@nunoplopes @aqjune
I had to add a new primitive to allow you to execute a tactic from the
`main` function. The `main` function is in the `io` monad. The new
primitive has type:
```
meta constant io.run_tactic {α : Type} (a : tactic α) : io α
```
I also added a new test that shows how to use it.
The test displays all declarations that have the `nat` prefix.
cc @kha
@aqjune @nunoplopes: See new tests at tests/lean/run/random.lean
We have two actions in `io`. By default, `io` uses the C++
random number generator, but we can force it to use a `std_gen` with
the action `set_rand_gen`.
def rand (lo : nat := std_range.1) (hi : nat := std_range.2) : io nat
def set_rand_gen : std_gen → io unit
@aqjune @nunoplopes: This commit adds basic support for random numbers.
It defines a random number generator interface, and an basic
implementation based on the Haskell one.
We can add more implementations in the future if neeeded.
The new test program has a few examples.
BTW, this is a pure Lean implementation.
If we need more performance we can provide an implementation
using C++.
@kha We can now solve unification constraints of the form
?m unit =?= itactic
I'm not very confident this new extension will improve usuability
instead of creating new counter-intuitive behavior.
At least, in the process of implementing it, I fixed two bugs,
and removed a nasty hack that was being used in the unifier.
Thus, even if we disable this feature in the future, some good came out
of it.
Although, the new extension locally increases the number of constraints
that can be solved, it may prevent terms that could be elaborated before
from being elaborated. I am not too concerned at this point because
I could not construct a natural example. I encountered one case, but it
was due to a problem that I fixed in the previous commit.
I reconstruct it here for the record. Suppose we have a constraint
?m_1 ?m_2 =?= itactic
Without the fix from the previous commit, `itactic` would unfold too
`id_rhs Type (tactic unit)`, and the constrain would be solved as
?m_1 := (id_rhs Type)
?m_2 := (tactic unit)
It succeeds locally, but the elaboration fails later when it tries to
synthesize the type class `has_bind (id_rhs Type)`.
The previous fixes the problem by making sure `itactic` is unfolded to
`tactic unit` as expected. `id_rhs` is an auxiliary definition
used to implement smart unfolding. That being said, the user could in
principle define `itactic` as `@id Type (tactic unit)`, and the constraint
?m_1 ?m_2 =?= itactic
will be solved as
?m_1 := (@id Type)
?m_2 := (tactic unit)
which is not the solution we want.
@kha This commit fixes the bug we discussed on slack.
I had to repair one of the tests. The broken test made me
realize that if we use the unbundled approach to define something like
`is_semiring`
```
class is_semiring (α : Type) (plus : α → α → α) (mul : α → α → α) (zero : out_param α) (one : out_param α) :=
...
```
Then, to retrieve a `is_semiring` instance, we need to know `α`, `plus`
and `mul`. This is problematic because we may be in a context where one
of them cannot be inferred. This would force user to manually provide
the missing (input) parameter. We are not considering the unbundled
approach for complex algebraic structures such as `semiring`, `ring` and
`field`, but I wanted to document this limitation here since we may face
it in other type classes.
I think it is a bad idea to add back `inout_param` and have both:
`inout_param` and `out_param`. The previous `inout_param` created
many instabilities and hard to diagnose failures.
- An new simp attribute may depend on other existing attributes
- Add `[norm]` simp attribute. It is an extension of the default `[simp]` attribute.
It should be used to add extra rules for normalizing goals.
These extra rules are used to produce normal forms and/or reduce the
number of constants used in a goal. Here is an example coming from a
discussion with @kha. When working with monads, we may want to
eliminate `<$>` by using the lemma `f <$> x = x >>= pure ∘ f`.
This lemma is in the `[norm]` simp set, but it is not in `[simp]`
