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evaluation - Unevaluated @ {args} versus Unevaluated /@ {args}


Working my way through Robby Villegas's lovely notes on withholding evaluation, I almost got Polish Notation on my first try. Here is my final solution, which seems to work well enough:


ClearAll[lispify];
SetAttributes[lispify, HoldAll];
lispify[h_[args___]] :=
  Prepend[
   lispify /@ Unevaluated @ {args},
   lispify[h]];

lispify[s_ /; AtomQ[s]] := s;

lispify[Unevaluated[2^4 * 3^2]]

produces



{Times, {Power, 2, 4}, {Power, 3, 2}}



My first try had only one difference, namely


lispify /@ Unevaluated /@ {args}


and sent me down a frustrating rabbit hole until I stumbled on the corrected one above.


Would someone be so kind as to explain the details of both the correct and incorrect solution?


EDIT:


As a minor bonus, this enables a nice way to visualize unevaluated expression trees:


ClearAll[stringulateLisp];
stringulateLisp[l_List] := stringulateLisp /@ l;
stringulateLisp[e_] := ToString[e];
ClearAll[stringTree];
stringTree[l_List] := First[l][Sequence @@ stringTree /@ Rest[l]];

stringTree[e_] := e;
ClearAll[treeForm];
treeForm = TreeForm@*stringTree@*stringulateLisp@*lispify;
treeForm[Unevaluated[2^4 + 3^2]]

Mathematica graphics



Answer



You must remember that Unevaluated only "works" when it is the explicit head of an expression. In the non-working format the structure looks like:


TreeForm @ HoldForm[lispify /@ Unevaluated /@ {arg1, arg2}]


enter image description here


Note that Unevaluated does not surround arg1 and arg2 therefore they evaluate prematurely.


Now compare the working structure:


TreeForm @ HoldForm[lispify /@ Unevaluated @ {arg1, arg2}]

enter image description here


Here Unevaluated does surround arg1 and arg2 and evaluation is prevented.


See also:





By the way you can show an unevaluated TreeForm by using an additional Unevaluated to compensate for an apparent evaluation leak.


treeForm =
  Function[expr, TreeForm @ Unevaluated @ Unevaluated @ expr, HoldFirst]

Test:


2^4*3^2 // treeForm

enter image description here


Also possibly of interest: Converting expressions to "edges" for use in TreePlot, Graph


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