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```
``````//! An alternative solver based around the SLG algorithm, which
//! implements the well-formed semantics. For an overview of how the solver
//! works, see [The On-Demand SLG Solver][guide] in the chalk book.
//!
//! [guide]: https://rust-lang.github.io/chalk/book/engine/slg.html
//!
//! This algorithm is very closed based on the description found in the
//! following paper, which I will refer to in the comments as EWFS:
//!
//! > Efficient Top-Down Computation of Queries Under the Well-founded Semantics
//! > (Chen, Swift, and Warren; Journal of Logic Programming '95)
//!
//! However, to understand that paper, I would recommend first
//! starting with the following paper, which I will refer to in the
//!
//! > A New Formulation of Tabled resolution With Delay
//! > (Swift; EPIA '99)
//!
//! In addition, I incorporated extensions from the following papers,
//! which I will refer to as SA and RR respectively, that
//! describes how to do introduce approximation when processing
//! subgoals and so forth:
//!
//! > Terminating Evaluation of Logic Programs with Finite Three-Valued Models
//! > Riguzzi and Swift; ACM Transactions on Computational Logic 2013
//! > (Introduces "subgoal abstraction", hence the name SA)
//! >
//! > Grosof and Swift; 2013
//!
//! Another useful paper that gives a kind of high-level overview of
//! concepts at play is the following, which I will refer to as XSB:
//!
//! > XSB: Extending Prolog with Tabled Logic Programming
//! > (Swift and Warren; Theory and Practice of Logic Programming '10)
//!
//! While this code is adapted from the algorithms described in those
//! papers, it is not the same. For one thing, the approaches there
//! had to be extended to our context, and in particular to coping
//! with hereditary harrop predicates and our version of unification
//! (which produces subgoals). I believe those to be largely faithful
//! extensions. However, there are some other places where I
//! intentionally diverged from the semantics as described in the
//! papers -- e.g. by more aggressively approximating -- which I
//! marked them with a comment DIVERGENCE. Those places may want to be
//! evaluated in the future.
//!
//! Glossary of other terms:
//!
//! - WAM: Warren abstract machine, an efficient way to evaluate Prolog programs.
//!   See <http://wambook.sourceforge.net/>.
//! - HH: Hereditary harrop predicates. What Chalk deals in.
//!   Popularized by Lambda Prolog.

use std::cmp::min;
use std::usize;

use chalk_derive::{HasInterner, TypeFoldable, TypeVisitable};
use chalk_ir::interner::Interner;
use chalk_ir::{
AnswerSubst, Canonical, ConstrainedSubst, Constraint, DebruijnIndex, Goal, InEnvironment,
Substitution,
};
use std::ops::ControlFlow;

pub mod context;
mod derived;
pub mod forest;
mod logic;
mod normalize_deep;
mod simplify;
pub mod slg;
pub mod solve;
mod stack;
mod strand;
mod table;
mod tables;

index_struct! {
pub struct TableIndex { // FIXME: pub b/c TypeFoldable
value: usize,
}
}

/// The paper describes these as `A :- D | G`.
#[derive(Clone, Debug, PartialEq, Eq, Hash, TypeFoldable, TypeVisitable, HasInterner)]
pub struct ExClause<I: Interner> {
/// The substitution which, applied to the goal of our table,
/// would yield A.
pub subst: Substitution<I>,

/// True if any subgoals were depended upon negatively and
/// were not fully evaluated, or if we encountered a `CannotProve`
/// goal. (In the full SLG algorithm, we would use delayed literals here,
/// but we don't bother, as we don't need that support.)
pub ambiguous: bool,

/// Region constraints we have accumulated.
pub constraints: Vec<InEnvironment<Constraint<I>>>,

/// Subgoals: literals that must be proven
pub subgoals: Vec<Literal<I>>,

/// We assume that negative literals cannot have coinductive cycles.
pub delayed_subgoals: Vec<InEnvironment<Goal<I>>>,

/// Time stamp that is incremented each time we find an answer to
/// some subgoal. This is used to figure out whether any of the
/// floundered subgoals may no longer be floundered: we record the
/// current time when we add something to the list of floundered
/// subgoals, and then we can compare whether its value has
/// changed since then. This is not the same `TimeStamp` of
/// `Forest`'s clock.

/// List of subgoals that have floundered. See `FlounderedSubgoal`
pub floundered_subgoals: Vec<FlounderedSubgoal<I>>,
}

/// The "time stamp" is a simple clock that gets incremented each time
/// we encounter a positive answer in processing a particular
/// strand. This is used as an optimization to help us figure out when
/// we *may* have changed inference variables.
#[derive(Copy, Clone, Debug, Default, PartialEq, Eq, PartialOrd, Ord, Hash)]
pub struct TimeStamp {
clock: u64,
}

impl TimeStamp {
const MAX: TimeStamp = TimeStamp {
clock: ::std::u64::MAX,
};

fn increment(&mut self) {
self.clock += 1;
}
}

/// A "floundered" subgoal is one that contains unbound existential
/// variables for which it cannot produce a value. The classic example
/// of floundering is a negative subgoal:
///
/// ```notrust
/// not { Implemented(?T: Foo) }
/// ```
///
/// The way the prolog solver works, it basically enumerates all the
/// ways that a given goal can be *true*. But we can't use this
/// technique to find all the ways that `?T: Foo` can be *false* -- so
/// we call it floundered. In other words, we can evaluate a negative
/// goal, but only if we know what `?T` is -- we can't use the
/// negative goal to help us figuring out `?T`.
///
/// In addition to negative goals, we use floundering to prevent the
/// trait solver from trying to enumerate very large goals with tons
/// of answers. For example, we consider a goal like `?T: Sized` to
/// "flounder", since we can't hope to enumerate all types that are
/// `Sized`. The same is true for other special traits like `Clone`.
///
/// Floundering can also occur indirectly. For example:
///
/// ```notrust
/// trait Foo { }
/// impl<T> Foo for T { }
/// ```
///
/// trying to solve `?T: Foo` would immediately require solving `?T:
/// Sized`, and hence would flounder.
#[derive(Clone, Debug, PartialEq, Eq, Hash, TypeFoldable, TypeVisitable)]
pub struct FlounderedSubgoal<I: Interner> {
/// Literal that floundered.
pub floundered_literal: Literal<I>,

/// Current value of the strand's clock at the time of
/// floundering.
pub floundered_time: TimeStamp,
}

/// An "answer" in the on-demand solver corresponds to a fully solved
/// goal for a particular table (modulo delayed literals). It contains
/// a substitution
#[derive(Clone, Debug)]
/// Contains values for the unbound inference variables for which
/// the table is true, along with any delayed subgoals (Which must
/// still be proven) and region constrained (which must still be
/// proven, but not by chalk).

/// If this flag is set, then the answer could be neither proven
/// nor disproven. This could be the size of the answer exceeded
/// `max_size` or because of a negative loop (e.g., `P :- not { P }`).
pub ambiguous: bool,
}

#[derive(Clone, Debug)]
/// Contains values for the unbound inference variables for which
/// the table is true, along with any region constrained (which must still be
/// proven, but not by chalk).
pub subst: Canonical<ConstrainedSubst<I>>,

/// If this flag is set, then the answer could be neither proven
/// nor disproven. This could be the size of the answer exceeded
/// `max_size` or because of a negative loop (e.g., `P :- not { P }`).
pub ambiguous: bool,
}

/// Either `A` or `~A`, where `A` is a `Env |- Goal`.
#[derive(Clone, Debug, TypeFoldable, TypeVisitable)]
pub enum Literal<I: Interner> {
// FIXME: pub b/c fold
Positive(InEnvironment<Goal<I>>),
Negative(InEnvironment<Goal<I>>),
}

/// The `Minimums` structure is used to track the dependencies between
/// some item E on the evaluation stack. In particular, it tracks
/// cases where the success of E depends (or may depend) on items
/// deeper in the stack than E (i.e., with lower DFNs).
///
/// `positive` tracks the lowest index on the stack to which we had a
/// POSITIVE dependency (e.g. `foo(X) :- bar(X)`) -- meaning that in
/// order for E to succeed, the dependency must succeed. It is
/// initialized with the index of the predicate on the stack. So
/// imagine we have a stack like this:
///
/// ```notrust
///     // 0 foo(X)   <-- bottom of stack
///     // 1 bar(X)
///     // 2 baz(X)   <-- top of stack
/// ```
///
/// In this case, `positive` would be initially 0, 1, and 2 for `foo`,
/// `bar`, and `baz` respectively. This reflects the fact that the
///
/// Now imagine that we had a clause `baz(X) :- foo(X)`, inducing a
/// cycle. In this case, we would update `positive` for `baz(X)` to be
/// 0, reflecting the fact that its answers depend on the answers for
/// `foo(X)`. Similarly, the minimum for `bar` would (eventually) be
/// updated, since it too transitively depends on `foo`. `foo` is
/// unaffected.
///
/// `negative` tracks the lowest index on the stack to which we had a
/// NEGATIVE dependency (e.g., `foo(X) :- not { bar(X) }`) -- meaning
/// that for E to succeed, the dependency must fail. This is initially
/// `usize::MAX`, reflecting the fact that the answers for `foo(X)` do
/// not depend on `not(foo(X))`. When negative cycles are encountered,
/// however, this value must be updated.
#[derive(Copy, Clone, Debug)]
struct Minimums {
positive: TimeStamp,
negative: TimeStamp,
}

impl Minimums {
const MAX: Minimums = Minimums {
positive: TimeStamp::MAX,
negative: TimeStamp::MAX,
};

/// Update our fields to be the minimum of our current value
/// and the values from other.
fn take_minimums(&mut self, other: &Minimums) {
self.positive = min(self.positive, other.positive);
self.negative = min(self.negative, other.negative);
}

fn minimum_of_pos_and_neg(&self) -> TimeStamp {
min(self.positive, self.negative)
}
}

#[derive(Copy, Clone, Debug)]
Complete,
Ambiguous,
}

chalk_ir::copy_fold!(TableIndex);
chalk_ir::copy_fold!(TimeStamp);

chalk_ir::const_visit!(TableIndex);
chalk_ir::const_visit!(TimeStamp);

#[macro_export]
macro_rules! index_struct {
(\$(#[\$m:meta])* \$v:vis struct \$n:ident {
\$vf:vis value: usize,
}) => {
#[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
\$(#[\$m])*
\$v struct \$n {
\$vf value: usize,
}

impl \$n {
// Not all index structs need this, so allow it to be dead
// code.
\$v fn get_and_increment(&mut self) -> Self {
let old_value = *self;
self.increment();
old_value
}

\$v fn increment(&mut self) {
self.value += 1;
}

// TODO: Once the Step trait is stabilized (https://github.com/rust-lang/rust/issues/42168), instead implement it and use the Iterator implementation of Range
pub fn iterate_range(range: ::std::ops::Range<Self>) -> impl Iterator<Item = \$n> {
(range.start.value..range.end.value).into_iter().map(|i| Self { value: i })
}
}

impl ::std::fmt::Debug for \$n {
fn fmt(&self, fmt: &mut ::std::fmt::Formatter<'_>) -> ::std::fmt::Result {
write!(fmt, "{}({})", stringify!(\$n), self.value)
}
}

impl From<usize> for \$n {
fn from(value: usize) -> Self {
Self { value }
}
}
}
}
``````