This PR adds lemmas for the `filter`, `map` and `filterMap` functions of
the hash map.
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Co-authored-by: jt0202 <johannes.tantow@gmail.com>
Co-authored-by: Johannes Tantow <44068763+jt0202@users.noreply.github.com>
Co-authored-by: Markus Himmel <markus@himmel-villmar.de>
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- `LawfulBEq` extends `ReflBEq`, so in particular `LawfulBEq.rfl` is no
longer valid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 generalizes the typeclass assumptions on monadic `Option`
functions.
`Option.mapA` is now an alias for `Option.mapM`, which now works for
applicative functors. The changed definition is exactly equivalent for
monads which use the default implementation of `map`, and those who
change it will hopefully choose a definition for `map` that is more
efficient and not less efficient. `Option.mapA` is not deprecated in
order to keep the API aligned with `List` (`List.mapA` and `List.mapM`
cannot be unified because the monadic version is much more efficient
than the applicative version).
This PR partially reverts #7818, because the function called
`Option.zipWith` in that PR does not actually correspond to
`List.zipWith`. We choose `Option.merge` as the name instead.
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 adds `Option.pfilter`, a variant of `Option.filter` and several
lemmas for it and other `Option` functions. These lemmas are split off
from #7400.
This PR upstreams `bind_congr` from Mathlib and proves that the minimum
of a sorted list is its head and weakens the antisymmetry condition of
`min?_eq_some_iff`. Instead of requiring an `Std.Antisymm` instance,
`min?_eq_some_iff` now only expects a proof that the relation is
antisymmetric *on the elements of the list*. If the new premise is left
out, an autoparam will try to derive it from `Std.Antisymm`, so existing
usages of the theorem will most likely continue to work.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR makes `simp` able to simplify basic `for` loops in monads other
than `Id`.
This is some prework for #7352, where the `Id` lemmas will be
deprecated.
This PR fixes the definition of `Min (Option α)`. This is a breaking
change. This treats `none` as the least element,
so `min none x = min x none = none` for all `x : Option α`. Prior to
nightly-2025-02-27, we instead had `min none (some x) = min (some x)
none = some x`. Also adds basic lemmas relating `min`, `max`, `≤` and
`<` on `Option`.
This PR adds `Array.replace` and `Vector.replace`, proves the
correspondences with `List.replace`, and reproduces the basic API. In
order to do so, it fills in some gaps in the `List.findX` APIs.
This PR introduces ordered map data structures, namely `DTreeMap`,
`TreeMap`, `TreeSet` and their `.Raw` variants, into the standard
library. There are still some operations missing that the hash map has.
As of now, the operations are unverified, but the corresponding lemmas
will follow in subsequent PRs. While the tree map has already been
optimized, more micro-optimization will follow as soon as the new code
generator is ready.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
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 PR completes aligning `List`/`Array`/`Vector` lemmas about
`flatten`. `Vector.flatten` was previously missing, and has been added
(for rectangular sizes only). A small number of missing `Option` lemmas
were also need to get the proofs to go through.
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 adds lemmas simplifying `for` loops over `Option` into
`Option.pelim`, giving parity with lemmas simplifying `for` loops of
`List` into `List.fold`.
I'd previously added an instance from `ForIn'` to `ForIn`, but this then
caused some non-defeq duplication. It seems fine to just remove the
concrete `ForIn` instances in cases where the `ForIn'` instance exists
too. We can even remove a number of type-specific lemmas in favour of
the general ones.
Should ensure we visit at most as many expr nodes as in the final expr
instead of many possibly overlapping mvar assignments. This is likely
the only way we can ensure acceptable performance in all cases.
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Co-authored-by: Kim Morrison <kim@tqft.net>
