elegance vs. 'quick and dirty': a Mathematica expression beauty contest

*To*: mathgroup at yoda.physics.unc.edu*Subject*: elegance vs. 'quick and dirty': a Mathematica expression beauty contest*From*: gaylord at ux1.cso.uiuc.edu*Date*: Fri, 3 Apr 1992 02:49:02 -0600

a recent discussion of Flattening dealt with going from startlist = {{a,a,a},{a,a},{{b,b},{b,b,b}},{a,a,a,a},{{b,b},{b}}} to finallist = {{a,a,a},{a,a},{b,b},{b,b,b},{a,a,a,a},{b,b},{b}} Three solutions have been proposed: #1 finallist = FixedPoint[ Replace[#,{A___,List[X___List],B___} :> {A,X,B}]&, startlist] Let $A be an unused or local symbol finallist = Flatten[List @@ ( startlist /. List[X___List] :> $A[X] /. {List->$A,$A->List} ) ] /. $A->List #2 f[x_List] := Apply[Join,Map[(If[Head[First[#]] === List, #, {#}] &), x]] #3 f[{x__}] := Sequence[x] /; Not[ And @@ AtomQ /@ {x} ] f[{x__}] := {x} f /@ startlist ========================== #2 and #3 have been proposed by their authors as being 'quick and dirty'. I don't agree at all with the authors. I rank these expressions in terms of 'elegance in the order #2, #3, #1 I think that the definition is #2 is by far the 'best-looking' expression because it is very easily understood and explainable to almost anyone. It also makes excellent use of list manipulation (Join, First), higher-order functions (Map) and anonymous functions (..#..&) and especially because it makes use of the fact that M is comprised of expressions (Head, Apply). I have alot of problems when I have to explain or even try to understand myself an M expression that has 'Hold' in it. It almost always looks like a 'work-around' or kludge. I certainly do not want everyone to write M expressions in the same way (one of the delights of M is that everything can be written almost every way) and i learn the most about M from reading the varied ways of doing the 'same thing' as in the above example. The question I want to raise is: how do people prefer their M expressions to look? Which of the above expressions do you like and why?