This PR adjusts the experimental module system to make `private` the
default visibility modifier in `module`s, introducing `public` as a new
modifier instead. `public section` can be used to revert the default for
an entire section, though this is more intended to ease gradual adoption
of the new semantics such as in `Init` (and soon `Std`) where they
should be replaced by a future decl-by-decl re-review of visibilities.
This PR adds basic lemmas about lexicographic order on Array and Vector,
achieving parity with List.
Many lemmas are still missing for all three, particularly about how
order interacts with `++`.
This PR upstreams the definition and basic lemmas about `List.finRange`
from Batteries.
Thanks for contributors to Batteries and Mathlib who've previously
worked on this material. Further PRs are welcome here. I'll be adding
more API later.
Defines `mergeSort`, a naive stable merge sort algorithm, replaces it
via a `@[csimp]` lemma with something faster at runtime, and proves the
following results:
* `mergeSort_sorted`: `mergeSort` produces a sorted list.
* `mergeSort_perm`: `mergeSort` is a permutation of the input list.
* `mergeSort_of_sorted`: `mergeSort` does not change a sorted list.
* `mergeSort_cons`: proves `mergeSort le (x :: xs) = l₁ ++ x :: l₂` for
some `l₁, l₂`
so that `mergeSort le xs = l₁ ++ l₂`, and no `a ∈ l₁` satisfies `le a
x`.
* `mergeSort_stable`: if `c` is a sorted sublist of `l`, then `c` is
still a sublist of `mergeSort le l`.
This PR neither adds nor removes material, but improves the organization
of `Init/Data/List/*`.
These files are essentially completely re-ordered, to ensure that
material is developed in a consistent order between `List.Basic`,
`List.Impl`, `List.BasicAux`, and `List.Lemmas`.
Everything is organised in subsections, and I've added some module docs.
This PR upstreams lemmas about List/Array operations already defined in
Lean from std/batteries.
Happy to take suggestions about increasing or decreasing scope.
---------
Co-authored-by: Mario Carneiro <di.gama@gmail.com>
@Kha The new `do` notation works for pure code too.
It automatically inserts `Id` if the expected type is not a monad.
This works great when we are not conflating data and control.
After deleting `Monad List`, we will be able to write functions such as
```lean
def mapWhen (p : Nat → Bool) (f : Nat → Nat) (xs : List Nat) : List Nat := do
for x in xs do
if p x then
x := f x
```
without adding `Id.run` before the `do`.
