Cannot Block Plus

Question

It is customary to use the following idiom to partially evaluate something inside a held expression:

f[x_] := 2 x
Block[{f}, Hold[f[1 + 1]] /. x_f :> With[{r = x}, r /; True]]

Out[]= Hold[f[2]]

This works also with built-in symbols, like

Block[{Abs}, Hold[Abs[1 + 1]] /. x_Abs :> With[{r = x}, r /; True]]

Out[]= Hold[Abs[2]]

However, I cannot understand the behaviour of the following

Block[{Plus}, Hold[1 + 2*2] /. x_Plus :> With[{r = x}, r /; True]]

which returns Hold[5] instead of Hold[1+4]. Can someone explain why?

Answer 1

I think my answer to Why does this pattern with Plus not work for numbers? is also the answer here.

---

See Plus in the reference manual:

Unlike other functions, Plus applies built-in rules before user-defined ones. As a result, it is not possible to make definitions such as 2+2=5.

The ability for user-defined rules to supersede built-in ones was lost in Version 3.

---

There is a similar property for Times.

Here is some evidence that rules for Plus are applied internally even when Plus is blocked:

Block[{Plus}, 1 + 2*2 /. Plus -> List]
(*  5  *)

p[x__] := Plus[x];
Block[{p}, p[1, 2*2] /. p -> List]
(*  {1, 4}  *)

Update -- some more evidence:

Block[{Plus}, 
  Hold[1 + 2*2] /. x_Plus :> With[{r = x}, r /; True]] // Trace

Block[{p}, 
  Hold[p[1, 2*2]] /. x_p :> With[{r = x}, r /; True]] // Trace

Answer 2

I closed this as a duplicate of Why does this pattern with Plus not work for numbers? but I think I have something that is general enough to be useful, and it's not applicable to that question.

We may observe that although a plain use of Block[{Plus}, . . .] does not prevent numeric evaluation of Plus we can still make a substitution that does:

Block[{Plus = plus}, Hold @@ {2 + 2}]

Hold[plus[2, 2]]

From there we could replace plus with Plus again. Automating this process:

Attributes[hardBlock] = {HoldAll};

hardBlock[sym : {___Symbol}, body_] :=
  Block[sym, sym = #; body] /. Thread[# :> sym] & @ Module[sym, sym]

Now:

expr := Hold @@ {1 + 2 + 3*4}

Block[{Plus, Times}, expr]   (* original Block behavior for reference *)

hardBlock[{Plus},        expr]
hardBlock[{Times},       expr]
hardBlock[{Plus, Times}, expr]

Hold[15]

Hold[1 + 2 + 12]
Hold[3 + 3 4]
Hold[1 + 2 + 3 4]

And for completeness:

hardBlock[{Plus}, Hold[1 + 2*2] /. x_Plus :> With[{r = x}, r /; True]]

Hold[1 + 2 2]