@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
Daniel is correct when he says the interaction between choice
case-splits, delta case-splits, and coercions can be subtle.
I believe the following condition
https://github.com/leanprover/lean/blob/master/src/frontends/lean/elaborator.cpp#L111
reduces counter-intuitive behavior. Example, the coercion should not
influence the resulting type.
BTW, by removing this condition, many files in the library broke when I
tried to compile from scratch
make clean-olean
make
I used the following workaround. Given a delta-delta constraint
f a =?= f b
If the terms are types, and no case-split will be performed, then
the delta-delta constraint is eagerly solved.
In principle, we don't need the condition that the terms are types.
However, many files break if we remove it. The problem is that many files in the standard
library are abusing the higher-order unification procedure. The
elaboration problems are quite tricky to solve.
I use the extra condition "the terms are types" because usually if they
are, "f" is morally injective, and we don't really want to unfold it.
Note that the following two cases do not work
check '{1, 2, 3}
check insert 1 (insert 2 (insert 3 empty))
Well, they work if we the num namespace is open, and they are
interpreted as having type (finset num)
