function construction - How to pass a list of arguments into HoldAll

I have a list of arguments (which in reality is lengthy):

arguments = {a, b, c}
arguments2 = {a_, b_, c_}
f[Sequence@@arguments2] := a + b + c

Note: It seems awkward to define two lists here, there should be a better way to do this.

And I want to numerically integrate a function of those arguments:

int[Sequence@@arguments2] := NIntegrate[f[Sequence@@arguments], {x, 0, 1}]

This does not work because of the HoldAll property of NIntegrate.

Is there a way to do this correctly?

Answer

If your question is a duplicate of Injecting a sequence of expressions into a held expression the simplest solution is the same, the so-called "injector pattern":

{a, b, c} /. _[args__] :> NIntegrate[f[args], {x, 0, 1}]

NIntegrate[f[a, b, c], {x, 0, 1}]

I did not close this as a duplicate however because it seems you would like to approach this problem differently.

You could store your symbols in a single object, e.g.:

syms = Hold[a, b, c];

Then create the Pattern sequence from these:

toPatSeq = ReleaseHold @ Quiet @ Replace[#, x_ :> x_, {1}] &;


toPatSeq @ syms

Sequence[a_, b_, c_]

Now you could define your function with:

syms /. _[args__] :>
  (int[toPatSeq @ syms] := NIntegrate[f[args], {x, 0, 1}])

Check:

? int

Global`int

int[a_,b_,c_]:=NIntegrate[f[a,b,c],{x,0,1}]

This works even if the symbols a, b, c, have values assigned.

If as this example shows you only want an arbitrary sequence of symbols you could also make use of Unique:

syms = Hold @@ Table[Unique[], {3}];

syms /. _[args__] :>
  (int[toPatSeq @ syms] := NIntegrate[f[args], {x, 0, 1}])

?int

Global`int


int[$1_,$2_,$3_]:=NIntegrate[f[$1,$2,$3],{x,0,1}]

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