Oh man, I came late to this party.<br><br>I'll throw what little weight I have here behind Jerry's argument. Yes, this change to base is not Haskell2010 compatible, but it's still a good change and I hope that Haskell2012 or 2013 or whatever the next version of the standard that comes out incorporates it.<br>
<br>As to why it's a good change:<br><br>(1) People were doing it anyways with bogus Eq instances; the syntactic benefit of being able to use integer literals is huge; using the standard +/-/* etc functions is a nice bonus. For an example, see <a href="http://twanvl.nl/blog/haskell/simple-reflection-of-expressions">http://twanvl.nl/blog/haskell/simple-reflection-of-expressions</a><br>
(2) Pattern matching on numeric literals is what requires Eq, and combined with (1) leads to fragile code. Now, for example,<br><br> fac 0 = 1<br> fac n = n * fac (n-1)<br><br>Now the type of fac explicitly states that it requires Eq to work; with the 'hack' version of Eq in the expressions above, "fac x" doesn't terminate and instead gives x * (x-1) * (x-1-1) * ... forever. Other versions (like the version in this thread with Num (e -> a)) turn fac into a function that always returns bottom.<br>
<br> -- ryan<br><br><div class="gmail_quote">On Tue, Mar 20, 2012 at 12:02 PM, Ryan Ingram <span dir="ltr"><<a href="mailto:ryani.spam@gmail.com">ryani.spam@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
This instance can be made more general without changing the code; change the first line to<br><br>instance Num a => Num (e -> a) where<br><br>I think this version doesn't even require FlexibleInstances.<br><br>This lets you do<br>
<br>f x = if x then 2 else 3<br>g x = if x then 5 else 10<br><br>-- f + g = \x -> if x then 7 else 13<span class="HOEnZb"><font color="#888888"><br><br> -- ryan<br><br></font></span><div class="gmail_quote"><div><div class="h5">
On Mon, Mar 19, 2012 at 10:38 AM, Ozgur Akgun <span dir="ltr"><<a href="mailto:ozgurakgun@gmail.com" target="_blank">ozgurakgun@gmail.com</a>></span> wrote:<br>
</div></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div class="h5">Hi,<div><br></div><div>If you are feeling adventurous enough, you can define a num instance for functions:<div>
<br></div>
<div><font face="'courier new', monospace">{-# LANGUAGE FlexibleInstances #-}</font></div><div>
<font face="'courier new', monospace"><br></font></div><div><font face="'courier new', monospace">instance Num a => Num (a -> a) where</font></div><div><font face="'courier new', monospace"> f + g = \ x -> f x + g x</font></div>
<div><font face="'courier new', monospace"> f - g = \ x -> f x - g x</font></div><div><font face="'courier new', monospace"> f * g = \ x -> f x * g x</font></div><div><font face="'courier new', monospace"> abs f = abs . f</font></div>
<div><font face="'courier new', monospace"> signum f = signum . f</font></div><div><div><font face="'courier new', monospace"> fromInteger = const . fromInteger</font></div><div><font face="'courier new', monospace"><br>
</font></div></div><div><font face="'courier new', monospace">ghci> let f x = x * 2</font></div><div><font face="'courier new', monospace">ghci> let g x = x * 3</font></div><div><font face="'courier new', monospace">ghci> (f + g) 3</font></div>
<div><font face="'courier new', monospace">15</font></div><div><font face="'courier new', monospace">ghci> (f+g+2) 2</font></div><div><font face="'courier new', monospace">17</font></div><div><br>
</div><div>HTH,</div><div>Ozgur <div><br><br><div class="gmail_quote">On 19 March 2012 16:57, <span dir="ltr"><<a href="mailto:sdiyazg@sjtu.edu.cn" target="_blank">sdiyazg@sjtu.edu.cn</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
By arithmetic I mean the everyday arithmetic operations used in engineering.<br>
In signal processing for example, we write a lot of expressions like f(t)=g(t)+h(t)+g'(t) or f(t)=g(t)*h(t).<br>
I feel it would be very natural to have in haskell something like<br>
g::Float->Float<br>
--define g here<br>
h::Float->Float<br>
--define h here<br>
f::Float->Float<br>
f = g+h --instead of f t = g t+h t<br>
--Of course, f = g+h is defined as f t = g t+h t<br>
</blockquote></div><br>
</div></div></div>
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