chalk_engine/slg/

resolvent.rs

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
    }
}