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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


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