Now, `cmp` is just a fixed helper function.
In the future, we will be able to use (more efficient) specialized
versions during code generation by defining simp rules.
for ordered_cancel_comm_monoid. The change to partial_order, with a derived lt relation, makes the lt axioms of ordered groups derivable with no additional assumptions.
This modification was suggested by @kha.
TODO:
- Use `simp [-f]` instead of `simp without f`
- Allow users to remove hypothesis from `*`. Example: `simp [*, -h]`
for simplify using all hypotheses but `h`.
See issue #1694.
There is an orthogonal issue. `simp` (and consequently `unfold`) cannot be used to
reduce projections (e.g., `has_add.add`). This issue has been
previously raised by @Armael, but it was not addressed yet.
See Section "Other goodies" at
https://github.com/leanprover/lean/wiki/Refactoring-structures
This commit also improves the support for projections in the
unifier/matcher.
Now, we consider the extra case-split for projections.
Given a projection `proj`, and the constraint `proj s =?= proj t`, we need to try first `s =?= t` and if it fails, then try to reduce.
This is needed in the standard library because we now have constraints such as:
```
@has_le.le ?A ?s ?a ?b =?= @has_le.le nat nat.has_add x y
```
If we reduce the right hand side, we get the unsolvable constraint
```
@has_le.le ?A ?s ?a ?b =?= nat.le x y
```
Before this change, the constraint was `@le ?A ?s ?a ?b =?= @le nat nat.has_add x y`, and we already perform a case-split in this case.
Moreover, projections were eagerly reduced whenever possible.
The extra case-split generates a performance problem in several tests. For example `fib 8 = 34` was timing out.
I worked around this issue by performing the case-split only when the constraint contains meta-variables.
There are also minor issues. Example. `<` is notation for `has_lt.lt`, but `>` is for `gt`.
See discussion at #1438https://github.com/leanprover/lean/pull/1438#discussion_r105007325
@digama0 With this commit, the original `array_list.write` will also
perform a destructive update when the reference counter for `l` is 1.
```lean def write {α} (l : array_list α) : fin l^.length → α → array_list α :=
λ ⟨n, h⟩ v, { l with data := l^.data^.write ⟨n, l^.lt_capacity h⟩ h v }
```
