This PR modifies the pretty printing of pi types. Now `∀` will be
preferred over `→` for propositions if the domain is not a proposition.
For example, `∀ (n : Nat), True` pretty prints as `∀ (n : Nat), True`
rather than as `Nat → True`. There is also now an option `pp.foralls`
(default true) that when false disables using `∀` at all, for
pedagogical purposes. This PR also adjusts instance implicit binder
pretty printing — nondependent pi types won't show the instance binder
name. Closes#1834.
The linked RFC also suggests using `_` for binder names in case of
non-dependance. We're tabling that idea. Potentially it is useful for
hygienic names; this could improve how `Nat → True` pretty prints as `∀
(a : Nat), True`, with this `a` that's chosen by implication notation
elaboration. Relatedly, this PR exposes even further the issue where
binder names are reused in a confusing way. Consider: `Nat → Nat → (a :
Nat) → a = a` pretty prints as `∀ (a a a : Nat), a = a`.
The previous implementation was using the following heuristic
```lean
-- heuristic: use non-dependent arrows only if possible for whole group to avoid
-- noisy mix like `(α : Type) → Type → (γ : Type) → ...`.
let dependent := curNames.any fun n => hasIdent n.getId stxBody
```
The result produced by this heuristic was **not** producing an
accidental name capture, but I agree
it was confusing to have `∀ (a : True), ∃ a, a = a : Prop` instead of
`True → ∃ a, a = a : Prop` since there is no dependency.
AFAICT, all examples affected by this commit have a better output now.
cc @digma0 @kha
This feature produced counterintuitive behavior and confused users.
See discussion at #770.
As pointed out by @tydeu, it is not too much work to write `Id.run <|`
before the `do` when we want to use the `do` notation in pure code.
closes#770
After this commit, we have to use an explicit `discard` in code such as
```
def g (x : Nat) : IO Nat := ...
def f (x : Nat) : IO Unit := do
discard <| g x -- type error without the `discard`
IO.println x
```
Motivation: prevent users from making mistakes such as
```
def f (xs : Array Nat) : IO Unit := do
xs.set! 0 1
IO.println xs
```
when they meant to write
```
def f (xs : Array Nat) : IO Unit := do
let xs := xs.set! 0 1
IO.println xs
```
