wolfram mathematica - custom function with non-standard evaluation (behaves like Table)

Question

I'd like a function AnyTrue[expr,{i,{i1,i2,...}}] which checks if expr is True for any of i1,i2... It should be as if AnyTrue was Table followed by Or@@%, with the difference that it only evaluates expr until first True is found.

Short-circuiting part is optional, what I'd really like to know is the proper way to emulate Table's non-standard evaluation sequence.

Update 11/14

Here's a solution due to Michael, you can use it to chain "for all" and "there exists" checks

SetAttributes[AllTrue, HoldAll];
SetAttributes[AnyTrue, HoldAll];
AllTrue[{var_Symbol, lis_List}, expr_] := 
  LengthWhile[lis, 
    TrueQ[ReleaseHold[Hold[expr] /. HoldPattern[var] -> #]] &] == 
   Length[lis];
AnyTrue[{var_Symbol, lis_List}, expr_] := 
  LengthWhile[lis, 
    Not[TrueQ[ReleaseHold[Hold[expr] /. HoldPattern[var] -> #]]] &] < 
   Length[lis];
AllTrue[{a, {1, 3, 5}}, AnyTrue[{b, {2, 4, 5}}, EvenQ[a + b]]]
AnyTrue[{a, {1, 3, 5}}, AllTrue[{b, {2, 4, 5}}, EvenQ[a + b]]]

Answer 1

How about this?

SetAttributes[AnyTrue, HoldAll];

AnyTrue[expr_, {var_Symbol, lis_List}] :=
  LengthWhile[lis, 
    Not[TrueQ[ReleaseHold[Hold[expr] /. HoldPattern[var] -> #]]] &
  ] < Length[lis]

Includes short-circuiting via LengthWhile and keeps everything held where necessary so that things work as expected with var has a value outside the function:

In[161]:= x = 777;

In[162]:= AnyTrue[Print["x=", x]; x == 3, {x, {1, 2, 3, 4, 5}}]
During evaluation of In[162]:= x=1
During evaluation of In[162]:= x=2    
During evaluation of In[162]:= x=3
Out[162]= True

The built-in Or is short-circuiting, too, for what it's worth. (but I realize building up the unevaluated terms with e.g. Table is a pain):

In[173]:= Or[Print[1];True, Print[2];False]
During evaluation of In[173]:= 1
Out[173]= True