Is there any way to implement a "sequential" With[] in Mathematica? [duplicate]

Question

I want the equivalent of Scheme's let*, or basically, a sequential With that works like this:

With[{a = 0,
      a = a + 1,
      a = a + 1},
      a]

Is there any way to implement this? Everything I tried with Hold/Unevaluated/etc. led nowhere.

Answer 1

This is outside the scope of With. The documentation says:

With[{x=x₀, y=y₀, ...}, expr]

specifies that all occurrences of the symbols x, y, ... in expr should be replaced by x₀, y₀, ...

So even if there was a "sequential" With, it wouldn't be able to understand a = a+1 as updating the value of a. It would always just be a replace rule.

I think you'd be best off with a Module:

Module[{a},
  a = 0;
  a = a+1;
  a = a+1;
  a]

You can write your own command which rewrites the form of the command for you, for example:

letstar[init_List, expr_] :=
  With[{vars = symbols[init]}, 
    Module[vars, CompoundExpression @@ Join[init, {expr}]]]
symbols[init_List] := Union@Hold[init][[1, All, 1]]
SetAttributes[symbols, HoldFirst]
SetAttributes[letstar, HoldFirst]

This assumes that the first argument of letstar is a list of assignments (this is not checked) and holds its form so that they are not performed. Instead, they are passed to symbols which only extracts the left-hand sides and lists unique variables appearing in them. This is passed to a Module as the local variables, the init block is converted into a compound expression and finally expr is evaluated. So if you call

letstar[{a = 0, a = a + 1, a = a + 1}, a]

this gets internally transformed to

Module[{a}, a = 0; a = a+1; a = a+1; a]

and returns

2