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MathGroup Archive 2004

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Re: Reordering Downvalues?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46610] Re: Reordering Downvalues?
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 25 Feb 2004 13:07:03 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <c1h0o9$9rv$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

you do nothing wrong, but Mathematica orders the patterns by itself
to ensure that more special patterns are applied first and this
happens in your case.

Regards
  Jens


Fred Klingener wrote:
> 
> Book Section 2.5.13 (Advanced Topic:  Manipulating Value Lists) walks
> through an example in which two more-or-less independent functions are
> defined in association with g.
> ------------------------------
> In[3]:= g[x_ + y_] := gp[x, y] ; g[x_ y_] := gm[x, y]
> 
> This shows the default ordering used for the definitions.
> 
> In[4]:= DownValues[g]
> Out[4]= {HoldPattern[g[x_ + y_]] :> gp[x, y], HoldPattern[g[x_ y_]] :> gm[x,
> y]}
> 
> This reverses the order of the definitions for g.
> 
> In[5]:= DownValues[g] = Reverse[DownValues[g]]
> Out[5]= {HoldPattern[g[x_ y_]] :> gm[x, y], HoldPattern[g[x_ + y_]] :> gp[x,
> y]}
> -----------------------------------
> I'm able to duplicate the observations here, and I think I understand the
> issues..
> 
> In a slightly different case from section 2.5.6 (Making Definitions for
> Functions) a specific function and a general function are defined.
> ---------------------------------
> In[1]:= f[x] = u
> Out[1]= u
> 
> When the specific expression f[x] appears, it is replaced by u. Other
> expressions of the form f[argument] are, however, not modified.
> 
> In[2]:= f[x] + f[y]
> Out[2]= u + f[y]
> 
> This defines a value for f with any expression as an "argument".
> In[3]:= f[x_] = x^2
> Out[3]= \!\(x\^2\)
> 
> The old definition for the specific expression f[x] is still used, but the
> new general definition for f[x_] is now used to find a value for f[y].
> In[4]:= f[x] + f[y]
> Out[4]= \!\(u + y\^2\)
> 
> ----------------------------
> 
> If I duplicate this definition set, I can query the rules:
> 
> In[213]:= ?f
> Global`f
> f[x] = u,
> f[x_] = x\^2\
> 
> In[223]:= DownValues[f]
> Out[223]= \!\({HoldPattern[f[x]] :> u, HoldPattern[f[x_]] :> x\^2}\)
> 
> But if I attempt to Reverse[] the order using the same approach as that used
> in 2.5.13 the result is different:
> 
> In[225]:= DownValues[f] = Reverse[DownValues[f]]
> Out[225]= \!\({HoldPattern[f[x_]] :> x\^2, HoldPattern[f[x]] :> u}\)
> 
> Here the Out seems to confirm the reversal, but a direct check of the order
> gives:
> 
> In[226]:= DownValues[f]
> Out[226]= \!\({HoldPattern[f[x]] :> u, HoldPattern[f[x_]] :> x\^2}\)
> 
> and a test of f[x]+f[y], which gives u + y^2, confirms that the order is
> unchanged.  What's going on?  What am I doing wrong?  What don't I
> understand?
> 
> TIA,
> 
> Fred Klingener
> 
> Mathematica 5.0.0, Examples from Help Browser


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