This PR introduces a no-op version of `Shrink`, a type that should allow
shrinking small types into smaller universes given a proof that the type
is small enough, and uses it in the iterator library. Because this type
would require special compiler support, the current version is just a
wrapper around the inner type so that the wrapper is equivalent, but not
definitionally equivalent.
While `Shrink` is unable to shrink universes right now, but introducing
it now will allow us to generalize the universes in the iterator library
with fewer breaking changes as soon as an actual `Shrink` is possible.
This PR "monomorphizes" the structure `Std.PRange shape α`, replacing it
with nine distinct structures `Std.Rcc`, `Std.Rco`, `Std.Rci` etc., one
for each possible shape of a range's bounds. This change was necessary
because the shape polymorphism is detrimental to attempts of automation.
**BREAKING CHANGE:** While range/slice notation itself is unchanged,
this essentially breaks the entire remaining (polymorphic) range and
slice API except for the dot-notation(`toList`, `iter`, ...). It is not
possible to deprecate old declarations that were formulated in a
shape-polymorphic way that is not available anymore.
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.
(Almost) only typos in constant names and doc-strings were considered;
grammar was not considered. Also, along others,
`mkDefinitionValInferrringUnsafe` has been fixed :-)
This PR improves the `congr` tactic so that it can handle function
applications with fewer arguments than the arity of the head function.
This also fixes a bug where `congr` could not make progress with
`Set`-valued functions in Mathlib, since `Set` was being unfolded and
making such functions have an apparently higher arity.
This addresses issue #2128 for the `congr` tactic, but not `simp` and
others.
This PR moves the construction of the `Option.SomeLtNone.lt` (and `le`)
relation, in which `some` is less than `none`, to
`Init.Data.Option.Basic` and moves well-foundedness proofs for
`Option.lt` and `Option.SomeLtNone.lt` into `Init.Data.Option.Lemmas`.
This PR proves that the default `toList`, `toListRev` and `toArray`
functions on slices can be described in terms of the slice iterator.
Relying on new lemmas for the `uLift` and `attachWith` iterator
combinators, a more concrete description of said functions is given for
`Subarray`.
This PR replaces all usages of `[:]` slice notation in `src` with the
new `[...]` notation in production code, tests and comments. The
underlying implementation of the `Subarray` functions stays the same.
Notation cheat sheet:
* `*...*` is the doubly-unbounded range.
* `*...a` or `*...<a` contains all elements that are less than `a`.
* `*...=a` contains all elements that are less than or equal to `a`.
* `a...*` contains all elements that are greater than or equal to `a`.
* `a...b` or `a...<b` contains all elements that are greater than or
equal to `a` and less than `b`.
* `a...=b` contains all elements that are greater than or equal to `a`
and less than or equal to `b`.
* `a<...*` contains all elements that are greater than `a`.
* `a<...b` or `a<...<b` contains all elements that are greater than `a`
and less than `b`.
* `a<...=b` contains all elements that are greater than `a` and less
than or equal to `b`.
Benchmarks have shown that importing the iterator-backed parts of the
polymorphic slice library in `Init` impacts build performance. This PR
avoids this problem by separating those parts of the library that do not
rely on iterators from those those that do. Whereever the new slice
notation is used, only the iterator-independent files are imported.
This PR introduces polymorphic slices in their most basic form. They
come with a notation similar to the new range notation. `Subarray` is
now also a slice and can produce an iterator now. It is intended to
migrate more operations of `Subarray` to the `Slice` wrapper type to
make them available for slices of other types, too.
The PR also moves the `filterMap` combinators into `Init` because they
are used internally to implement iterators on array slices.
This PR introduces ranges that are polymorphic, in contrast to the
existing `Std.Range` which only supports natural numbers.
Breakdown of core changes:
* `Lean.Parser.Basic`: Modified the number parser (`Lean.Parser.Basic`)
so that it will only consider a *single* dot to be part of a decimal
number. `1..` will no longer be parsed as `1.` followed by `.`, but as
`1` followed by `..`.
* The test `ellipsisProjIssue` ensures that `#check Nat.add ...succ`
produces a syntax error. After introducing the new range notation (see
below), it returns a different (less nice) error message. I updated the
test to reflect the new error message. (The error message will become
nicer as soon as a delaborator for the ranges is implemented. This is
out of scope for this PR.)
Breakdown of standard library changes:
Modified modules: `Init.Data.Range.Polymorphic` (added),
`Init.Data.Iterators`, `Std.Data.Iterators`
* Introduced the type `Std.PRange` that is parameterized over the type
in which the range operates and the shapes of the lower and upper bound.
* Introduced a new notation for ranges. Examples for this notation are:
`1...*`, `1...=3`, `1...<3`, `1<...=2`, `*...=3`.
* Defined lots of typeclasses for different capabilities of ranges,
depending on their shape and underlying type.
* Introduced `Iter(M).size`.
* Introduced the `Iter(M).stepSize n` combinator, which iterates over an
iterator with the given step size `n`. It will drop `n - 1` values
between every value it emits.
* Replaced `LawfulPureIterator` with a new and better typeclass
`LawfulDeterministicIterator`.
* Simplified some lemma statements in the iterator library such as
`IterM.toList_eq_match`, which unnecessarily matched over a `Subtype`,
hindering rewrites due to type dependencies.
Reasons for the concrete choice of notation:
* `lean4-cli` uses `...`-based notation for the `Cmd` notation and it
clashes with `...a` range notation.
* test `2461` fails when using two-dot-based notation because of the
existing `{ a.. }` notation.
This PR adds a generic `MonadLiftT Id m` instance. We do not implement a
`MonadLift Id m` instance because it would slow down instance resolution
and because it would create more non-canonical instances. This change
makes it possible to iterate over a pure iterator, such as `[1, 2,
3].iter`, in arbitrary monads.
Although `HEq` was abbreviated as `≍` in #8503, many instances of the
form `HEq x y` still remain.
Therefore, I searched for occurrences of `HEq x y` using the regular
expression `(?<![A-Za-z/@]|``)HEq(?![A-Za-z.])` and replaced as many as
possible with the form `x ≍ y`.
This PR introduces a `ForIn'` instance and a `size` function for
iterators in a minimal fashion. The `ForIn'` instance is not marked as
an instance because it is unclear which `Membership` relation is
sufficiently useful. The `ForIn'` instance existing as a `def` and
inducing the `ForIn` instance, it becomes possible to provide more
specialized `ForIn'` instances, with nice `Membership` relations, for
various types of iterators. The `size` function has no lemmas yet.
This PR moves parts of the iterator library from `Std` to `Init`. The
reason is that the polymorphic range API must be in `Init` and it
depends on the iterators.
This PR provides a special empty iterator type. Although its behavior
can be emulated with a list iterator (for example), having a special
type has the advantage of being easier to optimize for the compiler.
This PR replaces special, more optimized `IteratorLoop` instances, for
which no lawfulness proof has been made, with the verified default
implementation. The specialization of the loop/collect implementations
is low priority, but having lawfulness instances for all iterators is
important for verification.
This PR provides the means to reason about "equivalent" iterators.
Simply speaking, two iterators are equivalent if they behave the same as
long as consumers do not introspect their states.
This PR provides the iterator combinator `drop` that transforms any
iterator into one that drops the first `n` elements.
Additionally, the PR removes the specialized `IteratorLoop` instance on
`Take`. It currently does not have a `LawfulIteratorLoop` instance,
which needs to exist for the loop consumer lemmas to work. Having the
specialized instance is low priority.
This PR provides array iterators (`Array.iter(M)`,
`Array.iterFromIdx(M)`), infinite iterators produced by a step function
(`Iter.repeat`), and a `ForM` instance for finite iterators that is
implemented in terms of `ForIn`.
This PR provides the iterator combinators `takeWhile` (forwarding all
emitted values of another iterator until a predicate becomes false)
`dropWhile` (dropping values until some predicate on these values
becomes false, then forwarding all the others).
This PR provides the iterator combinator `filterMap` in a pure and
monadic version and specializations `map` and `filter`. This new
combinator allows to apply a function to the emitted values of a stream
while filtering out certain elements.
`map` should have an optimized `IteratorCollect` implementation but it
turns out that this is not possible without a major refactor of
`IteratorCollect`: `toArrayMapped` requires a proof that the iterator is
finite. If `it.mapM f` is `Finite` but `it` is not, then such a proof
does not exist. `IteratorCollect` needs to take a proof that the loop
will terminate for the given monadic function `f` instead. This will not
be done in this PR.
This PR provides the `take` iterator combinator that transforms any
iterator into an iterator that stops after a given number of steps. The
change contains the implementation and lemmas.
`take` has a special implementation of `IteratorLoop` that relies on a
potentially more efficient `forIn` implementation of the inner iterator.
The mysterious `@[specialize]` on a test has been removed because it is
not necessary anymore according to a manual inspection of the IR. Either
I erroneously concluded from experiments that it was necessary of
something has changed in the meantime that makes it unnecessary.
This PR reworks the `simp` set around the `Id` monad, to not elide or
unfold `pure` and `Id.run`
In particular, it stops encoding the "defeq abuse" of `Id X = X` in the
statements of theorems, instead using `Id.run` and `pure` to pass back
and forth between these two spellings. Often when writing these with
`pure`, they generalize to other lawful monads; though such changes were
split off to other PRs.
This fixes the problem with the current simp set where `Id.run (pure x)`
is simplified to `Id.run x`, instead of the desirable `x`.
This is particularly bad because the` x` is sometimes inferred with type
`Id X` instead of `X`, which prevents other `simp` lemmas about `X` from
firing.
Making `Id` reducible instead is not an option, as then the `Monad`
instances would have nothing to key on.
---------
Co-authored-by: Sebastian Graf <sg@lean-fro.org>
Co-authored-by: Kim Morrison <kim@tqft.net>
Co-authored-by: Paul Reichert <6992158+datokrat@users.noreply.github.com>
This PR provides simple lemmas about `toArray`, `toList` and `toListRev`
for the iterator library.
It also changes the definition of `Iter` and `IterM` so that they aren't
equal anymore and in particular not definitionally equal. While it was
very convenient to have them be definitionally equal when working with
dependent code, it was also confusing and annoying that one would
sometimes end up with something like `it.toList = IterM.toList it`,
where `it : Iter β`.
This PR introduces a very minimal version of the new iterator library.
It comes with list iterators and various consumers, namely `toArray`,
`toList`, `toListRev`, `ForIn`, `fold`, `foldM` and `drain`. All
consumers also come in a partial variant that can be used without any
proofs. This limited version of the iterator library generates decent
code, even with the old code generator.
