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`.
Before this commit, the `by_cases p` tactic would synthesize
`inst : decidable p` type class resolution, and then use the
`cases` tactic (dependent elimination). This would create
problems since occurrences of `inst` would be replaced with
`decidable.is_true h` in one branch, and `decidable.is_false h` in the
other. Where `h`s (we have two of them, one for each branch) are
fresh hypotheses introduced by the `cases` tactic.
For example, assume we have the term in our goal.
`@ite p inst A a b`
This term would become
`@ite p (decidable.is_true h) A a b` (in the first branch where `h : p`)
and
`@ite p (decidable.is_false h) A a b` (in the second where `h : not p`)
Now, suppose we try to executed the following tactic in the first branch
`rw [if_pos h]`
it will fail since `if_pos h` is actually `@if_pos p inst h`, and
we will not be able to unify
`@ite p (decidable.is_true h) A a b =?= @ite p inst ?A ?a ?b`
This commit workarounds this problem by applying cases on
`@decidable.em p inst : p or not p` instead of `inst : decidable p`.
Thus, the term `inst` is not replaced with `decidable.is_true h` and
`decidable.is_false h`.
The new test `tests/lean/run/simp_dif.lean` demonstrates the problem above.
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.
closes#1675
After this commit, the following example works as expected.
```
example (p : nat → Prop) (a b : nat) : a = 0 ∧ b = 0 → p (a + b) → p 0 :=
begin
intros h₁ h₂,
simp [h₁] at *,
/- produces the state
(p : nat → Prop) (a b : nat)
h₁ : true
h₂ : p 0
|- p 0
-/
assumption
end
```
as expected.
Remark: the original issue raised by issue #1675 is actually solved by the
`simp_all` tactic.
It now performs self simplification, and the performance is slightly
better. As described at issue #1675, only non dependent propositions
are considered.
@Armael: this tactic may be useful for you
`rewrite` tactic improvements
- Add support for `auto_param` and `opt_param`
- Order new goals using the same strategies available for `apply`
- Allow user to set configuration object in interactive mode.
@Armael This commit should address the issue you raised about the order
of new goals in the `rewrite` tactic.
See new test tests/lean/run/rw1.lean for examples.
@dselsam `simp` now supports lemmas containing metavariables.
The metavariables are automatically converted into tmp metavars.
The new test contains a few examples.
@dselsam The method `try_user_congr` was leaking a temporary
meta-variable into the formula. The problem in the congruence lemma
```
dif_ctx_simp_congr :
∀ {α : Sort u_1} {b c : Prop} [dec_b : decidable b] {x : b → α} {u : c → α} {y : ¬b → α} {v : ¬c → α}
(h_c : b ↔ c),
(∀ (h : c), x (h_c.mpr h) = u h) →
(∀ (h : ¬c), y ((not_iff_not_of_iff h_c).mpr h) = v h) → dite b x y = dite c u v
```
when the hypothesis `(∀ (h : c), x (h_c.mpr h) = u h)` is processed,
`h_c` is still unassigned. `h_c` was being assigned in a second
loop (the one that I deleted). Do you see any reason for having this
second pass? I think it is an optimization, we can skip the potentially
expensive
```
expr hyp = finalize(m_ctx, rel, r_congr_hyp).get_proof();
expr pf = local_factory.mk_lambda(hyp);
```
if the expression has not been simplified.
Anyway, I removed this code and merged both loops.
I don't think it should impact performance since we barely use custom
congruence lemmas.
