Re: defining a function whose parameter must be a function with two

*To*: mathgroup at smc.vnet.net*Subject*: [mg131001] Re: defining a function whose parameter must be a function with two*From*: David Bailey <dave at removedbailey.co.uk>*Date*: Sun, 2 Jun 2013 00:30:14 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <koch6b$t5t$1@smc.vnet.net>

On 01/06/2013 11:08, Roman wrote: > 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 > I don't think you can possibly achieve this with a simple pattern, but don't forget you can use an arbitrary predicate to control a pattern match: F[x_?suitableFunctionQ]:= ......... Now you can test all sorts of possibilities inside your function suitableFunctionQ : If x is an atom, you can retrieve its definitions with DownValues etc. Then you can look for the Function head. This will cover the shorthand pure function notation as well because: In[6]:= #1^2 - #2^2 - 3 #3 & // Head Out[6]= Function Etc. The only problem might be performance! David Bailey http://www.dbaileyconsultancy.co.uk