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<p>Because if you say that your function accept all types which are
instances of Num, then it must accept *all* of them. Even those
who do not define a division, or whose division has a different
behaviour than the fractional one.<br>
</p>
<br>
<div class="moz-cite-prefix">Le 23/09/2016 à 19:53, Lai Boon Hui a
écrit :<br>
</div>
<blockquote
cite="mid:%3CCAJdQggnoHL7N6xZv1Mi=TVe349d=EhwFe9fumgS8560Vi7SchQ@mail.gmail.com%3E"
type="cite">
<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 moz-do-not-send="true"
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
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rgb(204,204,204);padding-left:1ex">Send Beginners
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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 moz-do-not-send="true"
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
moz-do-not-send="true"
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 moz-do-not-send="true"
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 moz-do-not-send="true"
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
moz-do-not-send="true"
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
moz-do-not-send="true"
href="mailto:beginners-request@haskell.org">beginners-request@haskell.org</a><wbr>>
wrote:<br>
><br>
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>><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
moz-do-not-send="true"
href="mailto:laiboonh@gmail.com">laiboonh@gmail.com</a>><br>
>> To: <a moz-do-not-send="true"
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 moz-do-not-send="true"
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>
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>><br>
>> ------------------------------<br>
>><br>
>> Message: 2<br>
>> Date: Thu, 22 Sep 2016 19:36:04 +0530<br>
>> From: Tushar Tyagi <<a
moz-do-not-send="true"
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 moz-do-not-send="true"
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 moz-do-not-send="true"
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
moz-do-not-send="true"
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>
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>> ------------------------------<br>
>><br>
>> Message: 3<br>
>> Date: Thu, 22 Sep 2016 16:06:52 +0200<br>
>> From: Imants Cekusins <<a
moz-do-not-send="true" 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 moz-do-not-send="true"
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 moz-do-not-send="true"
href="mailto:CAP1qinZcONa4X3nozriFYnbkkguRfBmcFp2r3wMoZ6H3aLGGSQ@mail.gm">CAP1qinZcONa4X3nozriFYnbkkguR<wbr>fBmcFp2r3wMoZ6H3aLGGSQ@mail.gm</a><br>
>> <a moz-do-not-send="true"
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>
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>> 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
moz-do-not-send="true" 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 moz-do-not-send="true"
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 moz-do-not-send="true"
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
moz-do-not-send="true" href="mailto:bo@ct.de">bo@ct.de</a>>
(PGP key available from servers)<br>
>> Redaktion c't Tel.: <a
moz-do-not-send="true"
href="tel:%2B49%20511%205352-300"
value="+495115352300">+49 511 5352-300</a> Fax: <a
moz-do-not-send="true"
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>
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>><br>
>> ------------------------------<br>
>><br>
>> Message: 5<br>
>> Date: Thu, 22 Sep 2016 16:10:17 +0200<br>
>> From: Sylvain Henry <<a
moz-do-not-send="true" href="mailto:sylvain@haskus.fr">sylvain@haskus.fr</a>><br>
>> To: <a moz-do-not-send="true"
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 moz-do-not-send="true"
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 moz-do-not-send="true"
href="mailto:Beginners@haskell.org">Beginners@haskell.org</a><br>
>> > <a moz-do-not-send="true"
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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>><br>
>> ------------------------------<br>
>><br>
>> Message: 6<br>
>> Date: Thu, 22 Sep 2016 16:14:48 +0200<br>
>> From: Sylvain Henry <<a
moz-do-not-send="true" href="mailto:sylvain@haskus.fr">sylvain@haskus.fr</a>><br>
>> To: <a moz-do-not-send="true"
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 moz-do-not-send="true"
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
moz-do-not-send="true"
href="mailto:defigueiredo@ucdavis.edu">defigueiredo@ucdavis.edu</a>><br>
>> To: Haskell Cafe <<a moz-do-not-send="true"
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
moz-do-not-send="true"
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 moz-do-not-send="true"
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>
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>><br>
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>><br>
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>><br>
><br>
><br>
><br>
> --<br>
> Best Regards,<br>
> Boon Hui<br>
><br>
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</blockquote>
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<div><br>
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-- <br>
<div class="gmail_signature">
<div dir="ltr">Best Regards,
<div>Boon Hui</div>
</div>
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</blockquote>
<br>
<pre class="moz-signature" cols="72">--
ARJANEN Loïc Jean David
<a class="moz-txt-link-freetext" href="http://blog.luigiscorner.com">http://blog.luigiscorner.com</a>
---
“Computer science is no more about computers than astronomy is about telescopes, biology is about microscopes, or chemistry is about beakers and test tubes. Science is not about tools. It is about how we use them, and what we find out when we do.”
Michael R. Fellows and Ian Parberry</pre>
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