A smarter nested With?

Question

I often find myself writing code that looks a bit like this:

f[x_Integer] := 
  With[
   {
     range = Range[2] + x
   },
   With[
     {
       a = range[[1]],
       b = range[[2]],
       c = g[range]
     },
     h[a,b,c]
   ]
 ];

It would be nice if I could avoid Withs and just write

f[x_Integer] := 
  Let[
   range = Range[2] + x,
   {a,b} = range,
   c = g[range]
   ,
   h[a,b,c]
 ];

which would then automatically expand to the above at definition time.

What I'm asking is a bit similar to this question. There are additional requirements however. The new scoping construct (Let in the above) should:

• Group sequential disjoint assignments into single Withs.
• Thread over List assignments.

Of course, it should not evaluate the left-hand-sides and the right-hand-sides of the assignments while expanding to Withs.

Any proposals for such a scoping construct? (I'll post my version soon).

Answer 1

With this helper function:

SetAttributes[partThread, HoldAll];
partThread[l___, rhs_] :=
  Join @@ Replace[
    MapIndexed[Append[#, First@#2] &, Thread[Hold[{l}]]],
    Hold[s_, i_] :> Hold[s = rhs[[i]]],
    {1}];

The following modification of LetL seems to work according to your specs:

ClearAll[Let, let];
SetAttributes[{Let, let}, HoldAll];

Let /: Verbatim[SetDelayed][lhs_, rhs : HoldPattern[Let[__, _]]] := 
   Block[{With}, Attributes[With] = {HoldAll};
      lhs := Evaluate[rhs /. HoldPattern[With[{}, b_]] :> b]
   ];

Let[args___, body_] := let[{args}, body, {}, {}];

let[{}, body_, {}, _] := With[{}, body];

let[{Set[{s___}, rhs_], rest___}, body_, dec_, syms_] :=
   Module[{temp},
     partThread[s, temp] /. Hold[d___] :>
        let[{temp = rhs, d, rest}, body, dec, syms]
   ];

let[
   {Set[sym_, rhs_], rest___}, 
   body_, 
   {decs___}, 
   {syms___}
] /; FreeQ[Unevaluated[rhs], Alternatives[syms]] :=
     let[{rest}, body, {decs, sym = rhs}, {syms, HoldPattern[sym]}];

let[{args___}, body_, {decs__}, _] :=
   Block[{With},
     Attributes[With] = {HoldAll};
     With[{decs},Evaluate[let[{args}, body, {}, {}]]]
   ];

This works quite similarly to LetL. What it does in addition to LetL is that it collects previous declarations into auxiliary lists stored as extra arguments of let, so that it can group together disjoint declarations. It also threads over arguments, using the partThread helper function. In all other respects it is the same code as LetL.

Here is your example:

f[x_Integer] := 
   Let[range = Range[2] + x, {a, b} = range, c = g[range], h[a, b, c]];

we can check what was generated:

?f

Global`f

  f[x_Integer]:=
    With[{range=Range[2]+x},
       With[{a=range[[1]],b=range[[2]],c=g[range]},h[a,b,c]]]