chalk_ir/

fold.rs

//! Traits for transforming bits of IR.

use crate::*;
use std::convert::Infallible;
use std::fmt::Debug;

mod binder_impls;
mod boring_impls;
mod in_place;
pub mod shift;
mod subst;

pub use self::shift::Shift;
pub use self::subst::Subst;

/// A "folder" is a transformer that can be used to make a copy of
/// some term -- that is, some bit of IR, such as a `Goal` -- with
/// certain changes applied. The idea is that it contains methods that
/// let you swap types/lifetimes for new types/lifetimes; meanwhile,
/// each bit of IR implements the `TypeFoldable` trait which, given a
/// `FallibleTypeFolder`, will reconstruct itself, invoking the folder's
/// methods to transform each of the types/lifetimes embedded within.
///
/// As the name suggests, folds performed by `FallibleTypeFolder` can
/// fail (with type `Error`); if the folder cannot fail, consider
/// implementing `TypeFolder` instead (which is an infallible, but
/// otherwise equivalent, trait).
///
/// # Usage patterns
///
/// ## Substituting for free variables
///
/// Most of the time, though, we are not interested in adjust
/// arbitrary types/lifetimes, but rather just free variables (even
/// more often, just free existential variables) that appear within
/// the term.
///
/// For this reason, the `FallibleTypeFolder` trait extends two other
/// traits that contain methods that are invoked when just those particular
///
/// In particular, folders can intercept references to free variables
/// (either existentially or universally quantified) and replace them
/// with other types/lifetimes as appropriate.
///
/// To create a folder `F`, one never implements `FallibleTypeFolder`
/// directly, but instead implements one of each of these three sub-traits:
///
/// - `FreeVarFolder` -- folds `BoundVar` instances that appear free
///   in the term being folded (use `DefaultFreeVarFolder` to
///   ignore/forbid these altogether)
/// - `InferenceFolder` -- folds existential `InferenceVar` instances
///   that appear in the term being folded (use
///   `DefaultInferenceFolder` to ignore/forbid these altogether)
/// - `PlaceholderFolder` -- folds universal `Placeholder` instances
///   that appear in the term being folded (use
///   `DefaultPlaceholderFolder` to ignore/forbid these altogether)
///
/// To **apply** a folder, use the `TypeFoldable::try_fold_with` method,
/// like so
///
/// ```rust,ignore
/// let x = x.try_fold_with(&mut folder, 0);
/// ```
pub trait FallibleTypeFolder<I: Interner> {
    /// The type this folder returns when folding fails. This is
    /// commonly [`NoSolution`].
    type Error;

    /// Creates a `dyn` value from this folder. Unfortunately, this
    /// must be added manually to each impl of FallibleTypeFolder; it
    /// permits the default implements below to create a
    /// `&mut dyn FallibleTypeFolder` from `Self` without knowing what
    /// `Self` is (by invoking this method). Effectively, this limits
    /// impls of `FallibleTypeFolder` to types for which we are able to
    /// create a dyn value (i.e., not `[T]` types).
    fn as_dyn(&mut self) -> &mut dyn FallibleTypeFolder<I, Error = Self::Error>;

    /// Top-level callback: invoked for each `Ty<I>` that is
    /// encountered when folding. By default, invokes
    /// `try_super_fold_with`, which will in turn invoke the more
    /// specialized folding methods below, like `try_fold_free_var_ty`.
    fn try_fold_ty(
        &mut self,
        ty: Ty<I>,
        outer_binder: DebruijnIndex,
    ) -> Result<Ty<I>, Self::Error> {
        ty.try_super_fold_with(self.as_dyn(), outer_binder)
    }

    /// Top-level callback: invoked for each `Lifetime<I>` that is
    /// encountered when folding. By default, invokes
    /// `try_super_fold_with`, which will in turn invoke the more
    /// specialized folding methods below, like `try_fold_free_var_lifetime`.
    fn try_fold_lifetime(
        &mut self,
        lifetime: Lifetime<I>,
        outer_binder: DebruijnIndex,
    ) -> Result<Lifetime<I>, Self::Error> {
        lifetime.try_super_fold_with(self.as_dyn(), outer_binder)
    }

    /// Top-level callback: invoked for each `Const<I>` that is
    /// encountered when folding. By default, invokes
    /// `try_super_fold_with`, which will in turn invoke the more
    /// specialized folding methods below, like `try_fold_free_var_const`.
    fn try_fold_const(
        &mut self,
        constant: Const<I>,
        outer_binder: DebruijnIndex,
    ) -> Result<Const<I>, Self::Error> {
        constant.try_super_fold_with(self.as_dyn(), outer_binder)
    }

    /// Invoked for every program clause. By default, recursively folds the goals contents.
    fn try_fold_program_clause(
        &mut self,
        clause: ProgramClause<I>,
        outer_binder: DebruijnIndex,
    ) -> Result<ProgramClause<I>, Self::Error> {
        clause.try_super_fold_with(self.as_dyn(), outer_binder)
    }

    /// Invoked for every goal. By default, recursively folds the goals contents.
    fn try_fold_goal(
        &mut self,
        goal: Goal<I>,
        outer_binder: DebruijnIndex,
    ) -> Result<Goal<I>, Self::Error> {
        goal.try_super_fold_with(self.as_dyn(), outer_binder)
    }

    /// If overridden to return true, then folding will panic if a
    /// free variable is encountered. This should be done if free
    /// type/lifetime variables are not expected.
    fn forbid_free_vars(&self) -> bool {
        false
    }

    /// Invoked for `TyKind::BoundVar` instances that are not bound
    /// within the type being folded over:
    ///
    /// - `depth` is the depth of the `TyKind::BoundVar`; this has
    ///   been adjusted to account for binders in scope.
    /// - `binders` is the number of binders in scope.
    ///
    /// This should return a type suitable for a context with
    /// `binders` in scope.
    fn try_fold_free_var_ty(
        &mut self,
        bound_var: BoundVar,
        outer_binder: DebruijnIndex,
    ) -> Result<Ty<I>, Self::Error> {
        if self.forbid_free_vars() {
            panic!(
                "unexpected free variable with depth `{:?}` with outer binder {:?}",
                bound_var, outer_binder
            )
        } else {
            let bound_var = bound_var.shifted_in_from(outer_binder);
            Ok(TyKind::<I>::BoundVar(bound_var).intern(self.interner()))
        }
    }

    /// As `try_fold_free_var_ty`, but for lifetimes.
    fn try_fold_free_var_lifetime(
        &mut self,
        bound_var: BoundVar,
        outer_binder: DebruijnIndex,
    ) -> Result<Lifetime<I>, Self::Error> {
        if self.forbid_free_vars() {
            panic!(
                "unexpected free variable with depth `{:?}` with outer binder {:?}",
                bound_var, outer_binder
            )
        } else {
            let bound_var = bound_var.shifted_in_from(outer_binder);
            Ok(LifetimeData::<I>::BoundVar(bound_var).intern(self.interner()))
        }
    }

    /// As `try_fold_free_var_ty`, but for constants.
    fn try_fold_free_var_const(
        &mut self,
        ty: Ty<I>,
        bound_var: BoundVar,
        outer_binder: DebruijnIndex,
    ) -> Result<Const<I>, Self::Error> {
        if self.forbid_free_vars() {
            panic!(
                "unexpected free variable with depth `{:?}` with outer binder {:?}",
                bound_var, outer_binder
            )
        } else {
            let bound_var = bound_var.shifted_in_from(outer_binder);
            Ok(ConstData {
                ty: ty.try_fold_with(self.as_dyn(), outer_binder)?,
                value: ConstValue::<I>::BoundVar(bound_var),
            }
            .intern(self.interner()))
        }
    }

    /// If overridden to return true, we will panic when a free
    /// placeholder type/lifetime/const is encountered.
    fn forbid_free_placeholders(&self) -> bool {
        false
    }

    /// Invoked for each occurrence of a placeholder type; these are
    /// used when we instantiate binders universally. Returns a type
    /// to use instead, which should be suitably shifted to account
    /// for `binders`.
    ///
    /// - `universe` is the universe of the `TypeName::ForAll` that was found
    /// - `binders` is the number of binders in scope
    #[allow(unused_variables)]
    fn try_fold_free_placeholder_ty(
        &mut self,
        universe: PlaceholderIndex,
        outer_binder: DebruijnIndex,
    ) -> Result<Ty<I>, Self::Error> {
        if self.forbid_free_placeholders() {
            panic!("unexpected placeholder type `{:?}`", universe)
        } else {
            Ok(universe.to_ty::<I>(self.interner()))
        }
    }

    /// As with `try_fold_free_placeholder_ty`, but for lifetimes.
    #[allow(unused_variables)]
    fn try_fold_free_placeholder_lifetime(
        &mut self,
        universe: PlaceholderIndex,
        outer_binder: DebruijnIndex,
    ) -> Result<Lifetime<I>, Self::Error> {
        if self.forbid_free_placeholders() {
            panic!("unexpected placeholder lifetime `{:?}`", universe)
        } else {
            Ok(universe.to_lifetime(self.interner()))
        }
    }

    /// As with `try_fold_free_placeholder_ty`, but for constants.
    #[allow(unused_variables)]
    fn try_fold_free_placeholder_const(
        &mut self,
        ty: Ty<I>,
        universe: PlaceholderIndex,
        outer_binder: DebruijnIndex,
    ) -> Result<Const<I>, Self::Error> {
        if self.forbid_free_placeholders() {
            panic!("unexpected placeholder const `{:?}`", universe)
        } else {
            Ok(universe.to_const(
                self.interner(),
                ty.try_fold_with(self.as_dyn(), outer_binder)?,
            ))
        }
    }

    /// If overridden to return true, inference variables will trigger
    /// panics when folded. Used when inference variables are
    /// unexpected.
    fn forbid_inference_vars(&self) -> bool {
        false
    }

    /// Invoked for each occurrence of a inference type; these are
    /// used when we instantiate binders universally. Returns a type
    /// to use instead, which should be suitably shifted to account
    /// for `binders`.
    ///
    /// - `universe` is the universe of the `TypeName::ForAll` that was found
    /// - `binders` is the number of binders in scope
    #[allow(unused_variables)]
    fn try_fold_inference_ty(
        &mut self,
        var: InferenceVar,
        kind: TyVariableKind,
        outer_binder: DebruijnIndex,
    ) -> Result<Ty<I>, Self::Error> {
        if self.forbid_inference_vars() {
            panic!("unexpected inference type `{:?}`", var)
        } else {
            Ok(var.to_ty(self.interner(), kind))
        }
    }

    /// As with `try_fold_inference_ty`, but for lifetimes.
    #[allow(unused_variables)]
    fn try_fold_inference_lifetime(
        &mut self,
        var: InferenceVar,
        outer_binder: DebruijnIndex,
    ) -> Result<Lifetime<I>, Self::Error> {
        if self.forbid_inference_vars() {
            panic!("unexpected inference lifetime `'{:?}`", var)
        } else {
            Ok(var.to_lifetime(self.interner()))
        }
    }

    /// As with `try_fold_inference_ty`, but for constants.
    #[allow(unused_variables)]
    fn try_fold_inference_const(
        &mut self,
        ty: Ty<I>,
        var: InferenceVar,
        outer_binder: DebruijnIndex,
    ) -> Result<Const<I>, Self::Error> {
        if self.forbid_inference_vars() {
            panic!("unexpected inference const `{:?}`", var)
        } else {
            Ok(var.to_const(
                self.interner(),
                ty.try_fold_with(self.as_dyn(), outer_binder)?,
            ))
        }
    }

    /// Gets the interner that is being folded from.
    fn interner(&self) -> I;
}

/// A "folder" is a transformer that can be used to make a copy of
/// some term -- that is, some bit of IR, such as a `Goal` -- with
/// certain changes applied. The idea is that it contains methods that
/// let you swap types/lifetimes for new types/lifetimes; meanwhile,
/// each bit of IR implements the `TypeFoldable` trait which, given a
/// `TypeFolder`, will reconstruct itself, invoking the folder's methods
/// to transform each of the types/lifetimes embedded within.
///
/// Folds performed by `TypeFolder` cannot fail.  If folds might fail,
/// consider implementing `FallibleTypeFolder` instead (which is a
/// fallible, but otherwise equivalent, trait).
///
/// # Usage patterns
///
/// ## Substituting for free variables
///
/// Most of the time, though, we are not interested in adjust
/// arbitrary types/lifetimes, but rather just free variables (even
/// more often, just free existential variables) that appear within
/// the term.
///
/// For this reason, the `TypeFolder` trait extends two other traits that
/// contain methods that are invoked when just those particular
///
/// In particular, folders can intercept references to free variables
/// (either existentially or universally quantified) and replace them
/// with other types/lifetimes as appropriate.
///
/// To create a folder `F`, one never implements `TypeFolder` directly, but instead
/// implements one of each of these three sub-traits:
///
/// - `FreeVarFolder` -- folds `BoundVar` instances that appear free
///   in the term being folded (use `DefaultFreeVarFolder` to
///   ignore/forbid these altogether)
/// - `InferenceFolder` -- folds existential `InferenceVar` instances
///   that appear in the term being folded (use
///   `DefaultInferenceFolder` to ignore/forbid these altogether)
/// - `PlaceholderFolder` -- folds universal `Placeholder` instances
///   that appear in the term being folded (use
///   `DefaultPlaceholderFolder` to ignore/forbid these altogether)
///
/// To **apply** a folder, use the `TypeFoldable::fold_with` method, like so
///
/// ```rust,ignore
/// let x = x.fold_with(&mut folder, 0);
/// ```
pub trait TypeFolder<I: Interner>: FallibleTypeFolder<I, Error = Infallible> {
    /// Creates a `dyn` value from this folder. Unfortunately, this
    /// must be added manually to each impl of TypeFolder; it permits the
    /// default implements below to create a `&mut dyn TypeFolder` from
    /// `Self` without knowing what `Self` is (by invoking this
    /// method). Effectively, this limits impls of `TypeFolder` to types
    /// for which we are able to create a dyn value (i.e., not `[T]`
    /// types).
    fn as_dyn(&mut self) -> &mut dyn TypeFolder<I>;

    /// Top-level callback: invoked for each `Ty<I>` that is
    /// encountered when folding. By default, invokes
    /// `super_fold_with`, which will in turn invoke the more
    /// specialized folding methods below, like `fold_free_var_ty`.
    fn fold_ty(&mut self, ty: Ty<I>, outer_binder: DebruijnIndex) -> Ty<I> {
        ty.super_fold_with(TypeFolder::as_dyn(self), outer_binder)
    }

    /// Top-level callback: invoked for each `Lifetime<I>` that is
    /// encountered when folding. By default, invokes
    /// `super_fold_with`, which will in turn invoke the more
    /// specialized folding methods below, like `fold_free_var_lifetime`.
    fn fold_lifetime(&mut self, lifetime: Lifetime<I>, outer_binder: DebruijnIndex) -> Lifetime<I> {
        lifetime.super_fold_with(TypeFolder::as_dyn(self), outer_binder)
    }

    /// Top-level callback: invoked for each `Const<I>` that is
    /// encountered when folding. By default, invokes
    /// `super_fold_with`, which will in turn invoke the more
    /// specialized folding methods below, like `fold_free_var_const`.
    fn fold_const(&mut self, constant: Const<I>, outer_binder: DebruijnIndex) -> Const<I> {
        constant.super_fold_with(TypeFolder::as_dyn(self), outer_binder)
    }

    /// Invoked for every program clause. By default, recursively folds the goals contents.
    fn fold_program_clause(
        &mut self,
        clause: ProgramClause<I>,
        outer_binder: DebruijnIndex,
    ) -> ProgramClause<I> {
        clause.super_fold_with(TypeFolder::as_dyn(self), outer_binder)
    }

    /// Invoked for every goal. By default, recursively folds the goals contents.
    fn fold_goal(&mut self, goal: Goal<I>, outer_binder: DebruijnIndex) -> Goal<I> {
        goal.super_fold_with(TypeFolder::as_dyn(self), outer_binder)
    }

    /// If overridden to return true, then folding will panic if a
    /// free variable is encountered. This should be done if free
    /// type/lifetime variables are not expected.
    fn forbid_free_vars(&self) -> bool {
        false
    }

    /// Invoked for `TyKind::BoundVar` instances that are not bound
    /// within the type being folded over:
    ///
    /// - `depth` is the depth of the `TyKind::BoundVar`; this has
    ///   been adjusted to account for binders in scope.
    /// - `binders` is the number of binders in scope.
    ///
    /// This should return a type suitable for a context with
    /// `binders` in scope.
    fn fold_free_var_ty(&mut self, bound_var: BoundVar, outer_binder: DebruijnIndex) -> Ty<I> {
        if TypeFolder::forbid_free_vars(self) {
            panic!(
                "unexpected free variable with depth `{:?}` with outer binder {:?}",
                bound_var, outer_binder
            )
        } else {
            let bound_var = bound_var.shifted_in_from(outer_binder);
            TyKind::<I>::BoundVar(bound_var).intern(TypeFolder::interner(self))
        }
    }

    /// As `fold_free_var_ty`, but for lifetimes.
    fn fold_free_var_lifetime(
        &mut self,
        bound_var: BoundVar,
        outer_binder: DebruijnIndex,
    ) -> Lifetime<I> {
        if TypeFolder::forbid_free_vars(self) {
            panic!(
                "unexpected free variable with depth `{:?}` with outer binder {:?}",
                bound_var, outer_binder
            )
        } else {
            let bound_var = bound_var.shifted_in_from(outer_binder);
            LifetimeData::<I>::BoundVar(bound_var).intern(TypeFolder::interner(self))
        }
    }

    /// As `fold_free_var_ty`, but for constants.
    fn fold_free_var_const(
        &mut self,
        ty: Ty<I>,
        bound_var: BoundVar,
        outer_binder: DebruijnIndex,
    ) -> Const<I> {
        if TypeFolder::forbid_free_vars(self) {
            panic!(
                "unexpected free variable with depth `{:?}` with outer binder {:?}",
                bound_var, outer_binder
            )
        } else {
            let bound_var = bound_var.shifted_in_from(outer_binder);
            ConstData {
                ty: ty.fold_with(TypeFolder::as_dyn(self), outer_binder),
                value: ConstValue::<I>::BoundVar(bound_var),
            }
            .intern(TypeFolder::interner(self))
        }
    }

    /// If overridden to return true, we will panic when a free
    /// placeholder type/lifetime/const is encountered.
    fn forbid_free_placeholders(&self) -> bool {
        false
    }

    /// Invoked for each occurrence of a placeholder type; these are
    /// used when we instantiate binders universally. Returns a type
    /// to use instead, which should be suitably shifted to account
    /// for `binders`.
    ///
    /// - `universe` is the universe of the `TypeName::ForAll` that was found
    /// - `binders` is the number of binders in scope
    #[allow(unused_variables)]
    fn fold_free_placeholder_ty(
        &mut self,
        universe: PlaceholderIndex,
        outer_binder: DebruijnIndex,
    ) -> Ty<I> {
        if TypeFolder::forbid_free_placeholders(self) {
            panic!("unexpected placeholder type `{:?}`", universe)
        } else {
            universe.to_ty::<I>(TypeFolder::interner(self))
        }
    }

    /// As with `fold_free_placeholder_ty`, but for lifetimes.
    #[allow(unused_variables)]
    fn fold_free_placeholder_lifetime(
        &mut self,
        universe: PlaceholderIndex,
        outer_binder: DebruijnIndex,
    ) -> Lifetime<I> {
        if TypeFolder::forbid_free_placeholders(self) {
            panic!("unexpected placeholder lifetime `{:?}`", universe)
        } else {
            universe.to_lifetime(TypeFolder::interner(self))
        }
    }

    /// As with `fold_free_placeholder_ty`, but for constants.
    #[allow(unused_variables)]
    fn fold_free_placeholder_const(
        &mut self,
        ty: Ty<I>,
        universe: PlaceholderIndex,
        outer_binder: DebruijnIndex,
    ) -> Const<I> {
        if TypeFolder::forbid_free_placeholders(self) {
            panic!("unexpected placeholder const `{:?}`", universe)
        } else {
            universe.to_const(
                TypeFolder::interner(self),
                ty.fold_with(TypeFolder::as_dyn(self), outer_binder),
            )
        }
    }

    /// If overridden to return true, inference variables will trigger
    /// panics when folded. Used when inference variables are
    /// unexpected.
    fn forbid_inference_vars(&self) -> bool {
        false
    }

    /// Invoked for each occurrence of a inference type; these are
    /// used when we instantiate binders universally. Returns a type
    /// to use instead, which should be suitably shifted to account
    /// for `binders`.
    ///
    /// - `universe` is the universe of the `TypeName::ForAll` that was found
    /// - `binders` is the number of binders in scope
    #[allow(unused_variables)]
    fn fold_inference_ty(
        &mut self,
        var: InferenceVar,
        kind: TyVariableKind,
        outer_binder: DebruijnIndex,
    ) -> Ty<I> {
        if TypeFolder::forbid_inference_vars(self) {
            panic!("unexpected inference type `{:?}`", var)
        } else {
            var.to_ty(TypeFolder::interner(self), kind)
        }
    }

    /// As with `fold_inference_ty`, but for lifetimes.
    #[allow(unused_variables)]
    fn fold_inference_lifetime(
        &mut self,
        var: InferenceVar,
        outer_binder: DebruijnIndex,
    ) -> Lifetime<I> {
        if TypeFolder::forbid_inference_vars(self) {
            panic!("unexpected inference lifetime `'{:?}`", var)
        } else {
            var.to_lifetime(TypeFolder::interner(self))
        }
    }

    /// As with `fold_inference_ty`, but for constants.
    #[allow(unused_variables)]
    fn fold_inference_const(
        &mut self,
        ty: Ty<I>,
        var: InferenceVar,
        outer_binder: DebruijnIndex,
    ) -> Const<I> {
        if TypeFolder::forbid_inference_vars(self) {
            panic!("unexpected inference const `{:?}`", var)
        } else {
            var.to_const(
                TypeFolder::interner(self),
                ty.fold_with(TypeFolder::as_dyn(self), outer_binder),
            )
        }
    }

    /// Gets the interner that is being folded from.
    fn interner(&self) -> I;
}

/// Applies the given `TypeFolder` to a value, producing a folded result
/// of type `Self::Result`. The result type is typically the same as
/// the source type, but in some cases we convert from borrowed
/// to owned as well (e.g., the folder for `&T` will fold to a fresh
/// `T`; well, actually `T::Result`).
pub trait TypeFoldable<I: Interner>: Debug + Sized {
    /// Apply the given folder `folder` to `self`; `binders` is the
    /// number of binders that are in scope when beginning the
    /// folder. Typically `binders` starts as 0, but is adjusted when
    /// we encounter `Binders<T>` in the IR or other similar
    /// constructs.
    fn try_fold_with<E>(
        self,
        folder: &mut dyn FallibleTypeFolder<I, Error = E>,
        outer_binder: DebruijnIndex,
    ) -> Result<Self, E>;

    /// A convenient alternative to `try_fold_with` for use with infallible
    /// folders. Do not override this method, to ensure coherence with
    /// `try_fold_with`.
    fn fold_with(self, folder: &mut dyn TypeFolder<I>, outer_binder: DebruijnIndex) -> Self {
        self.try_fold_with(FallibleTypeFolder::as_dyn(folder), outer_binder)
            .unwrap()
    }
}

/// For types where "fold" invokes a callback on the `TypeFolder`, the
/// `TypeSuperFoldable` trait captures the recursive behavior that folds all
/// the contents of the type.
pub trait TypeSuperFoldable<I: Interner>: TypeFoldable<I> {
    /// Recursively folds the value.
    fn try_super_fold_with<E>(
        self,
        folder: &mut dyn FallibleTypeFolder<I, Error = E>,
        outer_binder: DebruijnIndex,
    ) -> Result<Self, E>;

    /// A convenient alternative to `try_super_fold_with` for use with
    /// infallible folders. Do not override this method, to ensure coherence
    /// with `try_super_fold_with`.
    fn super_fold_with(self, folder: &mut dyn TypeFolder<I>, outer_binder: DebruijnIndex) -> Self {
        self.try_super_fold_with(FallibleTypeFolder::as_dyn(folder), outer_binder)
            .unwrap()
    }
}

/// "Folding" a type invokes the `try_fold_ty` method on the folder; this
/// usually (in turn) invokes `try_super_fold_ty` to fold the individual
/// parts.
impl<I: Interner> TypeFoldable<I> for Ty<I> {
    fn try_fold_with<E>(
        self,
        folder: &mut dyn FallibleTypeFolder<I, Error = E>,
        outer_binder: DebruijnIndex,
    ) -> Result<Self, E> {
        folder.try_fold_ty(self, outer_binder)
    }
}

/// "Super fold" for a type invokes te more detailed callbacks on the type
impl<I> TypeSuperFoldable<I> for Ty<I>
where
    I: Interner,
{
    fn try_super_fold_with<E>(
        self,
        folder: &mut dyn FallibleTypeFolder<I, Error = E>,
        outer_binder: DebruijnIndex,
    ) -> Result<Ty<I>, E> {
        let interner = folder.interner();
        Ok(match self.kind(interner) {
            TyKind::BoundVar(bound_var) => {
                if let Some(bound_var1) = bound_var.shifted_out_to(outer_binder) {
                    // This variable was bound outside of the binders
                    // that we have traversed during folding;
                    // therefore, it is free. Let the folder have a
                    // crack at it.
                    folder.try_fold_free_var_ty(bound_var1, outer_binder)?
                } else {
                    // This variable was bound within the binders that
                    // we folded over, so just return a bound
                    // variable.
                    self
                }
            }
            TyKind::Dyn(clauses) => {
                TyKind::Dyn(clauses.clone().try_fold_with(folder, outer_binder)?)
                    .intern(folder.interner())
            }
            TyKind::InferenceVar(var, kind) => {
                folder.try_fold_inference_ty(*var, *kind, outer_binder)?
            }
            TyKind::Placeholder(ui) => folder.try_fold_free_placeholder_ty(*ui, outer_binder)?,
            TyKind::Alias(proj) => TyKind::Alias(proj.clone().try_fold_with(folder, outer_binder)?)
                .intern(folder.interner()),
            TyKind::Function(fun) => {
                TyKind::Function(fun.clone().try_fold_with(folder, outer_binder)?)
                    .intern(folder.interner())
            }
            TyKind::Adt(id, substitution) => TyKind::Adt(
                id.try_fold_with(folder, outer_binder)?,
                substitution.clone().try_fold_with(folder, outer_binder)?,
            )
            .intern(folder.interner()),
            TyKind::AssociatedType(assoc_ty, substitution) => TyKind::AssociatedType(
                assoc_ty.try_fold_with(folder, outer_binder)?,
                substitution.clone().try_fold_with(folder, outer_binder)?,
            )
            .intern(folder.interner()),
            TyKind::Scalar(scalar) => TyKind::Scalar(scalar.try_fold_with(folder, outer_binder)?)
                .intern(folder.interner()),
            TyKind::Str => TyKind::Str.intern(folder.interner()),
            TyKind::Tuple(arity, substitution) => TyKind::Tuple(
                *arity,
                substitution.clone().try_fold_with(folder, outer_binder)?,
            )
            .intern(folder.interner()),
            TyKind::OpaqueType(opaque_ty, substitution) => TyKind::OpaqueType(
                opaque_ty.try_fold_with(folder, outer_binder)?,
                substitution.clone().try_fold_with(folder, outer_binder)?,
            )
            .intern(folder.interner()),
            TyKind::Slice(substitution) => {
                TyKind::Slice(substitution.clone().try_fold_with(folder, outer_binder)?)
                    .intern(folder.interner())
            }
            TyKind::FnDef(fn_def, substitution) => TyKind::FnDef(
                fn_def.try_fold_with(folder, outer_binder)?,
                substitution.clone().try_fold_with(folder, outer_binder)?,
            )
            .intern(folder.interner()),
            TyKind::Ref(mutability, lifetime, ty) => TyKind::Ref(
                mutability.try_fold_with(folder, outer_binder)?,
                lifetime.clone().try_fold_with(folder, outer_binder)?,
                ty.clone().try_fold_with(folder, outer_binder)?,
            )
            .intern(folder.interner()),
            TyKind::Raw(mutability, ty) => TyKind::Raw(
                mutability.try_fold_with(folder, outer_binder)?,
                ty.clone().try_fold_with(folder, outer_binder)?,
            )
            .intern(folder.interner()),
            TyKind::Never => TyKind::Never.intern(folder.interner()),
            TyKind::Array(ty, const_) => TyKind::Array(
                ty.clone().try_fold_with(folder, outer_binder)?,
                const_.clone().try_fold_with(folder, outer_binder)?,
            )
            .intern(folder.interner()),
            TyKind::Closure(id, substitution) => TyKind::Closure(
                id.try_fold_with(folder, outer_binder)?,
                substitution.clone().try_fold_with(folder, outer_binder)?,
            )
            .intern(folder.interner()),
            TyKind::Coroutine(id, substitution) => TyKind::Coroutine(
                id.try_fold_with(folder, outer_binder)?,
                substitution.clone().try_fold_with(folder, outer_binder)?,
            )
            .intern(folder.interner()),
            TyKind::CoroutineWitness(id, substitution) => TyKind::CoroutineWitness(
                id.try_fold_with(folder, outer_binder)?,
                substitution.clone().try_fold_with(folder, outer_binder)?,
            )
            .intern(folder.interner()),
            TyKind::Foreign(id) => {
                TyKind::Foreign(id.try_fold_with(folder, outer_binder)?).intern(folder.interner())
            }
            TyKind::Error => TyKind::Error.intern(folder.interner()),
        })
    }
}

/// "Folding" a lifetime invokes the `fold_lifetime` method on the folder; this
/// usually (in turn) invokes `super_fold_lifetime` to fold the individual
/// parts.
impl<I: Interner> TypeFoldable<I> for Lifetime<I> {
    fn try_fold_with<E>(
        self,
        folder: &mut dyn FallibleTypeFolder<I, Error = E>,
        outer_binder: DebruijnIndex,
    ) -> Result<Self, E> {
        folder.try_fold_lifetime(self, outer_binder)
    }
}

impl<I> TypeSuperFoldable<I> for Lifetime<I>
where
    I: Interner,
{
    fn try_super_fold_with<E>(
        self,
        folder: &mut dyn FallibleTypeFolder<I, Error = E>,
        outer_binder: DebruijnIndex,
    ) -> Result<Lifetime<I>, E> {
        let interner = folder.interner();
        match self.data(interner) {
            LifetimeData::BoundVar(bound_var) => {
                if let Some(bound_var1) = bound_var.shifted_out_to(outer_binder) {
                    // This variable was bound outside of the binders
                    // that we have traversed during folding;
                    // therefore, it is free. Let the folder have a
                    // crack at it.
                    folder.try_fold_free_var_lifetime(bound_var1, outer_binder)
                } else {
                    // This variable was bound within the binders that
                    // we folded over, so just return a bound
                    // variable.
                    Ok(self)
                }
            }
            LifetimeData::InferenceVar(var) => {
                folder.try_fold_inference_lifetime(*var, outer_binder)
            }
            LifetimeData::Placeholder(universe) => {
                folder.try_fold_free_placeholder_lifetime(*universe, outer_binder)
            }
            LifetimeData::Static => Ok(LifetimeData::<I>::Static.intern(folder.interner())),
            LifetimeData::Erased => Ok(LifetimeData::<I>::Erased.intern(folder.interner())),
            LifetimeData::Error => Ok(LifetimeData::<I>::Error.intern(folder.interner())),
            LifetimeData::Phantom(void, ..) => match *void {},
        }
    }
}

/// "Folding" a const invokes the `fold_const` method on the folder; this
/// usually (in turn) invokes `super_fold_const` to fold the individual
/// parts.
impl<I: Interner> TypeFoldable<I> for Const<I> {
    fn try_fold_with<E>(
        self,
        folder: &mut dyn FallibleTypeFolder<I, Error = E>,
        outer_binder: DebruijnIndex,
    ) -> Result<Self, E> {
        folder.try_fold_const(self, outer_binder)
    }
}

impl<I> TypeSuperFoldable<I> for Const<I>
where
    I: Interner,
{
    fn try_super_fold_with<E>(
        self,
        folder: &mut dyn FallibleTypeFolder<I, Error = E>,
        outer_binder: DebruijnIndex,
    ) -> Result<Const<I>, E> {
        let interner = folder.interner();
        let ConstData { ref ty, ref value } = self.data(interner);
        let mut fold_ty = || ty.clone().try_fold_with(folder, outer_binder);
        match value {
            ConstValue::BoundVar(bound_var) => {
                if let Some(bound_var1) = bound_var.shifted_out_to(outer_binder) {
                    folder.try_fold_free_var_const(ty.clone(), bound_var1, outer_binder)
                } else {
                    Ok(self)
                }
            }
            ConstValue::InferenceVar(var) => {
                folder.try_fold_inference_const(ty.clone(), *var, outer_binder)
            }
            ConstValue::Placeholder(universe) => {
                folder.try_fold_free_placeholder_const(ty.clone(), *universe, outer_binder)
            }
            ConstValue::Concrete(ev) => Ok(ConstData {
                ty: fold_ty()?,
                value: ConstValue::Concrete(ConcreteConst {
                    interned: ev.interned.clone(),
                }),
            }
            .intern(folder.interner())),
        }
    }
}

/// Folding a goal invokes the `fold_goal` callback (which will, by
/// default, invoke super-fold).
impl<I: Interner> TypeFoldable<I> for Goal<I> {
    fn try_fold_with<E>(
        self,
        folder: &mut dyn FallibleTypeFolder<I, Error = E>,
        outer_binder: DebruijnIndex,
    ) -> Result<Self, E> {
        folder.try_fold_goal(self, outer_binder)
    }
}

/// Superfold folds recursively.
impl<I: Interner> TypeSuperFoldable<I> for Goal<I> {
    fn try_super_fold_with<E>(
        self,
        folder: &mut dyn FallibleTypeFolder<I, Error = E>,
        outer_binder: DebruijnIndex,
    ) -> Result<Self, E> {
        let interner = folder.interner();
        Ok(Goal::new(
            interner,
            self.data(interner)
                .clone()
                .try_fold_with(folder, outer_binder)?,
        ))
    }
}

/// Folding a program clause invokes the `fold_program_clause`
/// callback on the folder (which will, by default, invoke the
/// `super_fold_with` method on the program clause).
impl<I: Interner> TypeFoldable<I> for ProgramClause<I> {
    fn try_fold_with<E>(
        self,
        folder: &mut dyn FallibleTypeFolder<I, Error = E>,
        outer_binder: DebruijnIndex,
    ) -> Result<Self, E> {
        folder.try_fold_program_clause(self, outer_binder)
    }
}