This PR eliminates uses of `intros x y z` (with arguments) and updates
the `intros` docstring to suggest that `intro x y z` should be used
instead. The `intros` tactic is historical, and can be traced all the
way back to Lean 2, when `intro` could only introduce a single
hypothesis. Since 2020, the `intro` tactic has superceded it. The
`intros` tactic (without arguments) is currently still useful.
This PR introduces a canonical way to endow a type with an order
structure. The basic operations (`LE`, `LT`, `Min`, `Max`, and in later
PRs `BEq`, `Ord`, ...) and any higher-level property (a preorder, a
partial order, a linear order etc.) are then put in relation to `LE` as
necessary. The PR provides `IsLinearOrder` instances for many core types
and updates the signatures of some lemmas.
**BREAKING CHANGES:**
* The requirements of the `lt_of_le_of_lt`/`le_trans` lemmas for
`Vector`, `List` and `Array` are simplified. They now require an
`IsLinearOrder` instance. The new requirements are logically equivalent
to the old ones, but the `IsLinearOrder` instance is not automatically
inferred from the smaller typeclasses.
* Hypotheses of type `Std.Total (¬ · < · : α → α → Prop)` are replaced
with the equivalent class `Std.Asymm (· < · : α → α → Prop)`. Breakage
should be limited because there is now an instance that derives the
latter from the former.
* In `Init.Data.List.MinMax`, multiple theorem signatures are modified,
replacing explicit parameters for antisymmetry, totality, `min_ex_or`
etc. with corresponding instance parameters.
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 the `@[expose]` attribute to many functions (and changes
some theorems to be by `:= (rfl)`) in preparation for the `@[defeq]`
attribute change in #8419.
This PR adjusts the experimental module system to not export the bodies
of `def`s unless opted out by the new attribute `@[expose]` on the `def`
or on a surrounding `section`.
---------
Co-authored-by: Markus Himmel <markus@lean-fro.org>
This PR moves `ReflBEq` to `Init.Core` and changes `LawfulBEq` to extend
`ReflBEq`.
**BREAKING CHANGES:**
- The `refl` field of `ReflBEq` has been renamed to `rfl` to match
`LawfulBEq`
- `LawfulBEq` extends `ReflBEq`, so in particular `LawfulBEq.rfl` is no
longer valid
This PR cleans up the `Option` development, upstreaming some results
from mathlib in the process.
Notable changes:
- the name `<op>_eq_some_iff` is preferred over `<op>_eq_some`
- the `simp` normal form for `<$>` is `Option.map`, for `>>=` is
`Option.bind` and for `<|>` is `Option.orElse` (for the former two, this
was already true before this PR). All further lemmas about these
operations are now stated only in terms of
`Option.map`/`Option.bind`/`Option.orElse`. Previously, in some cases
both versions were available, with a prime used to disambiguate (the
primed version was usually the "non-ascii-art" version). Now, there are
no lemmas about the ascii-art versions besides the ones turning them
into the non-ascii-art operations, and there is only one version of
every lemma, about the non-ascii-art operation, and named without a
prime.
This PR changes definitions and theorems not to use the membership
instance on `Option` unless the theorem is specifically about the
membership instance.
The reasoning for this change is that the lemma `a ∈ o ↔ o = some a` is
a `simp` lemma, and we generally want theorem statements to use `simp`
normal forms.
One notable exception is the `ForIn'` instance, which must use
`Membership` because unlike `GetElem`, `ForIn'` requires the validity
predicate to be expressed via `Membership`.
This PR reviews the implicitness of arguments across List/Array/Vector,
generally trying to make arguments implicit where possible, although
sometimes correcting propositional arguments which were incorrectly
implicit to explicit.
This PR makes the style of all `List` docstrings that appear in the
language reference consistent.
Relies on #7240 for links and example formatting.
---------
Co-authored-by: Kim Morrison <kim@tqft.net>
This PR moves away from using `List.get` / `List.get?` / `List.get!` and
`Array.get!`, in favour of using the `GetElem` mediated getters. In
particular it deprecates `List.get?`, `List.get!` and `Array.get?`. Also
adds `Array.back`, taking a proof, matching `List.getLast`.
This PR extend the preprocessing of well-founded recursive definitions
to bring assumptions like `h✝ : x ∈ xs` into scope automatically.
This fixes#5471, and follows (roughly) the design written there.
See the module docs at `src/Lean/Elab/PreDefinition/WF/AutoAttach.lean`
for details on the implementation.
This only works for higher-order functions that have a suitable setup.
See for example section “Well-founded recursion preprocessing setup” in
`src/Init/Data/List/Attach.lean`.
This does not change the `decreasing_tactic`, so in some cases there is
still the need for a manual termination proof some cases. We expect a
better termination tactic in the near future.
This PR aligns current coverage of `find`-type theorems across
`List`/`Array`/`Vector`. There are still quite a few holes in this API,
which will be filled later.
This PR completes the alignment of lemmas about monadic functions on
`List/Array/Vector`. Amongst other changes, we change the simp normal
form from `List.forM` to `ForM.forM`, and correct the definition of
`List.flatMapM`, which previously was returning results in the incorrect
order. There remain many gaps in the verification lemmas for monadic
functions; this PR only makes the lemmas uniform across
`List/Array/Vector`.
This was not a great simp lemma, and hurts simp confluence. Better to
just use it locally where it is useful.
Similarly `List.head_eq_iff_head?_eq_some`.
