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<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'>Hi,<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'>I
was wondering what the best way to implement Natural number would be. Is there
a package which already does this?<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'>Here
are some options:<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l0 level1 lfo1'><![if !supportLists]><span
style='font-size:10.0pt;font-family:"Courier New"'><span style='mso-list:Ignore'>1.<span
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
style='font-size:10.0pt;font-family:"Courier New"'>Don’t bother. Just use
Integer.<o:p></o:p></span></p>
<p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l0 level1 lfo1'><![if !supportLists]><span
style='font-size:10.0pt;font-family:"Courier New"'><span style='mso-list:Ignore'>2.<span
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
style='font-size:10.0pt;font-family:"Courier New"'>Use the type <o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>data
Natural = Zero | Succ !Natural<o:p></o:p></span></p>
<p class=MsoListParagraph style='text-indent:-18.0pt;mso-list:l0 level1 lfo1'><![if !supportLists]><span
style='font-size:10.0pt;font-family:"Courier New"'><span style='mso-list:Ignore'>3.<span
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
style='font-size:10.0pt;font-family:"Courier New"'>Use the following definition
taken from the Gentle Introduction to Haskell 98<o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>newtype
Natural = MakeNatural Integer<o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>toNatural ::Integer->
Integer<o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>toNatural
x | x < 0 = error “Can’t create negative naturals!”<o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>
| otherwise = MakeNatural x<o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>fromNatural
:: Natural -> Integer<o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>fromNatural
(MakeNatural i) = i<o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>and
then...<o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'><o:p> </o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>instance
Num Natural where<o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>
fromInteger = toNAtural<o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>
x + y = toNatural (fromNatural x +
fromNatural y)<o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>
x – y = etc..<o:p></o:p></span></p>
<p class=MsoListParagraph><span style='font-size:10.0pt;font-family:"Courier New"'>
x * y = etc...<o:p></o:p></span></p>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal>Which method is best? So far, I’ve been picking option
#1 – just leaving things as they are and using Integer to keep things
simple.<o:p></o:p></p>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal>I’ve got that feeling that [2] would be fast and [3]
would be slow. Comment appreciated on the merits of each.<o:p></o:p></p>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal>Cheers,<o:p></o:p></p>
<p class=MsoNormal><o:p> </o:p></p>
<p class=MsoNormal>Mark Spezzano<o:p></o:p></p>
<p class=MsoNormal><o:p> </o:p></p>
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