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use crate::normalize_deep::DeepNormalizer;
use crate::slg::ResolventOps;
use crate::{ExClause, Literal, TimeStamp};
use chalk_ir::cast::Caster;
use chalk_ir::fold::shift::Shift;
use chalk_ir::fold::TypeFoldable;
use chalk_ir::interner::{HasInterner, Interner};
use chalk_ir::zip::{Zip, Zipper};
use chalk_ir::*;
use chalk_solve::infer::InferenceTable;
use tracing::{debug, instrument};
///////////////////////////////////////////////////////////////////////////
// SLG RESOLVENTS
//
// The "SLG Resolvent" is used to combine a *goal* G with some
// clause or answer *C*. It unifies the goal's selected literal
// with the clause and then inserts the clause's conditions into
// the goal's list of things to prove, basically. Although this is
// one operation in EWFS, we have specialized variants for merging
// a program clause and an answer (though they share some code in
// common).
//
// Terminology note: The NFTD and RR papers use the term
// "resolvent" to mean both the factor and the resolvent, but EWFS
// distinguishes the two. We follow EWFS here since -- in the code
// -- we tend to know whether there are delayed literals or not,
// and hence to know which code path we actually want.
//
// From EWFS:
//
// Let G be an X-clause A :- D | L1,...Ln, where N > 0, and Li be selected atom.
//
// Let C be an X-clause with no delayed literals. Let
//
// C' = A' :- L'1...L'm
//
// be a variant of C such that G and C' have no variables in
// common.
//
// Let Li and A' be unified with MGU S.
//
// Then:
//
// S(A :- D | L1...Li-1, L1'...L'm, Li+1...Ln)
//
// is the SLG resolvent of G with C.
impl<I: Interner> ResolventOps<I> for InferenceTable<I> {
/// Applies the SLG resolvent algorithm to incorporate a program
/// clause into the main X-clause, producing a new X-clause that
/// must be solved.
///
/// # Parameters
///
/// - `goal` is the goal G that we are trying to solve
/// - `clause` is the program clause that may be useful to that end
#[instrument(level = "debug", skip(self, interner, environment, subst))]
fn resolvent_clause(
&mut self,
db: &dyn UnificationDatabase<I>,
interner: I,
environment: &Environment<I>,
goal: &DomainGoal<I>,
subst: &Substitution<I>,
clause: &ProgramClause<I>,
) -> Fallible<ExClause<I>> {
// Relating the above description to our situation:
//
// - `goal` G, except with binders for any existential variables.
// - Also, we always select the first literal in `ex_clause.literals`, so `i` is 0.
// - `clause` is C, except with binders for any existential variables.
// C' in the description above is `consequence :- conditions`.
//
// Note that G and C' have no variables in common.
let ProgramClauseImplication {
consequence,
conditions,
constraints,
priority: _,
} = {
let ProgramClauseData(implication) = clause.data(interner);
self.instantiate_binders_existentially(interner, implication.clone())
};
debug!(?consequence, ?conditions, ?constraints);
// Unify the selected literal Li with C'.
let unification_result = self.relate(
interner,
db,
environment,
Variance::Invariant,
goal,
&consequence,
)?;
// Final X-clause that we will return.
let mut ex_clause = ExClause {
subst: subst.clone(),
ambiguous: false,
constraints: vec![],
subgoals: vec![],
delayed_subgoals: vec![],
answer_time: TimeStamp::default(),
floundered_subgoals: vec![],
};
// Add the subgoals/region-constraints that unification gave us.
ex_clause.subgoals.extend(
unification_result
.goals
.into_iter()
.casted(interner)
.map(Literal::Positive),
);
ex_clause
.constraints
.extend(constraints.as_slice(interner).to_owned());
// Add the `conditions` from the program clause into the result too.
ex_clause
.subgoals
.extend(conditions.iter(interner).map(|c| match c.data(interner) {
GoalData::Not(c1) => {
Literal::Negative(InEnvironment::new(environment, Goal::clone(c1)))
}
_ => Literal::Positive(InEnvironment::new(environment, Goal::clone(c))),
}));
Ok(ex_clause)
}
///////////////////////////////////////////////////////////////////////////
// apply_answer_subst
//
// Apply answer subst has the job of "plugging in" the answer to a
// query into the pending ex-clause. To see how it works, it's worth stepping
// up one level. Imagine that first we are trying to prove a goal A:
//
// A :- T: Foo<Vec<?U>>, ?U: Bar
//
// this spawns a subgoal `T: Foo<Vec<?0>>`, and it's this subgoal that
// has now produced an answer `?0 = u32`. When the goal A spawned the
// subgoal, it will also have registered a `PendingExClause` with its
// current state. At the point where *this* method has been invoked,
// that pending ex-clause has been instantiated with fresh variables and setup,
// so we have four bits of incoming information:
//
// - `ex_clause`, which is the remaining stuff to prove for the goal A.
// Here, the inference variable `?U` has been instantiated with a fresh variable
// `?X`.
// - `A :- ?X: Bar`
// - `selected_goal`, which is the thing we were trying to prove when we
// spawned the subgoal. It shares inference variables with `ex_clause`.
// - `T: Foo<Vec<?X>>`
// - `answer_table_goal`, which is the subgoal in canonical form:
// - `for<type> T: Foo<Vec<?0>>`
// - `canonical_answer_subst`, which is an answer to `answer_table_goal`.
// - `[?0 = u32]`
//
// In this case, this function will (a) unify `u32` and `?X` and then
// (b) return `ex_clause` (extended possibly with new region constraints
// and subgoals).
//
// One way to do this would be to (a) substitute
// `canonical_answer_subst` into `answer_table_goal` (yielding `T:
// Foo<Vec<u32>>`) and then (b) instantiate the result with fresh
// variables (no effect in this instance) and then (c) unify that with
// `selected_goal` (yielding, indirectly, that `?X = u32`). But that
// is not what we do: it's inefficient, to start, but it also causes
// problems because unification of projections can make new
// sub-goals. That is, even if the answers don't involve any
// projections, the table goals might, and this can create an infinite
// loop (see also #74).
//
// What we do instead is to (a) instantiate the substitution, which
// may have free variables in it (in this case, it would not, and the
// instantiation would have no effect) and then (b) zip
// `answer_table_goal` and `selected_goal` without having done any
// substitution. After all, these ought to be basically the same,
// since `answer_table_goal` was created by canonicalizing (and
// possibly truncating, but we'll get to that later)
// `selected_goal`. Then, whenever we reach a "free variable" in
// `answer_table_goal`, say `?0`, we go to the instantiated answer
// substitution and lookup the result (in this case, `u32`). We take
// that result and unify it with whatever we find in `selected_goal`
// (in this case, `?X`).
//
// Let's cover then some corner cases. First off, what is this
// business of instantiating the answer? Well, the answer may not be a
// simple type like `u32`, it could be a "family" of types, like
// `for<type> Vec<?0>` -- i.e., `Vec<X>: Bar` for *any* `X`. In that
// case, the instantiation would produce a substitution `[?0 :=
// Vec<?Y>]` (note that the key is not affected, just the value). So
// when we do the unification, instead of unifying `?X = u32`, we
// would unify `?X = Vec<?Y>`.
//
// Next, truncation. One key thing is that the `answer_table_goal` may
// not be *exactly* the same as the `selected_goal` -- we will
// truncate it if it gets too deep. so, in our example, it may be that
// instead of `answer_table_goal` being `for<type> T: Foo<Vec<?0>>`,
// it could have been truncated to `for<type> T: Foo<?0>` (which is a
// more general goal). In that case, let's say that the answer is
// still `[?0 = u32]`, meaning that `T: Foo<u32>` is true (which isn't
// actually interesting to our original goal). When we do the zip
// then, we will encounter `?0` in the `answer_table_goal` and pair
// that with `Vec<?X>` from the pending goal. We will attempt to unify
// `Vec<?X>` with `u32` (from the substitution), which will fail. That
// failure will get propagated back up.
#[instrument(level = "debug", skip(self, interner))]
fn apply_answer_subst(
&mut self,
interner: I,
unification_database: &dyn UnificationDatabase<I>,
ex_clause: &mut ExClause<I>,
selected_goal: &InEnvironment<Goal<I>>,
answer_table_goal: &Canonical<InEnvironment<Goal<I>>>,
canonical_answer_subst: Canonical<AnswerSubst<I>>,
) -> Fallible<()> {
debug!(selected_goal = ?DeepNormalizer::normalize_deep(self, interner, selected_goal.clone()));
// C' is now `answer`. No variables in common with G.
let AnswerSubst {
subst: answer_subst,
// Assuming unification succeeds, we incorporate the
// region constraints from the answer into the result;
// we'll need them if this answer (which is not yet known
// to be true) winds up being true, and otherwise (if the
// answer is false or unknown) it doesn't matter.
constraints: answer_constraints,
delayed_subgoals,
} = self.instantiate_canonical(interner, canonical_answer_subst);
AnswerSubstitutor::substitute(
interner,
unification_database,
self,
&selected_goal.environment,
&answer_subst,
ex_clause,
&answer_table_goal.value,
selected_goal,
)?;
ex_clause
.constraints
.extend(answer_constraints.as_slice(interner).to_vec());
// at that point we should only have goals that stemmed
// from non trivial self cycles
ex_clause.delayed_subgoals.extend(delayed_subgoals);
Ok(())
}
}
struct AnswerSubstitutor<'t, I: Interner> {
table: &'t mut InferenceTable<I>,
environment: &'t Environment<I>,
answer_subst: &'t Substitution<I>,
/// Tracks the debrujn index of the first binder that is outside
/// the term we are traversing. This starts as `DebruijnIndex::INNERMOST`,
/// since we have not yet traversed *any* binders, but when we visit
/// the inside of a binder, it would be incremented.
///
/// Example: If we are visiting `(for<type> A, B, C, for<type> for<type> D)`,
/// then this would be:
///
/// * `1`, when visiting `A`,
/// * `0`, when visiting `B` and `C`,
/// * `2`, when visiting `D`.
outer_binder: DebruijnIndex,
ex_clause: &'t mut ExClause<I>,
interner: I,
unification_database: &'t dyn UnificationDatabase<I>,
}
impl<I: Interner> AnswerSubstitutor<'_, I> {
fn substitute<T: Zip<I>>(
interner: I,
unification_database: &dyn UnificationDatabase<I>,
table: &mut InferenceTable<I>,
environment: &Environment<I>,
answer_subst: &Substitution<I>,
ex_clause: &mut ExClause<I>,
answer: &T,
pending: &T,
) -> Fallible<()> {
let mut this = AnswerSubstitutor {
interner,
unification_database,
table,
environment,
answer_subst,
ex_clause,
outer_binder: DebruijnIndex::INNERMOST,
};
Zip::zip_with(&mut this, Variance::Invariant, answer, pending)?;
Ok(())
}
fn unify_free_answer_var(
&mut self,
interner: I,
db: &dyn UnificationDatabase<I>,
variance: Variance,
answer_var: BoundVar,
pending: GenericArgData<I>,
) -> Fallible<bool> {
let answer_index = match answer_var.index_if_bound_at(self.outer_binder) {
Some(index) => index,
// This variable is bound in the answer, not free, so it
// doesn't represent a reference into the answer substitution.
None => return Ok(false),
};
let answer_param = self.answer_subst.at(interner, answer_index);
let pending_shifted = pending
.shifted_out_to(interner, self.outer_binder)
.expect("truncate extracted a pending value that references internal binder");
let result = self.table.relate(
interner,
db,
self.environment,
variance,
answer_param,
&GenericArg::new(interner, pending_shifted),
)?;
self.ex_clause.subgoals.extend(
result
.goals
.into_iter()
.casted(interner)
.map(Literal::Positive),
);
Ok(true)
}
/// When we encounter a variable in the answer goal, we first try
/// `unify_free_answer_var`. Assuming that this fails, the
/// variable must be a bound variable in the answer goal -- in
/// that case, there should be a corresponding bound variable in
/// the pending goal. This bit of code just checks that latter
/// case.
fn assert_matching_vars(
&mut self,
answer_var: BoundVar,
pending_var: BoundVar,
) -> Fallible<()> {
let BoundVar {
debruijn: answer_depth,
index: answer_index,
} = answer_var;
let BoundVar {
debruijn: pending_depth,
index: pending_index,
} = pending_var;
// Both bound variables are bound within the term we are matching
assert!(answer_depth.within(self.outer_binder));
// They are bound at the same (relative) depth
assert_eq!(answer_depth, pending_depth);
// They are bound at the same index within the binder
assert_eq!(answer_index, pending_index,);
Ok(())
}
}
impl<'i, I: Interner> Zipper<I> for AnswerSubstitutor<'i, I> {
fn zip_tys(&mut self, variance: Variance, answer: &Ty<I>, pending: &Ty<I>) -> Fallible<()> {
let interner = self.interner;
if let Some(pending) = self.table.normalize_ty_shallow(interner, pending) {
return Zip::zip_with(self, variance, answer, &pending);
}
// If the answer has a variable here, then this is one of the
// "inputs" to the subgoal table. We need to extract the
// resulting answer that the subgoal found and unify it with
// the value from our "pending subgoal".
if let TyKind::BoundVar(answer_depth) = answer.kind(interner) {
if self.unify_free_answer_var(
interner,
self.unification_database,
variance,
*answer_depth,
GenericArgData::Ty(pending.clone()),
)? {
return Ok(());
}
}
// Otherwise, the answer and the selected subgoal ought to be a perfect match for
// one another.
match (answer.kind(interner), pending.kind(interner)) {
(TyKind::BoundVar(answer_depth), TyKind::BoundVar(pending_depth)) => {
self.assert_matching_vars(*answer_depth, *pending_depth)
}
(TyKind::Dyn(answer), TyKind::Dyn(pending)) => {
Zip::zip_with(self, variance, answer, pending)
}
(TyKind::Alias(answer), TyKind::Alias(pending)) => {
Zip::zip_with(self, variance, answer, pending)
}
(TyKind::Placeholder(answer), TyKind::Placeholder(pending)) => {
Zip::zip_with(self, variance, answer, pending)
}
(TyKind::Function(answer), TyKind::Function(pending)) => Zip::zip_with(
self,
variance,
&answer.clone().into_binders(interner),
&pending.clone().into_binders(interner),
),
(TyKind::InferenceVar(_, _), _) | (_, TyKind::InferenceVar(_, _)) => panic!(
"unexpected inference var in answer `{:?}` or pending goal `{:?}`",
answer, pending,
),
(TyKind::Adt(id_a, substitution_a), TyKind::Adt(id_b, substitution_b)) => {
if id_a != id_b {
return Err(NoSolution);
}
self.zip_substs(
variance,
Some(self.unification_database().adt_variance(*id_a)),
substitution_a.as_slice(interner),
substitution_b.as_slice(interner),
)
}
(
TyKind::AssociatedType(id_a, substitution_a),
TyKind::AssociatedType(id_b, substitution_b),
) => {
if id_a != id_b {
return Err(NoSolution);
}
self.zip_substs(
variance,
None,
substitution_a.as_slice(interner),
substitution_b.as_slice(interner),
)
}
(TyKind::Scalar(scalar_a), TyKind::Scalar(scalar_b)) => {
Zip::zip_with(self, variance, scalar_a, scalar_b)
}
(TyKind::Str, TyKind::Str) => Ok(()),
(TyKind::Tuple(arity_a, substitution_a), TyKind::Tuple(arity_b, substitution_b)) => {
if arity_a != arity_b {
return Err(NoSolution);
}
self.zip_substs(
variance,
None,
substitution_a.as_slice(interner),
substitution_b.as_slice(interner),
)
}
(
TyKind::OpaqueType(id_a, substitution_a),
TyKind::OpaqueType(id_b, substitution_b),
) => {
if id_a != id_b {
return Err(NoSolution);
}
self.zip_substs(
variance,
None,
substitution_a.as_slice(interner),
substitution_b.as_slice(interner),
)
}
(TyKind::Slice(ty_a), TyKind::Slice(ty_b)) => Zip::zip_with(self, variance, ty_a, ty_b),
(TyKind::FnDef(id_a, substitution_a), TyKind::FnDef(id_b, substitution_b)) => {
if id_a != id_b {
return Err(NoSolution);
}
self.zip_substs(
variance,
Some(self.unification_database().fn_def_variance(*id_a)),
substitution_a.as_slice(interner),
substitution_b.as_slice(interner),
)
}
(
TyKind::Ref(mutability_a, lifetime_a, ty_a),
TyKind::Ref(mutability_b, lifetime_b, ty_b),
) => {
if mutability_a != mutability_b {
return Err(NoSolution);
}
// The lifetime is `Contravariant`
Zip::zip_with(
self,
variance.xform(Variance::Contravariant),
lifetime_a,
lifetime_b,
)?;
// The type is `Covariant` when not mut, `Invariant` otherwise
let output_variance = match mutability_a {
Mutability::Not => Variance::Covariant,
Mutability::Mut => Variance::Invariant,
};
Zip::zip_with(self, variance.xform(output_variance), ty_a, ty_b)
}
(TyKind::Raw(mutability_a, ty_a), TyKind::Raw(mutability_b, ty_b)) => {
if mutability_a != mutability_b {
return Err(NoSolution);
}
let ty_variance = match mutability_a {
Mutability::Not => Variance::Covariant,
Mutability::Mut => Variance::Invariant,
};
Zip::zip_with(self, variance.xform(ty_variance), ty_a, ty_b)
}
(TyKind::Never, TyKind::Never) => Ok(()),
(TyKind::Array(ty_a, const_a), TyKind::Array(ty_b, const_b)) => {
Zip::zip_with(self, variance, ty_a, ty_b)?;
Zip::zip_with(self, variance, const_a, const_b)
}
(TyKind::Closure(id_a, substitution_a), TyKind::Closure(id_b, substitution_b)) => {
if id_a != id_b {
return Err(NoSolution);
}
self.zip_substs(
variance,
None,
substitution_a.as_slice(interner),
substitution_b.as_slice(interner),
)
}
(TyKind::Coroutine(id_a, substitution_a), TyKind::Coroutine(id_b, substitution_b)) => {
if id_a != id_b {
return Err(NoSolution);
}
self.zip_substs(
variance,
None,
substitution_a.as_slice(interner),
substitution_b.as_slice(interner),
)
}
(
TyKind::CoroutineWitness(id_a, substitution_a),
TyKind::CoroutineWitness(id_b, substitution_b),
) => {
if id_a != id_b {
return Err(NoSolution);
}
self.zip_substs(
variance,
None,
substitution_a.as_slice(interner),
substitution_b.as_slice(interner),
)
}
(TyKind::Foreign(id_a), TyKind::Foreign(id_b)) => {
Zip::zip_with(self, variance, id_a, id_b)
}
(TyKind::Error, TyKind::Error) => Ok(()),
(_, _) => panic!(
"structural mismatch between answer `{:?}` and pending goal `{:?}`",
answer, pending,
),
}
}
fn zip_lifetimes(
&mut self,
variance: Variance,
answer: &Lifetime<I>,
pending: &Lifetime<I>,
) -> Fallible<()> {
let interner = self.interner;
if let Some(pending) = self.table.normalize_lifetime_shallow(interner, pending) {
return Zip::zip_with(self, variance, answer, &pending);
}
if let LifetimeData::BoundVar(answer_depth) = answer.data(interner) {
if self.unify_free_answer_var(
interner,
self.unification_database,
variance,
*answer_depth,
GenericArgData::Lifetime(pending.clone()),
)? {
return Ok(());
}
}
match (answer.data(interner), pending.data(interner)) {
(LifetimeData::BoundVar(answer_depth), LifetimeData::BoundVar(pending_depth)) => {
self.assert_matching_vars(*answer_depth, *pending_depth)
}
(LifetimeData::Static, LifetimeData::Static)
| (LifetimeData::Placeholder(_), LifetimeData::Placeholder(_))
| (LifetimeData::Erased, LifetimeData::Erased) => {
assert_eq!(answer, pending);
Ok(())
}
(LifetimeData::InferenceVar(_), _) | (_, LifetimeData::InferenceVar(_)) => panic!(
"unexpected inference var in answer `{:?}` or pending goal `{:?}`",
answer, pending,
),
(LifetimeData::Static, _)
| (LifetimeData::BoundVar(_), _)
| (LifetimeData::Placeholder(_), _)
| (LifetimeData::Erased, _)
| (LifetimeData::Error, _) => panic!(
"structural mismatch between answer `{:?}` and pending goal `{:?}`",
answer, pending,
),
(LifetimeData::Phantom(void, _), _) => match *void {},
}
}
fn zip_consts(
&mut self,
variance: Variance,
answer: &Const<I>,
pending: &Const<I>,
) -> Fallible<()> {
let interner = self.interner;
if let Some(pending) = self.table.normalize_const_shallow(interner, pending) {
return Zip::zip_with(self, variance, answer, &pending);
}
let ConstData {
ty: answer_ty,
value: answer_value,
} = answer.data(interner);
let ConstData {
ty: pending_ty,
value: pending_value,
} = pending.data(interner);
self.zip_tys(variance, answer_ty, pending_ty)?;
if let ConstValue::BoundVar(answer_depth) = answer_value {
if self.unify_free_answer_var(
interner,
self.unification_database,
variance,
*answer_depth,
GenericArgData::Const(pending.clone()),
)? {
return Ok(());
}
}
match (answer_value, pending_value) {
(ConstValue::BoundVar(answer_depth), ConstValue::BoundVar(pending_depth)) => {
self.assert_matching_vars(*answer_depth, *pending_depth)
}
(ConstValue::Placeholder(_), ConstValue::Placeholder(_)) => {
assert_eq!(answer, pending);
Ok(())
}
(ConstValue::Concrete(c1), ConstValue::Concrete(c2)) => {
assert!(c1.const_eq(answer_ty, c2, interner));
Ok(())
}
(ConstValue::InferenceVar(_), _) | (_, ConstValue::InferenceVar(_)) => panic!(
"unexpected inference var in answer `{:?}` or pending goal `{:?}`",
answer, pending,
),
(ConstValue::BoundVar(_), _)
| (ConstValue::Placeholder(_), _)
| (ConstValue::Concrete(_), _) => panic!(
"structural mismatch between answer `{:?}` and pending goal `{:?}`",
answer, pending,
),
}
}
fn zip_binders<T>(
&mut self,
variance: Variance,
answer: &Binders<T>,
pending: &Binders<T>,
) -> Fallible<()>
where
T: HasInterner<Interner = I> + Zip<I> + TypeFoldable<I>,
{
self.outer_binder.shift_in();
Zip::zip_with(
self,
variance,
answer.skip_binders(),
pending.skip_binders(),
)?;
self.outer_binder.shift_out();
Ok(())
}
fn interner(&self) -> I {
self.interner
}
fn unification_database(&self) -> &dyn UnificationDatabase<I> {
self.unification_database
}
}