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Pattern evaluation depending on order of definitions

• To: mathgroup at smc.vnet.net
• Subject: [mg74610] Pattern evaluation depending on order of definitions
• From: "Hannes Kessler" <HannesKessler at hushmail.com>
• Date: Wed, 28 Mar 2007 01:42:24 -0500 (EST)

Hello Mathematica experts,

please consider the following 2 examples:

_g[1] := -1;
_g[n_Integer] := 1;
g["something"][1]
--> -1

_h[n_Integer] := 1;
_h[1] := -1;
h["something"][1]
--> 1

The first example is what I want: Objects with head g applied to 1
should return -1 and applied to other integers should return +1. The
only difference in the second example is the order of the definitions.
It appears that Mathematica does not check for further definitions
matching h["something"][1] more accurate.

This is different in the following two examples:

gg[1] := -1;
gg[n_Integer] := 1;
gg[1]
--> -1

hh[n_Integer] := 1;
hh[1] := -1;
hh[1]
--> -1

Here, the order of the definitions has no influence. Mathematica
checks all definitions and chooses the best matching one. What is the
reason for this different behaviour?

Thanks in advance,
Hannes Kessler