This PR splits `Int.DivModLemmas` into a `Bootstrap` and `Lemmas` file,
where it is possible to use `omega` in `Lemmas`.
I'm going to add more theory, particularly about `fdiv` and `tdiv` to
the `Lemmas` file, and would prefer to have access to `omega`.
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 adds `LawfulBEq` instances for `Array` and `Vector`.
(Note this replaces a contribution of @mehbark to Batteries for the
LawfulBEq instance for Vector, which was dropped during the release
process due to conflicts. Thanks for that contribution!)
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 PR adds lemmas relating the operations on
findIdx?/findFinIdx?/idxOf?/findIdxOf?/eraseP/erase on List and on
Array. It's preliminary to aligning the verification lemmas for
`find...` and `erase...`.
This PR makes `take`/`drop`/`extract` available for each of
`List`/`Array`/`Vector`. The simp normal forms differ, however: in
`List`, we simplify `extract` to `take+drop`, while in `Array` and
`Vector` we simplify `take` and `drop` to `extract`. We also provide
`Array/Vector.shrink`, which simplifies to `take`, but is implemented by
repeatedly popping. Verification lemmas for `Array/Vector.extract` to
follow in a subsequent PR.
This PR makes the signatures of `find` functions across
`List`/`Array`/`Vector` consistent. Verification lemmas will follow in
subsequent PRs.
We were previously quite inconsistent about the signature of
`indexOf`/`findIdx` functions across `List` and `Array`. Moreover, there
are still quite large gaps in the verification lemma coverage for these
even at the `List` level.
My intention is to make the signatures consistent by providing:
`findIdx` / `findIdx?` / `findFinIdx?` (these all take a predicate, and
return respectively a `Nat`, `Option Nat`, `Option (Fin l.length)`) and
similarly `idxOf` / `idxOf?` / `finIdxOf?` (which look for an element)
for each of List/Array/Vector. I've seen enough examples by now where
each variant is genuinely the most convenient at the call-site, so I'm
going to accept the cost of having many closely related functions.
*Hopefully* for the verification lemmas we can simp all of these into
"projections" of the `Option (Fin l.length)` versions, and then only
have to specify that.
However, I will not plan on immediately either filling in the missing
verification lemmas (or even deciding what the simp normal forms
relating these operations are), and just reach parity amongst
List/Array/Vector for what is already there.
This PR adds missing monadic higher order functions on
`List`/`Array`/`Vector`. Only the most basic verification lemmas
(relating the operations on the three container types) are provided for
now.
This PR remove simp priorities that are not needed. Some of these will
probably cause complaints from the `simpNF` linter downstream in
Batteries, which I will re-address separately.
This PR uniformizes the naming of `enum`/`enumFrom` (on `List`) and
`zipWithIndex` (on `Array` on `Vector`), replacing all with `zipIdx`. At
the same time, we generalize to add an optional `Nat` parameter for the
initial value of the index (which previously existed, only for `List`,
as the separate function `enumFrom`).
This PR lowers the simp priority of `List/Array/Vector.mem_map`, as
downstream in Mathlib many lemmas currently need their priority raised
to fire before this.
This PR changes the arguments of `List/Array.mapFinIdx` from `(f : Fin
as.size → α → β)` to `(f : (i : Nat) → α → (h : i < as.size) → β)`, in
line with the API design elsewhere for `List/Array`.
This PR defines `Vector.flatMap`, changes the order of arguments in
`List.flatMap` for consistency, and aligns the lemmas for
`List`/`Array`/`Vector` `flatMap`.
