Most notably:
Give le.refl the attribute [refl]. This simplifies tactic proofs in various places.
Redefine the order of trunc_index, and instantiate it as weak order.
Add more about pointed equivalences.
quasireducible are also known as lazyreducible.
There is a lot of work to be done.
We still need to revise blast, and add a normalizer for type class
instances. This commit worksaround that by eagerly unfolding
quasireducible.
Convert two instances of has_zero and has_one to local instance,
and change one "[instance]" to a "[trans_instance]". This (by
accident) fixed a problem Rob had a couple of weeks ago.
@avigad, @fpvandoorn, @rlewis1988, @dselsam
I changed how transitive instances are named.
The motivation is to avoid a naming collision problem found by Daniel.
Before this commit, we were getting an error on the following file
tests/lean/run/collision_bug.lean.
Now, transitive instances contain the prefix "_trans_".
It makes it clear this is an internal definition and it should not be used
by users.
This change also demonstrates (again) how the `rewrite` tactic is
fragile. The problem is that the matching procedure used by it has
very little support for solving matching constraints that involving type
class instances. Eventually, we will need to reimplement `rewrite`
using the new unification procedure used in blast.
In the meantime, the workaround is to use `krewrite` (as usual).
At real.comm_ring, `add` is `@add real real_has_add`.
This is bad for any tactic (e.g., blast) that only unfolds reducible definitions.
`add` is not reducible. So, the tactic will not be able to establish
that `@add real real_has_add` is definitionally equal to `real.add`.
The motivation is to reduce the number of instances generated by ematching.
For example, given
inv_inv: forall a, (a⁻¹)⁻¹ = a
the new heuristic uses ((a⁻¹)⁻¹) as the pattern.
This matches the intuition that inv_inv should be used a simplification
rule.
The default pattern inference procedure would use (a⁻¹). This is bad
because it generates an infinite chain of instances whenever there is a
term (a⁻¹) in the proof state.
By using (a⁻¹), we get
(a⁻¹)⁻¹ = a
Now that we have (a⁻¹)⁻¹, we can match again and generate
((a⁻¹)⁻¹)⁻¹ = a⁻¹
and so on
