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<span style="font-family:"Arial",sans-serif">As soon as you have a distinct Lens type, and use something Category-like for composition, you are limiting yourself to composing two lenses to get back a lens (barring a terrible mptc 'solution'). And that is weak.
The only reason I (personally) think lens pulls its weight, and is worth using (unlike every prior lens library, which I never bothered with), is the ability for lenses, prisms, ismorphisms, traversals, folds, etc. to properly degrade to one another and compose
automatically.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Aha. I keep asking whether it’s just the cute ability to re-use (.) that justifies the lack of abstraction in the Lens type. But Dan’s comment has made me remember
something from my own talk on the subject. Here are the types of lenses and traversals (2-parameter versions):<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="Code">type Lens’ s a = forall f. Functor f <o:p></o:p></p>
<p class="Code"> => (a -> f a) -> (s -> f s)<o:p></o:p></p>
<p class="Code">type Traversal’ s a = forall f. Applicative f <o:p></o:p></p>
<p class="Code"> => (a -> f a) -> (s -> f s)<o:p></o:p></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Suppose we have<o:p></o:p></span></p>
<p class="Code">ln1 :: Lens' s1 s2<o:p></o:p></p>
<p class="Code">tr1 :: Traversal' s1 s2<o:p></o:p></p>
<p class="Code">ln2 :: Lens' s2 a<o:p></o:p></p>
<p class="Code">tr2 :: Traversal' s2 a<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Now these compositions are all well typed<o:p></o:p></span></p>
<p class="Code">ln1 . ln2 :: Lens' s1 a<o:p></o:p></p>
<p class="Code">tr1 . tr2 :: Traversal' s1 a<o:p></o:p></p>
<p class="Code">tr1 . ln2 :: Traversal' s1 a<o:p></o:p></p>
<p class="Code">ln1 . tr2 :: Traversal' s1 a<o:p></o:p></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">which is quite remarkable. If Lens’ and Traversal’ were newtypes, you’d need four different operators. (I think that what Dan means by “a terrible mptc solution”
is trying to overload those four operators into one.)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">I don’t know if this exhausts the reasons that lenses are not abstract. I would love to know more, explained in a smilar style.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Incidentally has anyone explored this?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="Code">newtype PolyLens c s a = PL (forall f. c f => (a -> f a) -> s -> f s)<o:p></o:p></p>
<p class="Code"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">I’ve just abstracted over the Functor/Applicative part, so that Lens’ and Traversal’ are both PolyLenses. Now perhaps we can do (.), with a type like<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="Code">(.) :: PolyLens c1 s1 s2 -> PolyLens c2 s2 a -> PolyLens (And c1 c2) s1 a<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">where And is a type function<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="Code">type instance And Functor Applicative = Applicative<o:p></o:p></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">etc<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">I have no idea whether this could be made to work out, but it seems like an obvious avenue so I wonder if anyone has explored it.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:"Calibri",sans-serif;mso-fareast-language:EN-US">Simon<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif">From:</span></b><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri",sans-serif"> Dan Doel [mailto:dan.doel@gmail.com]
<br>
<b>Sent:</b> 28 January 2015 00:27<br>
<b>To:</b> Edward Kmett<br>
<b>Cc:</b> Simon Peyton Jones; ghc-devs@haskell.org<br>
<b>Subject:</b> Re: GHC support for the new "record" package<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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On Tue, Jan 27, 2015 at 6:47 PM, Edward Kmett <<a href="mailto:ekmett@gmail.com" target="_blank">ekmett@gmail.com</a>> wrote:<o:p></o:p></p>
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<o:p> </o:p></p>
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This works great for lenses that don't let you change types.<o:p></o:p></p>
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<o:p> </o:p></p>
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<span style="font-family:"Arial",sans-serif">This is not the only restriction required for this to be an acceptable solution.<o:p></o:p></span></p>
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<span style="font-family:"Arial",sans-serif">As soon as you have a distinct Lens type, and use something Category-like for composition, you are limiting yourself to composing two lenses to get back a lens (barring a terrible mptc 'solution'). And that is weak.
The only reason I (personally) think lens pulls its weight, and is worth using (unlike every prior lens library, which I never bothered with), is the ability for lenses, prisms, ismorphisms, traversals, folds, etc. to properly degrade to one another and compose
automatically. So if we're settling on a nominal Lens type in a proposal, then it is automatically only good for one thing to me: defining values of the better lens type.<o:p></o:p></span></p>
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<span style="font-family:"Arial",sans-serif">-- Dan<o:p></o:p></span></p>
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