How to set Block local variables by code?

Question

I need to create a user-defined Block function where the Block variables' values are defined by code. For example, imagine I have:

SetAttributes[myBlock1,HoldAll]
myBlock1[args_]:=Block[{a=1,b=2,c=3,d=4},args]
myBlock1[{a,b,c,d}]

{1, 2, 3, 4}

Now, what I need is something like:

SetAttributes[myBlock2,HoldAll]
varList={"a","b","c","d"};

myBlock2[args_]:=Module[{varArgs},
    varArgs=MapIndexed[ToString@Row[{#1,"=",#2[[1]]}]&,varList];
    ToExpression@ToString@Row[{"Block[",varArgs,",",ToString@args,"]"}]
]

myBlock2[{a,b,c,d}]

{1, 2, 3, 4}

The above function works, but it's very clumsy (using ToExpression) and error-susceptible. I tried something like:

SetAttributes[myBlock3,HoldAll]
varList={"a","b","c","d"};

myBlock3[args_]:=ReleaseHold[Hold@Block[varDef,args]/.varDef:>MapIndexed[(Evaluate@Symbol[#1]=#2[[1]])&,varList]]
myBlock3[{a,b,c,d}]

But without success in the "variables injection." One important point is that a, b, c and d should not escape from the block scope. How can I do that?

Answer 1

The two standard methods are SlotSequence, and the "injector pattern."
Related question on StackOverflow: How to Block Symbols without evaluating them?

SlotSequence

ClearAll[myBlock]

SetAttributes[myBlock, HoldAll]

varList = {"a", "b", "c", "d"};

myBlock[args_] :=
 Function[Null, Block[{##}, args], HoldAll] @@
  (MapIndexed[Set, Join @@ MakeExpression@varList] /. {x_} :> x)

myBlock[{a, b, c, d}]

{1, 2, 3, 4}

Injector pattern

ClearAll[myBlock]

SetAttributes[myBlock, HoldAll]

varList = {"a", "b", "c", "d"};

myBlock[args_] :=
 (MapIndexed[Set, Join @@ MakeExpression@varList] /. {x_} :> x) /.
   _[sets__] :> Block[{sets}, args]

myBlock[{a, b, c, d}]

{1, 2, 3, 4}

Answer 2

Just an alternative, the abuse of Hold pattern

varList = {"a", "b", "c", "d"};

    SetAttributes[myBlock, HoldFirst];

myBlock[args_]:=
   Hold[Block][
      MakeExpression@varList~Hold[Set]~Range@Length@varList // Thread, 
      Hold[args]] // ReleaseHold

Answer 3

I'd like to add that I personally prefer to deal with lists of symbols rather than lists of strings that are implied to convert into symbols later in functions. That way I get errors from incorrectly formated strings early rather then getting them buried deeply in an application when something runs Symbol[string] or worse ToExpression[string] and expects a single symbol. Naturally you can't just have a list of symbols, since they might evaluate, but you can just pretend HoldComplete is List for a moment, and in fact most build-in functions (Map, Sort... the list goes on), don't actually require you to pass things with the List head. Anyway to cut a long rant short, here's a function to convert a list of strings to a HoldComplete filled with symbols:

stringsToSymbols[strings_] := 
 With[{ res =       
       strings/.a_String:>ToExpression[a,InputForm,Hold]//HoldComplete@@#/.Hold[a_]:>a& },
 res/;MatchQ[res,HoldComplete[___Symbol]]]

stringsToSymbols::wrdf="Input strings did not convert nicely to symbol list `1` ";
stringlistToSymHold[s_]:=Message[stringsToSymbols::wrdf,s]

So when needing something like your block function I'll just assume the format:

varList=HoldComplete[a,b,c,d]

Now the above works nicely with the methods presented by Mr. Wizard and Rojo, but I'll show another one just to add it, which is one I've used occasionally. What I do is build the expression-structure using HoldComplete and Lists instead of for instance With Block and similar. I then substitute out all the desired heads at once at the end:

 myBlock[args_] := 
   ReplacePart[
   List[MapIndexed[Set, varList] /. {x_} :> x, 
      args], {{0} -> Block, {1, 0} -> List}]

Here I'd note that I would typically take varList as an input adding varList : HoldComplete[__Symbol] to the function definition, just to avoid reliance on globals.

Answer 4

Here's another possibility worth mentioning that I copy from Daniel Huber, found here
http://forums.wolfram.com/mathgroup/archive/2010/Nov/msg00217.html.

It lacks the conversion from string to symbol, but it's already in other answers.

SetAttributes[CreateBlock, HoldAll];
CreateBlock[lvals_, rvals_, expr_] :=
Module[{v, myBlock, mySet, vals},
    v = Thread[mySet[lvals, rvals]];
    SetAttributes[myBlock, HoldAll];
    myBlock[vals, expr] /. vals -> v /. mySet -> Set /. myBlock -> Block
];