@Kha `withReader` is a well-behaved version of `adaptReader`. `adaptReader` is
too general, and it often produces counterintuitive elaboration
errors.
Here are two super annoying issues I hit all the time:
1- `adaptReader` + polymorphic code
```
def ex1 : ReaderT Nat IO Unit :=
adaptReader (fun x => x + 1) $
IO.println "foo" -- 3 Errors here failed to synthesize `Monad ?m` and `MonadIO ?m`, and don't know how to synthesize `Type → Type`
```
2- `adaptReader` and notation that requires the expected type
```
structure Context :=
(x y : Nat)
def ex2 : ReaderT Context IO Nat :=
adaptReader (fun s => { s with x := 10 }) $ -- Error at the structure instance
...
```
In the example above, I have to write `fun (s : Context) => ...` to
fix the problem.
The two problems above happen in the old and new frontends. However,
there is a new problem specific for the new frontend. In the new
frontend, a `do` is only elaborated when the expected type is known.
So, `adaptReader (fun ctx => ...) do ...` seldom works :(
As I said above, the issue is that `adaptReader` is too general. Its
type is
```
{ρ ρ' : Type u_1} → {m m' : Type u_1 → Type u_2} → [MonadReaderAdapter ρ ρ' m m'] → {α : Type u_1} → (ρ' → ρ) → m α → m' α
```
`withReader` is a simpler version of `adaptReader`
```
withReader : {ρ : Type u_1} → {m : Type u_1 → Type u_2} → [MonadWithReader ρ m] → {α : Type u_1} → (ρ → ρ) → m α → m α
```
It doesn't have any of the problems above. Moreover, I managed to replace
every single instance of `adaptReader` with `withReader` at the stdlib
and tests. We don't need the `adaptReader` generality.
Now, the following example produces a syntax error.
```lean
macro "foo!" x:term : term => `($x + 1)
check id foo! 10
```
@Kha, I think the heuristic is simple and defensible.
If the new syntax starts and ends with token, than the precedence is
`maxPrec`. Otherwise, it is `leadPrec`.
see #180
@Kha I elaborated it as a definition. It works because we can now
reference Parser declarations in `syntax` command.
This change allowed us to replace `p.getArg 0` with `p` in the
`Websever` demo.
@Kha Note that I had to change the pattern. After I replaced,
```
syntax text : child
```
with
```
syntax Prelim.text : child
```
Thus, I wrote
```
`(child|$t:text)
```
as
```
`(child|$t)
```
It works for this example, but it may be a problem in general.
@Kha We can now delete the command
```
@[termParser] def childStxQuot : Parser :=
checkPrec maxPrec >> (node `Lean.Parser.Term.stxQuot $ symbol "`(child|" >> categoryParser `child 0 >> symbol ")")
```
from the web demo.
@Kha Note that I had to write the weird pattern
```
match_syntax stx with
| `(notation:$prec $items* => $rhs) => expandNotationAux stx prec items rhs
| `(notation $noprec* $items* => $rhs) => expandNotationAux stx none items rhs
| _ => Macro.throwUnsupported
```
with the weird `$noprec*` to match the case where the optional
precedence is not provided. I realized this is not a bug, but
I guess most users will be puzzled by this behavior. If we had a kind
for `notationItem`, I would be able to write
```
`(notation $items:notationItems* => $rhs)
```
@Kha It is not clear to me why I had to change the following line
```
-syntax term ">>>" term : foo
+syntax term:1 ">>>":1 term : foo
```
The test breaks without it.
