After this commit we need some more advanced theorems in init/wf, notably function extenstionality.
For this reason I had to refactor the init folder a little bit.
To keep the init folders in both libraries similar, I did the same refactorization in the standard library, even though that was not required for the standard library
@avigad, @fpvandoorn, @rlewis1988, @dselsam
This commit modifies how have-expressions are elaborated.
Now, to process
have H : <type>, from <proof>,
<rest>
we first process the constraints in <type> and <proof> simultaneously.
After all these constraints are solved, the elaborator performs
a Prolog-like cut, and process the constraints in <rest>.
So, all overloads, type classes and coercions in <type> and <proof> are solved
before we start processing <rest>. Moreover, while processing <rest>, we
cannot backtrack to <type> and <proof> anymore.
I fixed all affected proofs in the standard and HoTT libraries in
previous commits pushed today and yesterday. I think most affected proofs were not using a good
style and/or were easy to fix. Here is a common pattern that does not
work anymore.
structure has_scalar [class] (F V : Type) :=
(smul : F → V → V)
infixl ` • `:73 := has_scalar.smul
proposition smul_zero (a : R) : a • (0 : M) = 0 :=
have a • 0 + a • 0 = a • 0 + 0, by rewrite [-smul_left_distrib, *add_zero],
!add.left_cancel this
The `have` doesn't work because Lean can't figure out the type of 0 before
it starts processing `!add.left_cancel this`. This is easy to fix, we just have to
annotate one of the `0`s in the `have`:
proposition smul_zero (a : R) : a • (0 : M) = 0 :=
have a • (0:M) + a • 0 = a • 0 + 0, by rewrite [-smul_left_distrib, *add_zero],
!add.left_cancel this
BTW, all tactics are still being executed after all constraints are solved.
We may change that in the future. I didn't want to execute
the tactics at <proof> before <rest> because of universe
meta-variables. In Lean, unassigned universe meta-variables become
parameters. Moreover, we perform this conversion *before*
we start processing tactics. Reason: universe meta-variables
create many problems for tactics such as `rewrite`, `blast` and `simp`.
Finally, we can recover the previous behavior using the option
set_option parser.checkpoint_have false
Lean was crashing because separate_tokes was traversing a DAG as a tree.
Lean was dying without memory (and getting stack overflows) because the procedure was also converting
the DAG into a tree.
This example also suggests we should reduce the limits for the pretty printer.
@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).
