Re: composing functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg45556] Re: composing functions*From*: poujadej at yahoo.fr (Jean-Claude Poujade)*Date*: Wed, 14 Jan 2004 01:26:11 -0500 (EST)*References*: <btthta$so5$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Pedro L <pedrito6 at softhome.net> wrote in message news:<btthta$so5$1 at smc.vnet.net>... > Hi! > > I would like to find a way for composing a list of functions over a > list of numbers. > > I have the list {{f, g, h}, {a, b, c, d}} > (f, g, h are functions and a, b, c, d are numbers) > I would like to obtain h[g[f[a, b], c], d] > > Since it's for a real program, I had to do it in "any" way. So I did > it as I show below: > > > In[1]:= kk = {{f, g, h}, {a, b, c, d}} > > Out[1]= {{f, g, h}, {a, b, c, d}} > > In[2]:= result1 = {kk[[2,1]]}; For[i = 1, i < Length[kk[[2]]], i++, AppendTo[result1, kk[[1,i]]]; > AppendTo[result1, kk[[2,i + 1]]]]; result1 > > Out[2]= {a, f, b, g, c, h, d} > > In[3]:= result2 = StringJoin @@ ToString /@ result1 > > Out[3]= afbgchd > > In[4]:= result3 = StringInsert[result2, "~", Range[2, StringLength[result2]]] > > Out[4]= a~f~b~g~c~h~d > > In[5]:= result4 = ToExpression[result3] > > Out[5]= h[g[f[a, b], c], d] > > > > > But I'm really sure that it can be done much better. > > Could you help me? This is my solution: In[1]:=transform[fgh_List, abcd_List]:= First[{fgh, abcd} //. {{{f_,ff___},{a_,b_,bb___}} -> {f[a,b],{ff},{bb}}, {ff_,{g_,h___},{c_,d___}} -> {g[ff,c],{h},{d}}}]; In[2]:=transform[{f,g,h,i},{a,b,c,d,e}] Out[2]=i[h[g[f[a,b],c],d],e] hth --- jcp