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You can reach the person managing the list at beginners-ow...@haskell.org When replying, please edit your Subject line so it is more specific than "Re: Contents of Beginners digest..." Today's Topics: 1. Re: Type * and * -> * (Matthew Low) ---------------------------------------------------------------------- Message: 1 Date: Sat, 13 Mar 2021 00:58:21 -0700 From: Matthew Low <m...@ualberta.ca> To: The Haskell-Beginners Mailing List - Discussion of primarily beginner-level topics related to Haskell <beginners@haskell.org> Subject: Re: [Haskell-beginners] Type * and * -> * Message-ID: <CAC=gtkxyfx4zmcq7r1f4asmkkm4t5zz_ur9ubkfloit-vvd...@mail.gmail.com> Content-Type: text/plain; charset="utf-8" Thanks for the book recommendation! On Fri, Mar 12, 2021 at 11:52 PM Bob Ippolito <b...@redivi.com> wrote: > The first definition is only used as an analogy, it’s a way to represent > Peano numbers as values. > > The second definition is only related to the first in that it uses the > same concept. It is not a breakdown of the first one, it is a completely > separate (and incompatible) way to represent Peano numbers at the type > level (and only as types, notice there are no constructors). You can not > define both of these in the same module with the same names. > > In Haskell a kind is (basically) the type of a type. In modern GHC to make > it even more clear (and to free up * for type operators) you can say Type > instead of *. > > Zero has the kind Type (or *) because it has no arguments, just like Zero > has the type Peano because the constructor has no arguments. > > Succ has the kind Type -> Type because you pass it a Type as an argument > to get a concrete Type. Maybe also has the kind Type -> Type, as does []. > > Generally, beginner Haskell doesn’t use any of this type level > programming. If this is a topic of interest, I recommend this book: > https://thinkingwithtypes.com > > On Fri, Mar 12, 2021 at 22:19 Galaxy Being <borg...@gmail.com> wrote: > >> I found this interesting page <https://wiki.haskell.org/Peano_numbers> >> at Wiki Haskell. Confusing, however, is how it first establishes >> >> data Peano = Zero | Succ Peano >> >> It says >> >> Here Zero and Succ are values (constructors). Zero has type Peano, >> and Succ has type Peano -> Peano. >> >> but then it breaks down each member further a few lines later >> >> data Zero >> data Succ a >> >> and then says >> >> Zero has kind *, and Succ has kind * -> *. The natural numbers are >> represented by types (of kind *) Zero, Succ Zero, Succ (Succ Zero) etc. >> >> Why is it giving two separate treatments and what is meant by the * and * >> -> * ? There's something fundamental I'm missing. >> >> If anyone knows of a really thorough and definitive *and *understandable >> treatment of Haskell types, I'd appreciate it. >> >> LB >> _______________________________________________ >> Beginners mailing list >> Beginners@haskell.org >> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners >> > _______________________________________________ > Beginners mailing list > Beginners@haskell.org > http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://mail.haskell.org/pipermail/beginners/attachments/20210313/acd43640/attachment-0001.html> ------------------------------ Subject: Digest Footer _______________________________________________ Beginners mailing list Beginners@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners ------------------------------ End of Beginners Digest, Vol 152, Issue 6 *****************************************