This PR reworks the `simp` set around the `Id` monad, to not elide or
unfold `pure` and `Id.run`
In particular, it stops encoding the "defeq abuse" of `Id X = X` in the
statements of theorems, instead using `Id.run` and `pure` to pass back
and forth between these two spellings. Often when writing these with
`pure`, they generalize to other lawful monads; though such changes were
split off to other PRs.
This fixes the problem with the current simp set where `Id.run (pure x)`
is simplified to `Id.run x`, instead of the desirable `x`.
This is particularly bad because the` x` is sometimes inferred with type
`Id X` instead of `X`, which prevents other `simp` lemmas about `X` from
firing.
Making `Id` reducible instead is not an option, as then the `Monad`
instances would have nothing to key on.
---------
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
Co-authored-by: Kim Morrison <kim@tqft.net>
Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
I'd previously added an instance from `ForIn'` to `ForIn`, but this then
caused some non-defeq duplication. It seems fine to just remove the
concrete `ForIn` instances in cases where the `ForIn'` instance exists
too. We can even remove a number of type-specific lemmas in favour of
the general ones.
Sebastian mentioned that the use of the kernel defeq was to work around
a performance issue that was fixed since. Let's see if we can do
without.
This is also a semantic change: Ground terms (no free vars, no mvars)
are reduced at
“all” transparency even if the the transparency setting is default. This
was the case
even before 03f6b87647 switched to the
kernel defeq
checking for performance. It seems that this is rather surprising
behavior from the user
point of view. The fallout on batteries and mathlib is rather limited,
only a few
`rfl` proofs seem to have (inadvertently or not) have relied on this.
The speedcenter reports no significant regressions on core or mathlib.
