<div dir="ltr">Hi,<div><br></div><div>still does not compile</div><div><br></div><div><div>sumList :: (Fractional a) => [a] -> a</div><div>sumList [] = 0</div><div>sumList (x:xs) = x + (sumList xs)</div><div><br></div><div>lengthList :: (Fractional a) => [t] -> a</div><div>lengthList [] = 0</div><div>lengthList (_:xs) = 1 + (lengthList xs)</div><div><br></div><div>meanList :: (Num a, Fractional b) => [a] -> b</div><div>meanList xs = (sumList xs) / (lengthList xs)</div></div><div><br></div><div>i know </div><div><br></div><div><div>meanList :: (Fractional b) => [b] -> b</div><div>meanList xs = (sumList xs) / (lengthList xs)</div></div><div><br></div><div>compiles. But why do i have to restrict the inputs to be a list of Fractionals and not Nums??</div><div><br><div class="gmail_extra"><br><div class="gmail_quote">On Fri, Sep 23, 2016 at 11:18 AM, <span dir="ltr"><<a href="mailto:beginners-request@haskell.org" target="_blank">beginners-request@haskell.org</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Send Beginners mailing list submissions to<br>
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1. Re: Beginners Digest, Vol 99, Issue 13 (Tushar Tyagi)<br>
<br>
<br>
------------------------------<wbr>------------------------------<wbr>----------<br>
<br>
Message: 1<br>
Date: Fri, 23 Sep 2016 09:01:18 +0530<br>
From: Tushar Tyagi <<a href="mailto:tushar4r@gmail.com">tushar4r@gmail.com</a>><br>
To: The Haskell-Beginners Mailing List - Discussion of primarily<br>
beginner-level topics related to Haskell <<a href="mailto:beginners@haskell.org">beginners@haskell.org</a>><br>
Subject: Re: [Haskell-beginners] Beginners Digest, Vol 99, Issue 13<br>
Message-ID:<br>
<<a href="mailto:CAEDPzikCmLEpiop-5BGbDaKZK1TifAu6ymF%2BjmJq_rEuMNN_Kg@mail.gmail.com">CAEDPzikCmLEpiop-<wbr>5BGbDaKZK1TifAu6ymF+jmJq_<wbr>rEuMNN_Kg@mail.gmail.com</a>><br>
Content-Type: text/plain; charset="utf-8"<br>
<br>
You can read more about Numbers here:<br>
<a href="https://www.haskell.org/tutorial/numbers.html" rel="noreferrer" target="_blank">https://www.haskell.org/<wbr>tutorial/numbers.html</a><br>
<br>
In your implementation sumList and lengthList both return 'Num' which<br>
doesn't define a division operator. So you have to convert them into<br>
fractional by either changing the signatures of these 2 functions from Num<br>
to Fractional, or use fromIntegral function, (or something else) . Two of<br>
these approaches have been suggested by people here. :)<br>
<br>
Typed using my phone, so excuse my brevity.<br>
<br>
On 23 Sep 2016 6:14 a.m., "Lai Boon Hui" <<a href="mailto:laiboonh@gmail.com">laiboonh@gmail.com</a>> wrote:<br>
<br>
> Hi All,<br>
><br>
> i am overwhelmed by all the helpful responses. Thanks guys.<br>
><br>
> I am more curious about why<br>
><br>
> meanList :: (Num a, Fractional b) => [a] -> b<br>
> meanList xs = (sumList xs) / (lengthList xs)<br>
><br>
> does not compile.<br>
><br>
> 'a' being a Num type seems perfectly fine, (/) returns a Fractional type<br>
> hence 'b' being Fractional seems also fine.<br>
><br>
><br>
><br>
> On Fri, Sep 23, 2016 at 7:13 AM, <<a href="mailto:beginners-request@haskell.org">beginners-request@haskell.org</a><wbr>> wrote:<br>
><br>
>> Send Beginners mailing list submissions to<br>
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>><br>
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>> than "Re: Contents of Beginners digest..."<br>
>><br>
>><br>
>> Today's Topics:<br>
>><br>
>> 1. Newbie question about function type constraints (Lai Boon Hui)<br>
>> 2. Re: Newbie question about function type constraints<br>
>> (Tushar Tyagi)<br>
>> 3. Re: Newbie question about function type constraints<br>
>> (Imants Cekusins)<br>
>> 4. Re: Newbie question about function type constraints<br>
>> (Harald Bögeholz)<br>
>> 5. Re: Newbie question about function type constraints<br>
>> (Sylvain Henry)<br>
>> 6. Re: Newbie question about function type constraints<br>
>> (Sylvain Henry)<br>
>> 7. The meaning of categories constructed from HASK<br>
>> (Dimitri DeFigueiredo)<br>
>><br>
>><br>
>> ------------------------------<wbr>------------------------------<wbr>----------<br>
>><br>
>> Message: 1<br>
>> Date: Thu, 22 Sep 2016 21:19:12 +0800<br>
>> From: Lai Boon Hui <<a href="mailto:laiboonh@gmail.com">laiboonh@gmail.com</a>><br>
>> To: <a href="mailto:beginners@haskell.org">beginners@haskell.org</a><br>
>> Subject: [Haskell-beginners] Newbie question about function type<br>
>> constraints<br>
>> Message-ID:<br>
>> <CAJdQgg=jJYfdRsq+QfBr1aC-<wbr>hS1ft9+4Sp4jopoktg=JnDMirg@<wbr>mail.<br>
>> <a href="http://gmail.com" rel="noreferrer" target="_blank">gmail.com</a>><br>
>> Content-Type: text/plain; charset="utf-8"<br>
>><br>
>> Hi, can someone explain to me why i cannot define meanList as:<br>
>><br>
>> meanList :: (Integral a, Fractional b) => [a] -> a<br>
>> meanList xs = (sumList xs) / (lengthList xs)<br>
>><br>
>> I want to restrict the function to only accept lists like [1,2,3] and<br>
>> return answer 2.0<br>
>><br>
>><br>
>> sumList :: (Num a) => [a] -> a<br>
>> sumList [] = 0<br>
>> sumList (x:xs) = x + (sumList xs)<br>
>><br>
>> lengthList :: (Num a) => [t] -> a<br>
>> lengthList [] = 0<br>
>> lengthList (_:xs) = 1 + (lengthList xs)<br>
>> -------------- next part --------------<br>
>> An HTML attachment was scrubbed...<br>
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>> 20160922/45389bc3/attachment-<wbr>0001.html><br>
>><br>
>> ------------------------------<br>
>><br>
>> Message: 2<br>
>> Date: Thu, 22 Sep 2016 19:36:04 +0530<br>
>> From: Tushar Tyagi <<a href="mailto:tushar4r@gmail.com">tushar4r@gmail.com</a>><br>
>> To: The Haskell-Beginners Mailing List - Discussion of primarily<br>
>> beginner-level topics related to Haskell <<a href="mailto:beginners@haskell.org">beginners@haskell.org</a>><br>
>> Subject: Re: [Haskell-beginners] Newbie question about function type<br>
>> constraints<br>
>> Message-ID:<br>
>> <CAEDPzin_vcZA+hh9ZLFo-<wbr>k91Bn63vaemgQJKqN_P4hsAk+ALzQ@<wbr>mail.<br>
>> <a href="http://gmail.com" rel="noreferrer" target="_blank">gmail.com</a>><br>
>> Content-Type: text/plain; charset="utf-8"<br>
>><br>
>> What happens if you change the signature of meanList to<br>
>><br>
>> meanList :: ( Fractional b) => [b] ->b<br>
>><br>
>> The integrals in [1,2,3] would be converted to [1.0, 2.0, 3.0] before you<br>
>> act upon them.<br>
>><br>
>> On 22 Sep 2016 6:49 p.m., "Lai Boon Hui" <<a href="mailto:laiboonh@gmail.com">laiboonh@gmail.com</a>> wrote:<br>
>><br>
>> Hi, can someone explain to me why i cannot define meanList as:<br>
>><br>
>> meanList :: (Integral a, Fractional b) => [a] -> a<br>
>> meanList xs = (sumList xs) / (lengthList xs)<br>
>><br>
>> I want to restrict the function to only accept lists like [1,2,3] and<br>
>> return answer 2.0<br>
>><br>
>><br>
>> sumList :: (Num a) => [a] -> a<br>
>> sumList [] = 0<br>
>> sumList (x:xs) = x + (sumList xs)<br>
>><br>
>> lengthList :: (Num a) => [t] -> a<br>
>> lengthList [] = 0<br>
>> lengthList (_:xs) = 1 + (lengthList xs)<br>
>><br>
>><br>
>><br>
>> ______________________________<wbr>_________________<br>
>> Beginners mailing list<br>
>> <a href="mailto:Beginners@haskell.org">Beginners@haskell.org</a><br>
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>> 20160922/a092897b/attachment-<wbr>0001.html><br>
>><br>
>> ------------------------------<br>
>><br>
>> Message: 3<br>
>> Date: Thu, 22 Sep 2016 16:06:52 +0200<br>
>> From: Imants Cekusins <<a href="mailto:imantc@gmail.com">imantc@gmail.com</a>><br>
>> To: The Haskell-Beginners Mailing List - Discussion of primarily<br>
>> beginner-level topics related to Haskell <<a href="mailto:beginners@haskell.org">beginners@haskell.org</a>><br>
>> Subject: Re: [Haskell-beginners] Newbie question about function type<br>
>> constraints<br>
>> Message-ID:<br>
>> <<a href="mailto:CAP1qinZcONa4X3nozriFYnbkkguRfBmcFp2r3wMoZ6H3aLGGSQ@mail.gm">CAP1qinZcONa4X3nozriFYnbkkguR<wbr>fBmcFp2r3wMoZ6H3aLGGSQ@mail.gm</a><br>
>> <a href="http://ail.com" rel="noreferrer" target="_blank">ail.com</a>><br>
>> Content-Type: text/plain; charset="utf-8"<br>
>><br>
>> Hello,<br>
>><br>
>> this works too:<br>
>><br>
>> meanList :: (Fractional a) => [a] -> a<br>
>> meanList xs = (sumList xs) / (lengthList xs)<br>
>><br>
>><br>
>> sumList :: (Fractional a) => [a] -> a<br>
>> sumList [] = 0<br>
>> sumList (x:xs) = x + (sumList xs)<br>
>><br>
>><br>
>> lengthList :: (Fractional a) => [t] -> a<br>
>> lengthList [] = 0<br>
>> lengthList (_:xs) = 1 + (lengthList xs)<br>
>> -------------- next part --------------<br>
>> An HTML attachment was scrubbed...<br>
>> URL: <<a href="http://mail.haskell.org/pipermail/beginners/attachments/" rel="noreferrer" target="_blank">http://mail.haskell.org/<wbr>pipermail/beginners/<wbr>attachments/</a><br>
>> 20160922/4c967a0d/attachment-<wbr>0001.html><br>
>><br>
>> ------------------------------<br>
>><br>
>> Message: 4<br>
>> Date: Thu, 22 Sep 2016 16:08:56 +0200<br>
>> From: Harald Bögeholz <<a href="mailto:bo@ct.de">bo@ct.de</a>><br>
>> To: The Haskell-Beginners Mailing List - Discussion of primarily<br>
>> beginner-level topics related to Haskell <<a href="mailto:beginners@haskell.org">beginners@haskell.org</a>><br>
>> Subject: Re: [Haskell-beginners] Newbie question about function type<br>
>> constraints<br>
>> Message-ID: <<a href="mailto:a134a975-6b0f-b364-7db9-6b6a0d99759a@ct.de">a134a975-6b0f-b364-7db9-<wbr>6b6a0d99759a@ct.de</a>><br>
>> Content-Type: text/plain; charset=utf-8<br>
>><br>
>> Am 22.09.16 um 15:19 schrieb Lai Boon Hui:<br>
>> > Hi, can someone explain to me why i cannot define meanList as:<br>
>> ><br>
>> > meanList :: (Integral a, Fractional b) => [a] -> a<br>
>> > meanList xs = (sumList xs) / (lengthList xs)<br>
>> ><br>
>> > I want to restrict the function to only accept lists like [1,2,3] and<br>
>> > return answer 2.0<br>
>><br>
>> It will work like this:<br>
>><br>
>> meanList :: (Integral a, Fractional b) => [a] -> b<br>
>> meanList xs = fromIntegral (sumList xs) / (lengthList xs)<br>
>><br>
>> You probably meant -> b in the type signature, that was a typo.<br>
>><br>
>> And you need to insert fromIntegral to convert to Fractional before you<br>
>> can divide. Now that I see it I am beginning to wonder why it works,<br>
>> though, because I was just about to insert another fromIntegral before<br>
>> lengthList ...<br>
>><br>
>><br>
>> > sumList :: (Num a) => [a] -> a<br>
>> > sumList [] = 0<br>
>> > sumList (x:xs) = x + (sumList xs)<br>
>> ><br>
>> > lengthList :: (Num a) => [t] -> a<br>
>> > lengthList [] = 0<br>
>> > lengthList (_:xs) = 1 + (lengthList xs)<br>
>><br>
>> Hope this helps<br>
>><br>
>><br>
>> --<br>
>> Harald Bögeholz <<a href="mailto:bo@ct.de">bo@ct.de</a>> (PGP key available from servers)<br>
>> Redaktion c't Tel.: <a href="tel:%2B49%20511%205352-300" value="+495115352300">+49 511 5352-300</a> Fax: <a href="tel:%2B49%20511%205352-417" value="+495115352417">+49 511 5352-417</a><br>
>><br>
>> int f[9814],b,c=9814,g,i;long a=1e4,d,e,h;<br>
>> main(){for(;b=c,c-=14;i=<wbr>printf("%04d",e+d/a),e=d%a)<br>
>> while(g=--b*2)d=h*b+a*(i?f[b]:<wbr>a/5),h=d/--g,f[b]=d%g;}<br>
>> (Arndt/Haenel)<br>
>><br>
>> Affe Apfel Vergaser<br>
>><br>
>> /*Heise Medien GmbH & Co. KG * Karl-Wiechert-Allee 10 * 30625 Hannover<br>
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>> Geschäftsführer: Ansgar Heise, Dr. Alfons Schräder*/<br>
>><br>
>><br>
>> ------------------------------<br>
>><br>
>> Message: 5<br>
>> Date: Thu, 22 Sep 2016 16:10:17 +0200<br>
>> From: Sylvain Henry <<a href="mailto:sylvain@haskus.fr">sylvain@haskus.fr</a>><br>
>> To: <a href="mailto:beginners@haskell.org">beginners@haskell.org</a><br>
>> Subject: Re: [Haskell-beginners] Newbie question about function type<br>
>> constraints<br>
>> Message-ID: <<a href="mailto:66b119b3-ff51-74d7-80c5-d19450164508@haskus.fr">66b119b3-ff51-74d7-80c5-<wbr>d19450164508@haskus.fr</a>><br>
>> Content-Type: text/plain; charset="utf-8"; Format="flowed"<br>
>><br>
>> Hi,<br>
>><br>
>> You can define it, but in practice there is no instance of "a" that<br>
>> satisfies both constraints: Integral a and Fractional a<br>
>> > meanList ([1,2,3] :: [Int])<br>
>><br>
>> <interactive>:4:1: error:<br>
>> • No instance for (Fractional Int) arising from a use of ‘meanList’<br>
>><br>
>> > meanList ([1,2,3] :: [Float])<br>
>><br>
>> <interactive>:5:1: error:<br>
>> • No instance for (Integral Float) arising from a use of ‘meanList’<br>
>><br>
>> What you probably want is:<br>
>> meanList :: (Integral a, Fractional b) => [a] -> b<br>
>> meanList xs = fromIntegral (sumList xs) / fromIntegral (lengthList xs)<br>
>><br>
>> Where we convert from the integral type "a" to the fractional type "b"<br>
>> before performing the division.<br>
>><br>
>> > meanList ([1,2,3] :: [Int])<br>
>> 2.0<br>
>><br>
>> Cheers<br>
>> Sylvain<br>
>><br>
>><br>
>> On 22/09/2016 15:19, Lai Boon Hui wrote:<br>
>> > Hi, can someone explain to me why i cannot define meanList as:<br>
>> ><br>
>> > meanList :: (Integral a, Fractional b) => [a] -> a<br>
>> > meanList xs = (sumList xs) / (lengthList xs)<br>
>> ><br>
>> > I want to restrict the function to only accept lists like [1,2,3] and<br>
>> > return answer 2.0<br>
>> ><br>
>> ><br>
>> > sumList :: (Num a) => [a] -> a<br>
>> > sumList [] = 0<br>
>> > sumList (x:xs) = x + (sumList xs)<br>
>> ><br>
>> > lengthList :: (Num a) => [t] -> a<br>
>> > lengthList [] = 0<br>
>> > lengthList (_:xs) = 1 + (lengthList xs)<br>
>> ><br>
>> ><br>
>> ><br>
>> ><br>
>> > ______________________________<wbr>_________________<br>
>> > Beginners mailing list<br>
>> > <a href="mailto:Beginners@haskell.org">Beginners@haskell.org</a><br>
>> > <a href="http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners" rel="noreferrer" target="_blank">http://mail.haskell.org/cgi-<wbr>bin/mailman/listinfo/beginners</a><br>
>><br>
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>> An HTML attachment was scrubbed...<br>
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>> 20160922/1be73068/attachment-<wbr>0001.html><br>
>><br>
>> ------------------------------<br>
>><br>
>> Message: 6<br>
>> Date: Thu, 22 Sep 2016 16:14:48 +0200<br>
>> From: Sylvain Henry <<a href="mailto:sylvain@haskus.fr">sylvain@haskus.fr</a>><br>
>> To: <a href="mailto:beginners@haskell.org">beginners@haskell.org</a><br>
>> Subject: Re: [Haskell-beginners] Newbie question about function type<br>
>> constraints<br>
>> Message-ID: <<a href="mailto:074cbf97-2316-9d70-3fb8-7c8c9904c602@haskus.fr">074cbf97-2316-9d70-3fb8-<wbr>7c8c9904c602@haskus.fr</a>><br>
>> Content-Type: text/plain; charset=utf-8; format=flowed<br>
>><br>
>> On 22/09/2016 16:08, Harald Bögeholz wrote:<br>
>> > It will work like this:<br>
>> > meanList :: (Integral a, Fractional b) => [a] -> b<br>
>> > meanList xs = fromIntegral (sumList xs) / (lengthList xs)<br>
>> ><br>
>> > You probably meant -> b in the type signature, that was a typo.<br>
>> ><br>
>> > And you need to insert fromIntegral to convert to Fractional before you<br>
>> > can divide. Now that I see it I am beginning to wonder why it works,<br>
>> > though, because I was just about to insert another fromIntegral before<br>
>> > lengthList ...<br>
>> It works because in this case lengthList uses the fractional type b to<br>
>> perfom its summation (it doesn't care about the type of the elements in<br>
>> xs).<br>
>><br>
>> Cheers<br>
>> Sylvain<br>
>><br>
>><br>
>> ------------------------------<br>
>><br>
>> Message: 7<br>
>> Date: Thu, 22 Sep 2016 17:26:36 -0600<br>
>> From: Dimitri DeFigueiredo <<a href="mailto:defigueiredo@ucdavis.edu">defigueiredo@ucdavis.edu</a>><br>
>> To: Haskell Cafe <<a href="mailto:haskell-cafe@haskell.org">haskell-cafe@haskell.org</a>>, The Haskell-Beginners<br>
>> Mailing List - Discussion of primarily beginner-level topics<br>
>> related<br>
>> to Haskell <<a href="mailto:beginners@haskell.org">beginners@haskell.org</a>><br>
>> Subject: [Haskell-beginners] The meaning of categories constructed<br>
>> from HASK<br>
>> Message-ID: <<a href="mailto:36383e22-0b32-426d-7c9f-5e611bbca233@ucdavis.edu">36383e22-0b32-426d-7c9f-<wbr>5e611bbca233@ucdavis.edu</a>><br>
>> Content-Type: text/plain; charset=utf-8<br>
>><br>
>> In category theory, there are many ways one can make new categories out<br>
>> of an old one.<br>
>><br>
>> In particular, given a category C one can construct:<br>
>><br>
>> 1. The arrows category of C:<br>
>> arrows in C become objects and<br>
>> commutative squares in C become arrows<br>
>> 2. The slice category of C given an object A:<br>
>> arrows into a distinguished object A become objects in the slice<br>
>> commutative triangles become arrows<br>
>><br>
>> There are also functors going from C to these new categories (and back).<br>
>><br>
>> Are these constructed categories useful when C = `Hask` (the category of<br>
>> haskell types and functions)?<br>
>> What do they represent in programming terms?<br>
>><br>
>> In other words, is there intuition for what the arrows category of Hask<br>
>> is?<br>
>> What about the slice category of Hask over a specific type?<br>
>> Do the functors between these match some programming abstractions?<br>
>><br>
>> Any pointers are much appreciated.<br>
>><br>
>> Thanks,<br>
>><br>
>> Dimitri<br>
>><br>
>><br>
>><br>
>><br>
>> ------------------------------<br>
>><br>
>> Subject: Digest Footer<br>
>><br>
>> ______________________________<wbr>_________________<br>
>> Beginners mailing list<br>
>> <a href="mailto:Beginners@haskell.org">Beginners@haskell.org</a><br>
>> <a href="http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners" rel="noreferrer" target="_blank">http://mail.haskell.org/cgi-<wbr>bin/mailman/listinfo/beginners</a><br>
>><br>
>><br>
>> ------------------------------<br>
>><br>
>> End of Beginners Digest, Vol 99, Issue 13<br>
>> ******************************<wbr>***********<br>
>><br>
><br>
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</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature"><div dir="ltr">Best Regards,<div>Boon Hui</div></div></div>
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