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Re: functional programming excercise from Mastering Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg55280] Re: [mg55212] functional programming excercise from Mastering Mathematica
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Fri, 18 Mar 2005 05:33:56 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

>-----Original Message-----
>From: Torsten Coym [mailto:torsten.coym at eas.iis.fraunhofer.de] 
To: mathgroup at smc.vnet.net
>Sent: Thursday, March 17, 2005 9:29 AM
>Subject: [mg55280] [mg55212] functional programming excercise from 
>Mastering Mathematica
>
>I'm quite new to Mathematica and its functional programming 
>capabilities 
>so I did some reading in John Gray's "Mastering Mathematica". There is 
>an excercise in chapter 6 as follows
>
>Write your own function composeList that works just like the built-in 
>operation with the same name, using FoldList. Conversely, 
>write your own 
>function foldList that works just like the built-in operation with the 
>same name, using ComposeList.
>
>Unfortunately, there is no solution given at the end of the book (or I 
>didn't find it). I could figure out a way to do the first task:
>
>composeList[funlist_List, var_] := FoldList[(#2[#1]) &, var, funlist]
>
>but I can't manage the second task...
>
>I know it's rather academic, but ... any help is welcome!
>
>Torsten
>
>

Torsten,
as...

In[3]:= FoldList[f, x, {a1, a2, a3, a4}]
Out[3]=
{x, f[x, a1], f[f[x, a1], a2], f[f[f[x, a1], a2], a3], 
  f[f[f[f[x, a1], a2], a3], a4]}


...is

In[5]:=
ComposeList[{f[#, a1] &, f[#, a2] &, f[#, a3] &, f[#, a4] &}, x]
Out[5]=
{x, f[x, a1], f[f[x, a1], a2], f[f[f[x, a1], a2], a3], 
  f[f[f[f[x, a1], a2], a3], a4]}

we just have to build the first element in ComposeList from f and {a1,
a2, a3, a4}.



Several ways exist, e.g.

In[35]:= Function[e, f[#, e] &] /@ {a1, a2, a3, a4}
Out[35]=
{f[#1, a1] &, f[#1, a2] &, f[#1, a3] &, f[#1, a4] &}

In[36]:= Function[z, f[z, #]] & /@ {a1, a2, a3, a4}
Out[36]=
{Function[z, f[z, a1]], Function[z, f[z, a2]], Function[z, f[z, a3]], 
  Function[z, f[z, a4]]}

In[37]:= Function /@ Thread[f[#, {a1, a2, a3, a4}]]
Out[37]=
{f[#1, a1] &, f[#1, a2] &, f[#1, a3] &, f[#1, a4] &}

In[38]:=
Thread[Unevaluated[Composition[Function, f][#, {a1, a2, a3, a4}]]]
Out[38]=
{f[#1, a1] &, f[#1, a2] &, f[#1, a3] &, f[#1, a4] &}



--
Hartmut Wolf