div></body></html>