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`.
I kept a few core methods (e.g., exact_core and apply_core). Reason:
if we use default parameters
meta constant exact (e : expr) (md := semireducible) : tactic unit
then, we will not be able to write
to_expr p >>= exact
The workaround is
do t <- to_expr p, exact t
or
to_expr p >>= (fun x, exact x)
One alternative is to change how we handle default parameters, and
eta-expand applications that involve default parameters.
We may also have an attribute [eta_expand]. Then
attribute [eta_expand] foo
instructs the elaborator to automatically eta-expand foo-applications.
The attribute would give users more control, and avoid potential
performance problems. Without the attribute, then for every function
application the elaborator has to check the type and decide whether it
must be eta-expanded or not.
@gebner @kha What do you think?
simp interacts badly with super's term ordering. I believe a better
approach is to pick the term ordering according to the available simp
rules, as in "More SPASS with Isabelle".
