Building a proper `equations` pexpr in Lean is not feasible right now because we
need global+local name resolution, [pattern] attribute retrieval, ... to
reimplement `patexpr_to_pattern`. The `pre_equations` will instead be converted
by the old elaborator using this function (TBD).
With this change, `to_pexpr` can now translate every basic definition body in
`core.lean`.
@kha, `eqn_compiler.lemmas` is false by default.
I will keep them disabled until I remove the inductive compiler.
I'm building the new inductive datatype module (to replace the inductive
compiler), and the lemmas will fail to be proved in the next commits
until the transition is complete.
The idea is to match the precedence used in regular programming
languages, where `x = y || x = z` is parsed as `(x = y) || (x = z)`.
This commit also adds `!x` as notation for `bnot x`
Now tactics supporting locations can also specify the goal among the locations by using the name `⊢` or `|-`. Also `rw at *` is implemented so that it will rewrite any hypotheses or the goal for which the whole sequence of rewrites succeeds. (This is different from `rw at h1 h2 ... hn |-`, which requires that all rewrites run to completion on each specified target.)
@digama0 I moved bitvec back to the main repo, and many nat lemmas.
I want these lemmas here for now. I will need some of them for future
decision procedures.
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`.
