This PR adds the types `Std.ExtDTreeMap`, `Std.ExtTreeMap` and
`Std.ExtTreeSet` of extensional tree maps and sets. These are very
similar in construction to the existing extensional hash maps with one
exception: extensional tree maps and sets provide all functions from
regular tree maps and sets. This is possible because in contrast to hash
maps, tree maps are always ordered.
This PR adds an equivalence relation to tree maps akin to the existing
one for hash maps. In order to get many congruence lemmas to eventually
use for defining functions on extensional tree maps, almost all of the
remaining tree map functions have also been given lemmas to relate them
to list functions, although these aren't currently used to prove lemmas
other than congruence lemmas.
This PR adjusts the grind annotation on
`Std.HashMap.map_fst_toList_eq_keys` and variants, so `grind` can reason
bidirectionally between `m.keys` and `m.toList`.
This PR adds unconditional lemmas for
`HashMap.getElem?_insertMany_list`, alongside the existing ones that
have quite strong preconditions. Also for TreeMap (and
dependent/extensional variants).
This PR introduces the modules `Std.Data.DTreeMap.Raw`,
`Std.Data.TreeMap.Raw` and `Std.Data.TreeSet.Raw` and imports them into
`Std.Data`. All modules related to the raw tree maps are imported into
these new modules so that they are now a transitive dependency of `Std`.
This PR is a follow-up to #7695, which removed `simp` attributes from
tree map lemmas with bad discrimination patterns. In this PR, we
introduce some `Ord`-based lemmas that are more simp-friendly.
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Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
This PR provides tests for those tree map functions that are not
verified yet.
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Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
This PR provides lemmas about the tree map function `maxKeyD` and its
interactions with other functions for which lemmas already exist.
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Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
This PR removes simp lemmas about the tree map with a metavariable in
the head of the discrimination pattern.
Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
This PR provides lemmas for the tree map function `maxKey!` and its
interactions with other functions for which lemmas already exist.
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Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
This PR fixes a bug in the definition of the tree map functions `maxKey`
and `maxEntry`. Moreover, it provides lemmas for this function and its
interactions with other function for which lemmas already exist.
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Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
This PR provides lemmas for the tree map function `maxKey?` and its
interations with other functions for which lemmas already exist.
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Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
This PR add missing lemmas about the tree map: `minKey*` variants return
the head of `keys`, `keys` and `toList` are ordered and `getKey*
t.minKey?` equals the minimum.
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Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
This PR provides lemmas for the tree map function `minKeyD` and its
interations with other functions for which lemmas already exist.
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Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
This PR provides lemmas about the tree map function `minKey!` and its
interactions with other functions for which lemmas already exist.
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Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
This PR provides lemmas for the tree map function `minKey` and its
interations with other functions for which lemmas already exist.
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Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
This PR provides lemmas about the tree map function `minKey?` and its
interaction with other functions for which lemmas already exist.
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Co-authored-by: Paul Reichert <datokrat@users.noreply.github.com>
This PR provides lemmas about the tree map that have been introduced to
the hash map in #7289.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR renames the member `insert_emptyc_eq` of the `LawfulSingleton`
typeclass to `insert_empty_eq` to conform to the recommended spelling of
`∅` as `empty`.
See also #7447.
This PR provides lemmas about the tree map function `modify` and its
interactions with other functions for which lemmas already exist.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR provides lemmas for the tree map functions `alter` and `modify`
and their interactions with other functions for which lemmas already
exist.
BREAKING CHANGE: The signature of `size_alter` was corrected for all
four hash map types. Instead of relying on the boolean operations
`contains` and `&&` in the if statements, we now use the `Prop`-based
operations `Membership` and `And`.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR provides lemmas about the tree map function `ofList` and
interactions with other functions for which lemmas already exist.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR provides lemmas about the tree map function `insertMany` and its
interaction with other functions for which lemmas already exist. Most
lemmas about `ofList`, which is related to `insertMany`, are not
included.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR provides lemmas about the tree map functions `foldlM`, `foldl`,
`foldrM` and `foldr` and their interactions with other functions for
which lemmas already exist. Additionally, it generalizes the
`fold*`/`keys` lemmas to arbitrary tree maps, which were previously
stated only for the `DTreeMap α Unit` case.
A later PR will make the hash map functions `fold` and `revFold`
internal and also update their signature to conform to the tree map and
list API. This is out of scope for this PR.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR changes the order of arguments of the folding function expected
by the tree map's `foldr` and `foldrM` functions so that they are
consistent with the API of `List`.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR provides lemmas about the tree map functions `keys` and `toList`
and their interactions with other functions for which lemmas already
exist. Moreover, a bug in `foldr` (calling `foldlM` instead of `foldrM`)
is fixed.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR provides proofs that the raw tree map operations are well-formed
and refactors the file structure of the tree map, introducing new
modules `Std.{DTreeMap,TreeMap,TreeSet}.Raw` and splittting
`AdditionalOperations` into separate files for bundled and raw types.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR provides lemmas about the tree map functions `getKey?`,
`getKey`, `getKey!`, `getKeyD` and `insertIfNew` and their interaction
with other functions for which lemmas already exist.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR provides lemmas for the tree map functions `get`, `get!` and
`getD` in relation to the other operations for which lemmas already
exist.
Internally, the `simp_to_model` tactic was provided two new simp lemmas
to eliminate some common complications that require `rw`'ing before
using `simp_to_model`. However, it is still necessary to sometimes
`revert` some hypotheses.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR provides tree map lemmas for the interaction of `get?` with the
other operations for which lemmas already exist.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR provides tree map lemmas about the interaction of
`containsThenInsert(IfNew)` with `contains` and `insert(IfNew)`.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR adds all missing tree map lemmas about the interactions of the
functions `empty`, `isEmpty`, `contains`, `size`, `insert(IfNew)` and
`erase`.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR implements the functions `modify` and `alter` on the tree map.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR implements the `getKey` functions on the tree map. It also fixes
the naming of the `entryAtIdx` function on the tree set, which should
have been called `atIdx`.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR implements the `getThenInsertIfNew?` and `partition` functions
on the tree map.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR implements the methods `min`, `max`, `minKey`, `maxKey`,
`atIndex`, `getEntryLE`, `getKeyLE` and consorts on the tree map.
In order to implement the proof-based functions such as `min` and
`getEntryLT` in `Queries.lean`, it was necessary to extract `Balanced`
and `Ordered` into new files so that they can be used from
`Queries.lean`.
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Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
