FoldWhile and FoldWhileList

Question

Mathematica has had NestWhile and NestWhileList for some time. But, to date, it has not implemented a built-in FoldWhile or a FoldWhileList. So, since these constructs seem useful to me, I have tried to brew my own. Here are my current implementations. Anyone have suggestions on how either of these might be improved. I'd be particularly interested in a variant of FoldWhile that did not require as much memory as FoldWhileList.

 FoldWhileList[f_, init_, list_, test_, m_, max_] := 
 Block[{i = 0}, 
    NestWhileList[(i = i + 1; f[#, Part[list, i]]) &, init, test, m, max]]

and

 FoldWhile[f_, init_, list_, test_, m_, max_] := 
    Last[FoldWhileList[f, init, list, test, m, max]]

Answer 1

Implementation

Here are my versions. I will start with FoldWhile:

Clear[dressInCtr];
dressInCtr[test_, max_] := 
   Module[{ctr = 0}, (++ctr <= max ) && test[##] &]

Clear[FoldWhile];
FoldWhile[f_, test_, start_, secargs_List, max_Integer] :=
   FoldWhile[f, dressInCtr[test, max], start, secargs];

FoldWhile[f_, test_, start_, secargs_List] :=
  Module[{last = start},
    Fold[
      If[test[##], last = f[##], Return[last, Fold]] &, 
      start, 
      secargs]];

The FoldWhileList is a bit more involved:

Clear[FoldWhileList];
FoldWhileList[f_, test_, start_, secargs_List, max_Integer] :=
   FoldWhileList[f, dressInCtr[test, max], start, secargs];
FoldWhileList[f_, test_, start_, secargs_List] :=
Module[{tag},
   If[# === {}, {start}, Prepend[First@#, start]] &@
    Reap[
      Fold[
        If[test[##], Sow[f[##],tag], Return[Null, Fold]] &, 
        start, 
        secargs], 
      _, #2 &][[2]]]

Examples

Here are some examples:

FoldWhileList[Plus,#2<5&,0,Range[30]]

(* {0,1,3,6,10}  *)

FoldWhileList[Plus,#2<5&,0,Range[30],3]

(* {0,1,3,6} *)

FoldWhile[Plus,#2<5&,0,Range[30]]

(* 10  *)

FoldWhile[Plus,#2<5&,0,Range[30],3]

(* 6 *)

Remarks

I chose to use Fold itself as an economical way to implement FoldWhile and FoldWhileList. It helped that the two-argument version of Return (undocumented) could be used here. I also found it simplest to implement the extended form with a fifth parameter giving maximal number of iterations, by dressing the test criteria in a closure, which is done via a closure generator function dressInCtr. This also seems to be a good illustration of the usefulness of closures.

Answer 2

These are the first methods that came to mind. I'll have to leave comparing them to the other answers for later.

FoldWhile[f_, start_, rest_, test_] :=
 Module[{g},
   g[_, x_?test] := x;
   g[last_, _] := Return[last, Fold];
   Fold[# ~g~ f@## &, start, rest]
 ]

FoldWhile[Plus, 0, Range@100, # < 30 &]

28

FoldWhileList[f_, start_, rest_, test_] :=
 Module[{bag = Internal`Bag[start], g},
  g[x_?test] := (Internal`StuffBag[bag, x]; x);
  g[else_] := Return[Null, Fold];
  Fold[g @ f @ ## &, start, rest];
  Internal`BagPart[bag, All]
 ]

FoldWhileList[Plus, 0, Range@100, # < 30 &]

{0, 1, 3, 6, 10, 15, 21, 28}

Answer 3

foldWhile[function_, check_, x_, list_, m_: Infinity] :=
 Module[{counter = 0, out, restart, newValue, result = x, 
   max = Min[m, Length@list]},
  Label[restart];
  ++counter;
  newValue = list[[counter]];
  If[! check[result, newValue] || counter >= max, Goto[out]];
  result = function[result, newValue];
  Goto[restart];
  Label[out];
  result
  ]

Another one

foldWhile[function_, check_, x_, list_, m_: Infinity] :=
 Module[{max = Min[m, Length@list]},
  (Composition @@ list~Take~max)[#][x] //. {
    res_[Except[#, next_][rest_]][val_] /; check[res, next] :> 
     function[val, res][rest][next],
    res_[_][val_] :> function[val, res]
    }
  ]

For both

foldWhileList[f_, test_, start_, rest___] := Module[{tag}, Reap[
    foldWhile[
     Sow[f@##, tag] &, test, Sow[start, tag], rest], tag][[-1, 1]]]

Answer 4

Just FYI, Mathematica 12.2 introduces FoldWhile and FoldWhileList with the intended usages.