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defining a function whose parameter must be a function with two parameters

  • To: mathgroup at smc.vnet.net
  • Subject: [mg130992] defining a function whose parameter must be a function with two parameters
  • From: Roman <rschmied at gmail.com>
  • Date: Sat, 1 Jun 2013 06:28:29 -0400 (EDT)
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  • Delivered-to: l-mathgroup@wolfram.com
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Dear all,
I am trying to define a function F which will only execute if its parameter is a function with two parameters. Let's say I define it thus, without any checks on the parameter pattern f:

In[1] := F[f_] := f[2,3]

There are several ways of calling F:
1) pass it a function of two parameters:
In[2] := F[Function[{a,b},a^2-b^2]]
Out[2] = -5

2) pass it an anonymous function of two parameters:
In[3] := F[#1^2-#2^2 &]
Out[3] = -5

3) pass it a pre-defined function:
In[4] := g[a_,b_] = a^2-b^2;
In[5] := F[g]
Out[5] = -5

My question is: how can I define a pattern in the definition of F[f_] such that this function F will execute these three cases while not executing if called with any other kind of parameter? The following calls should fail, for example:

In[6] := F[Function[{a,b,c},a^2-b^2-3c]]
Out[6] = F[Function[{a,b,c},a^2-b^2-3c]]

In[7] := F[#1^2-#2^2-3#3 &]
Out[7] = F[#1^2-#2^2-3#3 &]

In[8] := h[a_,b_,c_] = a^2-b^2-3c;
In[9] := F[h]
Out[9] = F[h]

Further, for bonus points, if there are multiple definitions of a function, I'd like to pick the one with two parameters:
In[10] := k[a_,b_] = a^2-b^2;
In[11] := k[a_,b_,c_] = a^2-b^2-3c;
In[12] := F[k]
Out[12] = -5

Thanks for any help!
Roman



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