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//! Partially ordered elements with a least upper bound.
//!
//! Lattices form the basis of differential dataflow's efficient execution in the presence of
//! iterative sub-computations. All logical times in differential dataflow must implement the
//! `Lattice` trait, and all reasoning in operators are done it terms of `Lattice` methods.

use timely::order::PartialOrder;
use timely::progress::{Antichain, frontier::AntichainRef};

/// A bounded partially ordered type supporting joins and meets.
pub trait Lattice : PartialOrder {

/// The smallest element greater than or equal to both arguments.
///
/// # Examples
///
/// ```
/// # use timely::PartialOrder;
/// # use timely::order::Product;
/// # use differential_dataflow::lattice::Lattice;
/// # fn main() {
///
/// let time1 = Product::new(3, 7);
/// let time2 = Product::new(4, 6);
/// let join = time1.join(&time2);
///
/// assert_eq!(join, Product::new(4, 7));
/// # }
/// ```
fn join(&self, other: &Self) -> Self;

/// Updates `self` to the smallest element greater than or equal to both arguments.
///
/// # Examples
///
/// ```
/// # use timely::PartialOrder;
/// # use timely::order::Product;
/// # use differential_dataflow::lattice::Lattice;
/// # fn main() {
///
/// let mut time1 = Product::new(3, 7);
/// let time2 = Product::new(4, 6);
/// time1.join_assign(&time2);
///
/// assert_eq!(time1, Product::new(4, 7));
/// # }
/// ```
fn join_assign(&mut self, other: &Self) where Self: Sized {
*self = self.join(other);
}

/// The largest element less than or equal to both arguments.
///
/// # Examples
///
/// ```
/// # use timely::PartialOrder;
/// # use timely::order::Product;
/// # use differential_dataflow::lattice::Lattice;
/// # fn main() {
///
/// let time1 = Product::new(3, 7);
/// let time2 = Product::new(4, 6);
/// let meet = time1.meet(&time2);
///
/// assert_eq!(meet, Product::new(3, 6));
/// # }
/// ```
fn meet(&self, other: &Self) -> Self;

/// Updates `self` to the largest element less than or equal to both arguments.
///
/// # Examples
///
/// ```
/// # use timely::PartialOrder;
/// # use timely::order::Product;
/// # use differential_dataflow::lattice::Lattice;
/// # fn main() {
///
/// let mut time1 = Product::new(3, 7);
/// let time2 = Product::new(4, 6);
/// time1.meet_assign(&time2);
///
/// assert_eq!(time1, Product::new(3, 6));
/// # }
/// ```
fn meet_assign(&mut self, other: &Self) where Self: Sized  {
*self = self.meet(other);
}

/// Advances self to the largest time indistinguishable under `frontier`.
///
/// This method produces the "largest" lattice element with the property that for every
/// lattice element greater than some element of `frontier`, both the result and `self`
/// compare identically to the lattice element. The result is the "largest" element in
/// the sense that any other element with the same property (compares identically to times
/// greater or equal to `frontier`) must be less or equal to the result.
///
/// When provided an empty frontier `self` is not modified.
///
/// # Examples
///
/// ```
/// # use timely::PartialOrder;
/// # use timely::order::Product;
/// # use differential_dataflow::lattice::Lattice;
/// # fn main() {
///
/// use timely::progress::frontier::{Antichain, AntichainRef};
///
/// let time = Product::new(3, 7);
/// let mut advanced = Product::new(3, 7);
/// let frontier = Antichain::from(vec![Product::new(4, 8), Product::new(5, 3)]);
///
/// // `time` and `advanced` are indistinguishable to elements >= an element of `frontier`
/// for i in 0 .. 10 {
///     for j in 0 .. 10 {
///         let test = Product::new(i, j);
///         // for `test` in the future of `frontier` ..
///         if frontier.less_equal(&test) {
///         }
///     }
/// }
///
/// # }
/// ```
#[inline]
fn advance_by(&mut self, frontier: AntichainRef<Self>) where Self: Sized {
let mut iter = frontier.iter();
if let Some(first) = iter.next() {
let mut result = self.join(first);
for f in iter {
result.meet_assign(&self.join(f));
}
*self = result;
}
}
}

use timely::order::Product;

impl<T1: Lattice, T2: Lattice> Lattice for Product<T1, T2> {
#[inline]
fn join(&self, other: &Product<T1, T2>) -> Product<T1, T2> {
Product {
outer: self.outer.join(&other.outer),
inner: self.inner.join(&other.inner),
}
}
#[inline]
fn meet(&self, other: &Product<T1, T2>) -> Product<T1, T2> {
Product {
outer: self.outer.meet(&other.outer),
inner: self.inner.meet(&other.inner),
}
}
}

/// A type that has a unique maximum element.
pub trait Maximum {
/// The unique maximal element of the set.
fn maximum() -> Self;
}

/// Implements `Maximum` for elements with a `MAX` associated constant.
macro_rules! implement_maximum {
(\$(\$index_type:ty,)*) => (
\$(
impl Maximum for \$index_type {
fn maximum() -> Self { Self::MAX }
}
)*
)
}

implement_maximum!(usize, u128, u64, u32, u16, u8, isize, i128, i64, i32, i16, i8, Duration,);
impl Maximum for () { fn maximum() -> () { () }}

use timely::progress::Timestamp;

// Tuples have the annoyance that they are only a lattice for `T2` with maximal elements,
// as the `meet` operator on `(x, _)` and `(y, _)` would be `(x meet y, maximum())`.
impl<T1: Lattice+Clone, T2: Lattice+Clone+Maximum+Timestamp> Lattice for (T1, T2) {
#[inline]
fn join(&self, other: &(T1, T2)) -> (T1, T2) {
if self.0.eq(&other.0) {
(self.0.clone(), self.1.join(&other.1))
} else if self.0.less_than(&other.0) {
other.clone()
} else if other.0.less_than(&self.0) {
self.clone()
} else {
(self.0.join(&other.0), T2::minimum())
}
}
#[inline]
fn meet(&self, other: &(T1, T2)) -> (T1, T2) {
if self.0.eq(&other.0) {
(self.0.clone(), self.1.meet(&other.1))
} else if self.0.less_than(&other.0) {
self.clone()
} else if other.0.less_than(&self.0) {
other.clone()
} else {
(self.0.meet(&other.0), T2::maximum())
}
}
}

macro_rules! implement_lattice {
(\$index_type:ty, \$minimum:expr) => (
impl Lattice for \$index_type {
#[inline] fn join(&self, other: &Self) -> Self { ::std::cmp::max(*self, *other) }
#[inline] fn meet(&self, other: &Self) -> Self { ::std::cmp::min(*self, *other) }
}
)
}

use std::time::Duration;

implement_lattice!(Duration, Duration::new(0, 0));
implement_lattice!(usize, 0);
implement_lattice!(u128, 0);
implement_lattice!(u64, 0);
implement_lattice!(u32, 0);
implement_lattice!(u16, 0);
implement_lattice!(u8, 0);
implement_lattice!(isize, 0);
implement_lattice!(i128, 0);
implement_lattice!(i64, 0);
implement_lattice!(i32, 0);
implement_lattice!(i16, 0);
implement_lattice!(i8, 0);
implement_lattice!((), ());

/// Returns the "smallest" minimal antichain "greater or equal" to both inputs.
///
/// This method is primarily meant for cases where one cannot use the methods
/// of `Antichain`'s `PartialOrder` implementation, such as when one has only
/// references rather than owned antichains.
///
/// # Examples
///
/// ```
/// # use timely::PartialOrder;
/// # use timely::order::Product;
/// # use differential_dataflow::lattice::Lattice;
/// # use differential_dataflow::lattice::antichain_join;
/// # fn main() {
///
/// let f1 = &[Product::new(3, 7), Product::new(5, 6)];
/// let f2 = &[Product::new(4, 6)];
/// let join = antichain_join(f1, f2);
/// assert_eq!(&*join.elements(), &[Product::new(4, 7), Product::new(5, 6)]);
/// # }
/// ```
pub fn antichain_join<T: Lattice>(one: &[T], other: &[T]) -> Antichain<T> {
let mut upper = Antichain::new();
antichain_join_into(one, other, &mut upper);
upper
}

/// Returns the "smallest" minimal antichain "greater or equal" to both inputs.
///
/// This method is primarily meant for cases where one cannot use the methods
/// of `Antichain`'s `PartialOrder` implementation, such as when one has only
/// references rather than owned antichains.
///
/// This function is similar to [antichain_join] but reuses an existing allocation.
/// The provided antichain is cleared before inserting elements.
///
/// # Examples
///
/// ```
/// # use timely::PartialOrder;
/// # use timely::order::Product;
/// # use timely::progress::Antichain;
/// # use differential_dataflow::lattice::Lattice;
/// # use differential_dataflow::lattice::antichain_join_into;
/// # fn main() {
///
/// let mut join = Antichain::new();
/// let f1 = &[Product::new(3, 7), Product::new(5, 6)];
/// let f2 = &[Product::new(4, 6)];
/// antichain_join_into(f1, f2, &mut join);
/// assert_eq!(&*join.elements(), &[Product::new(4, 7), Product::new(5, 6)]);
/// # }
/// ```
pub fn antichain_join_into<T: Lattice>(one: &[T], other: &[T], upper: &mut Antichain<T>) {
upper.clear();
for time1 in one {
for time2 in other {
upper.insert(time1.join(time2));
}
}
}

/// Returns the "greatest" minimal antichain "less or equal" to both inputs.
///
/// This method is primarily meant for cases where one cannot use the methods
/// of `Antichain`'s `PartialOrder` implementation, such as when one has only
/// references rather than owned antichains.
///
/// # Examples
///
/// ```
/// # use timely::PartialOrder;
/// # use timely::order::Product;
/// # use differential_dataflow::lattice::Lattice;
/// # use differential_dataflow::lattice::antichain_meet;
/// # fn main() {
///
/// let f1 = &[Product::new(3, 7), Product::new(5, 6)];
/// let f2 = &[Product::new(4, 6)];
/// let meet = antichain_meet(f1, f2);
/// assert_eq!(&*meet.elements(), &[Product::new(3, 7), Product::new(4, 6)]);
/// # }
/// ```
pub fn antichain_meet<T: Lattice+Clone>(one: &[T], other: &[T]) -> Antichain<T> {
let mut upper = Antichain::new();
for time1 in one {
upper.insert(time1.clone());
}
for time2 in other {
upper.insert(time2.clone());
}
upper
}

impl<T: Lattice+Clone> Lattice for Antichain<T> {
fn join(&self, other: &Self) -> Self {
let mut upper = Antichain::new();
for time1 in self.elements().iter() {
for time2 in other.elements().iter() {
upper.insert(time1.join(time2));
}
}
upper
}
fn meet(&self, other: &Self) -> Self {
let mut upper = Antichain::new();
for time1 in self.elements().iter() {
upper.insert(time1.clone());
}
for time2 in other.elements().iter() {
upper.insert(time2.clone());
}
upper
}
}