# Impossible to bypass evaluation on returned values?

Following all the great advice on this other question, I'm now fluent with HoldAllComplete and Unevaluated on the input side of quote-type functions. I continued my investigations and produced the following attempt at a generic conversion from expression to captive (or quoted) expression:

ClearAll[captive];
SetAttributes[captive, HoldAllComplete];
captive[expr_ /; AtomQ @ Unevaluated @ expr] := expr
{captive @ head} ~Join~ (captive /@ (Unevaluated @ {args}))
captive[x___] := Throw[{x}];

This is really great and handles almost all my scenarios. To wit, the following abbreviated test set produces the desired results

testSet = {"foo", foo, 12, 0, 3/4, 3.14, 2.72 + 3.14 I,
Infinity, {1, 2, 3}, {1, "a", b}, f, f[b], f[1, "a", b], f[{}],
f[{1, "a", b}], f[a][b], f[a][1, "a", b], f[a][{}],
f[a][{1, "a", b}], Hold[Plus @@ {}], Hold[Plus @@ {1, 2, 3}],
Plus @@ {1, "a", b}, 1 + "a" b, a + b*c};

as we can see in the output of

InputForm /@ testSet,
InputForm /@ captive /@ testSet}] // TraditionalForm

(input on left, output on right)

$\left( \begin{array}{cc} \text{foo} & \text{foo} \\ \text{foo} & \text{foo} \\ 12 & 12 \\ 0 & 0 \\ 3/4 & 3/4 \\ 3.14 & 3.14 \\ 2.72 + 3.14*I & 2.72 + 3.14*I \\ \text{Infinity} & \{\text{DirectedInfinity}, 1\} \\ \{1, 2, 3\} & \{\text{List}, 1, 2, 3\} \\ \{1, \text{a}, b\} & \{\text{List}, 1, \text{a}, b\} \\ f & f \\ f[b] & \{f, b\} \\ f[1, \text{a}, b] & \{f, 1, \text{a}, b\} \\ f[\{\}] & \{f, \{\text{List}\}\} \\ f[\{1, \text{a}, b\}] & \{f, \{\text{List}, 1, \text{a}, b\}\} \\ f[a][b] & \{\{f, a\}, b\} \\ f[a][1, \text{a}, b] & \{\{f, a\}, 1, \text{a}, b\} \\ f[a][\{\}] & \{\{f, a\}, \{\text{List}\}\} \\ f[a][\{1, \text{a}, b\}] & \{\{f, a\}, \{\text{List}, 1, \text{a}, b\}\} \\ \text{Hold}[\text{Plus} \text{@@} \{\}] & \{\text{Hold}, \{\text{Apply}, \text{Plus}, \{\text{List}\}\}\} \\ \text{Hold}[\text{Plus} \text{@@} \{1, 2, 3\}] & \{\text{Hold}, \{\text{Apply}, \text{Plus}, \{\text{List}, 1, 2, 3\}\}\} \\ 1 + \text{a} + b & \{\text{Plus}, 1, \text{a}, b\} \\ 1 + \text{a}*b & \{\text{Plus}, 1, \{\text{Times}, \text{a}, b\}\} \\ a + b*c & \{\text{Plus}, a, \{\text{Times}, b, c\}\} \\ \end{array} \right)$

I get into trouble, however, when a return value of a captive expression has a value. For instance, something as simple as

x = y
(* Out[10]= y *)
captive[x]
(* Out[11]= y *)

traceView2 reveals that captive inspects the Held input, as required, but that the evaluator apparently snatches it on the way out, and we don't get x, the desired result.

In hindsight, I suppose I shouldn't expect more, since the ever-present term-rewriter (evaluator) is just the way MMA is supposed to work. On a guess, I tried

captive[expr_ /; AtomQ @ Unevaluated @ expr] := Unevaluated @ expr

which doesn't seem to make any difference (and, after reading the docs, I'm not surprised, since Unevaluated only seems to have an effect when supplied in a function-argument slot (see this other question in progress related to behavior of Unevaluated).

I could do

captive[expr_ /; AtomQ @ Unevaluated @ expr] := Hold @ expr

or, better,

captive[expr_ /; AtomQ @ Unevaluated @ expr] := If[ValueQ @ expr, Hold @ expr,expr]

but now my output will always have Hold wrapping symbols that have values. I am beginning to suspect that this may be the best I can do, and I'm prepared to accept that answer (it means that my other function, which frees the captive, will have to have to release the particular holds inserted by this process (and not the Holds that were in the original source expressions!?! which means I probably have to mark them specially, but that's for another topic!)

But before giving up, I thought I'd consult you all, who have already been so generous.

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please tell me you did not write that latex array by hand... –  The Toad Mar 19 '12 at 22:19
"Copy as LaTeX" on right click in MMA -- too easy! –  Reb.Cabin Mar 19 '12 at 22:25
I think you almost certainly want something like HoldForm or Defer. –  Mr.Wizard Mar 19 '12 at 22:56
helpful Grid-form displays for captive expressions: gist.github.com/2128704 –  Reb.Cabin Mar 20 '12 at 0:04