Choosing an initializer list in With

Question

I'm trying to have several initializer lists in a With function and choose which one I want to use. So far I have this:

With[Evaluate@{Unevaluated@{a = 2, b = 3}, Unevaluated@{a = 4, b = 6}}[[1]], a + b]

which doesn't work on a pretext that "Local variable specification Unevaluated[{a=2,b=3}] is not a List.", and gives me With[Unevaluated[{a = 2, b = 3}], a + b] for an answer. Now, if I just feed this same purportedly erroneous expression back to the kernel, it evaluates just fine with the correct result of 5, showing that Unevaluated list not being a list is a rather moot point. But how do I connect Unevaluated with With without me in between?

Answer 1

You can use injector pattern for that:

{Hold[{a = 2, b = 3}], Hold[{a = 4, b = 6}]}[[1]] /. Hold[init_] :> With[init, a + b]

(* 5  *)

{Hold[{a = 2, b = 3}], Hold[{a = 4, b = 6}]}[[2]] /. Hold[init_] :> With[init, a + b]

(* 10 *)

but you can see that Hold is preferred over Unevaluated in such cases.

As an alternative, you can define your own version of With, that would take the held version of initialization:

ClearAll[with]; 
SetAttributes[with, HoldRest];
with[Hold[init_], body_] := With[init, body];

and then

with[{Hold[{a = 2, b = 3}], Hold[{a = 4, b = 6}]}[[1]], a + b]

(* 5 *)

with[{Hold[{a = 2, b = 3}], Hold[{a = 4, b = 6}]}[[2]], a + b]

(* 10 *)

---

EDIT

As a bonus, here is a way to use your code verbatim - wrap it in Block:

Block[{With},        
    SetAttributes[With,HoldAll];        
    With[Evaluate[{Unevaluated[{a=2,b=3}],Unevaluated[{a=4,b=6}]}[[2]]],
        a+b
    ]
]

(* 10 *)

The explanation of why this works is left as an exercise to the reader :)

Answer 2

Variations of this question have been asked before, e.g.: How to set Block local variables by code?
You may also find this question (and linked) of interest: Assigning values to a list of variable names

Your question stands out because of your use of Unevaluated and the confusion that arises. It is key to understand that Unevaluated must appear as the explicit head of an argument before evaluation for it to be stripped. For this an other details of the use of Unevaluated please read this.

In this case you can use Function or (another) With to pass your extracted Unevaluated expression to With:

sets = {Unevaluated@{a = 2, b = 3}, Unevaluated@{a = 4, b = 6}};

With[#, a + b] &[First @ sets]

With[{x = First @ sets}, With[x, a + b]]

5

5

You could also leverage this property of Part to avoid having to apply Unevaluated (or Hold) to every set list manually. Note that with Unevaluated you need the outer { } to prevent this evaluating inside Set.

sets = {Unevaluated[{a = 2, b = 3}, {a = 4, b = 6}]};  (* ignore syntax warning *)

With[#, a + b] &[sets[[1, {1}]]]
With[#, a + b] &[sets[[1, {2}]]]

5
10

Or using the injector pattern than Leonid showed and Hold:

sets = Hold[{a = 2, b = 3}, {a = 4, b = 6}];

sets[[{1}]] /. _[x_] :> With[x, a + b]
sets[[{2}]] /. _[x_] :> With[x, a + b]