// Relationship between objects represented on ASG
//
//  Copyright (C) 2014-2023 Ryan Specialty, LLC.
//
//  This file is part of TAME.
//
//  This program is free software: you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation, either version 3 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program.  If not, see <http://www.gnu.org/licenses/>.

//! Relationship betwen objects on the ASG.
//!
//! See (parent module)[super] for more information.

use super::{
    Doc, Expr, Ident, Meta, Object, ObjectIndex, ObjectKind, OiPairObjectInner,
    Pkg, Root,
};
use crate::{
    asg::{graph::object::Tpl, Asg},
    f::Functor,
    parse::util::SPair,
    span::Span,
};
use std::{fmt::Display, marker::PhantomData};

pub use super::ObjectTy as ObjectRelTy;

impl Display for ObjectRelTy {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        // At the time of writing,
        //   this happens to be sufficient.
        std::fmt::Debug::fmt(self, f)
    }
}

/// Declare relations for an [`ObjectKind`].
///
/// This generates an [`ObjectRel`] type for the provided [`ObjectKind`] and
///   binds it to the kind using [`ObjectRelatable`].
///
/// Each relationship must be explicitly specified as either a `tree` or
///   `cross` edge.
/// For more information on cross edges,
///   see [`ObjectRel::is_cross_edge`].
macro_rules! object_rel {
    (
        $(#[$attr:meta])+
        $from:ident -> {
            $($ety:ident $kind:ident,)*
        }
        $(can_recurse($rec_obj:ident) if $rec_expr:expr)?
    ) => {paste::paste! {
        /// Subset of [`ObjectKind`]s that are valid targets for edges from
        #[doc=concat!("[`", stringify!($from), "`].")]
        ///
        $(#[$attr])+
        ///
        /// See [`ObjectRel`] for more information.
        ///
        /// [`ObjectKind`]: crate::asg::ObjectKind
        #[derive(Debug, PartialEq, Eq)]
        pub enum [<$from Rel>] {
            $($kind(ObjectIndex<$kind>),)*
        }

        impl ObjectRel<$from> for [<$from Rel>] {
            fn narrow_ref<OB: ObjectRelFrom<$from> + ObjectRelatable>(
                &self,
            ) -> Option<ObjectIndex<OB>> {
                match *self {
                    $(Self::$kind(oi) => oi.filter_rel(),)*
                }
            }

            /// The root of the graph by definition has no cross edges.
            fn is_cross_edge<S, T>(
                &self,
                #[allow(unused_variables)] // used only for `dyn` edges
                rel: &$crate::asg::graph::object::rel::DynObjectRel<S, T>
            ) -> bool {
                match self {
                    $(
                        Self::$kind(..) => object_rel!(@is_cross_edge $ety rel),
                    )*

                    #[allow(unreachable_patterns)] // for empty Rel types
                    _ => unreachable!(
                        concat!(stringify!($from), "Rel is empty")
                    ),
                }
            }

            $(
                fn can_recurse(&self, asg: &Asg) -> bool {
                    self.narrow_ref::<$from>()
                        .map(|oi| oi.resolve(asg))
                        .map(|$rec_obj| $rec_expr)
                        .unwrap_or(false)
                }
            )?
        }

        impl ObjectRelatable for $from {
            type Rel = [<$from Rel>];

            fn rel_ty() -> ObjectRelTy {
                ObjectRelTy::$from
            }

            fn new_rel_dyn(
                ty: ObjectRelTy,
                #[allow(unused_variables)] // for empty Rel
                oi: ObjectIndex<Object>,
            ) -> Option<[<$from Rel>]> {
                match ty {
                    $(
                        ObjectRelTy::$kind => {
                            Some(Self::Rel::$kind(oi.must_narrow_into()))
                        },
                    )*
                    _ => None,
                }
            }

            fn oi_rel_to_dyn<OB: ObjectRelatable>(
                #[allow(unused_variables)] // for empty Rel
                oi: ObjectIndex<Self>,
            ) -> Option<$crate::asg::graph::object::ObjectIndexTo<OB>> {
                #[allow(unused_imports)]
                use $crate::asg::graph::object::ObjectIndexTo;

                match OB::rel_ty() {
                    $(
                        ObjectRelTy::$kind => {
                            ObjectIndexTo::<$kind>::from(oi).reflexivity()
                        },
                    )*
                    _ => None,
                }
            }
        }

        $(
            impl From<ObjectIndex<$kind>> for [<$from Rel>] {
                fn from(value: ObjectIndex<$kind>) -> Self {
                    Self::$kind(value)
                }
            }

            object_rel!{ @impl_rel_to $from $ety $kind }
        )*

        impl From<[<$from Rel>]> for ObjectIndex<Object> {
            fn from(value: [<$from Rel>]) -> Self {
                match value {
                    $(
                        [<$from Rel>]::$kind(oi) => oi.widen(),
                    )*
                }
            }
        }
    }};

    // Static edge types.
    (@is_cross_edge cross $_:ident) => { true };
    (@is_cross_edge tree $_:ident)  => { false };

    // Dynamic edge type.
    //
    // We consider an edge to be a cross edge iff it contains a context
    //   span.
    // If it were _not_ a cross edge,
    //   then the edge would represent ownership,
    //   and the span information on the target would be sufficient context
    //     on its own;
    //       an edge only needs supplemental span information if there is
    //       another context in which that object is referenced.
    (@is_cross_edge dyn $rel:ident)  => { $rel.ctx_span().is_some() };

    // Similar to above but providing _static_ information to the type
    //   system.
    // The above could be rolled into this at some point.
    (@impl_rel_to $from:ident cross $kind:ident) => {};
    (@impl_rel_to $from:ident tree $kind:ident)  => {
        impl ObjectTreeRelTo<$kind> for $from {}
    };
    (@impl_rel_to $from:ident dyn $kind:ident)  => {
        // It _could_ be a tree edge;
        //   we can't know statically.
        impl ObjectTreeRelTo<$kind> for $from {}
    };
}

/// A dynamic relationship (edge) from one object to another before it has
///   been narrowed.
///
/// The source and target of this edge are usually [`ObjectIndex`]es,
///   but it is made generic (`S, T`) to support mapping while retaining
///   useful metadata,
///     e.g. to resolve an object while retaining the edge information.
#[derive(Debug, PartialEq)]
pub struct DynObjectRel<S = ObjectIndex<Object>, T = ObjectIndex<Object>>(
    (ObjectRelTy, ObjectRelTy),
    (S, T),
    Option<Span>,
);

impl<S, T> DynObjectRel<S, T> {
    pub(in super::super) fn new(
        from_ty: ObjectRelTy,
        to_ty: ObjectRelTy,
        src: S,
        target: T,
        ctx_span: Option<Span>,
    ) -> Self {
        Self((from_ty, to_ty), (src, target), ctx_span)
    }

    /// The type of the source edge.
    pub fn source_ty(&self) -> ObjectRelTy {
        match self {
            Self((ty, _), ..) => *ty,
        }
    }

    /// The type of the target edge.
    pub fn target_ty(&self) -> ObjectRelTy {
        match self {
            Self((_, ty), ..) => *ty,
        }
    }

    /// The source of this relationship.
    pub fn source(&self) -> &S {
        match self {
            Self(_, (oi, _), _) => oi,
        }
    }

    /// The target of this relationship.
    ///
    /// This type generally originates as [`ObjectIndex`] but can be mapped
    ///   over to retain the structured edge data.
    pub fn target(&self) -> &T {
        match self {
            Self(_, (_, oi), _) => oi,
        }
    }

    /// A [`Span`] associated with the _relationship_ between the source and
    ///   target objects,
    ///     if any.
    pub fn ctx_span(&self) -> Option<Span> {
        match self {
            Self(_, _, ctx_span) => *ctx_span,
        }
    }
}

impl<S> DynObjectRel<S, ObjectIndex<Object>> {
    /// Attempt to narrow the target into the [`ObjectRel`] of `O`.
    ///
    /// See [`ObjectRelatable::new_rel_dyn`] for more information.
    pub fn narrow_target<O: ObjectKind + ObjectRelatable>(
        &self,
    ) -> Option<O::Rel> {
        O::new_rel_dyn(self.target_ty(), *self.target())
    }

    /// Attempt to convert [`Self`] into an [`ObjectIndex`] with an
    ///   [`ObjectKind`] of type `O`.
    ///
    /// This method allows marrying a dynamically determined type with a
    ///   context requiring a static type.
    /// If the type `O` does not match the type stored at runtime,
    ///   [`None`] is returned.
    pub fn filter_into_target<O: ObjectKind + ObjectRelatable>(
        &self,
    ) -> Option<ObjectIndex<O>> {
        if self.target_ty() == O::rel_ty() {
            Some(self.target().must_narrow_into())
        } else {
            None
        }
    }

    /// Pair the target [`ObjectIndex`] with its resolved [`Object`].
    ///
    /// This allows the [`ObjectIndex`] to be refined alongside the inner
    ///   [`ObjectKind`] so that callers can make use of the refined
    ///   [`ObjectIndex`] without having to explicitly narrow themselves.
    /// While isn't any more or less safe than the manual alternative,
    ///   it _does_ defend against logic bugs.
    pub fn resolve_target_oi_pair(
        self,
        asg: &Asg,
    ) -> DynObjectRel<S, Object<OiPairObjectInner>> {
        self.map(|(soi, toi)| (soi, toi.resolve(asg).pair_oi(toi)))
    }

    /// Retrieve the target [`ObjectIndex`] as an [`ObjectIndexTo<OB>`](ObjectIndexTo),
    ///   if the object can be related to objects of type `OB`.
    ///
    /// This method may be confusing in that it represents another
    ///   _possible_ relation on top of the relation represented by
    ///   [`Self`].
    /// That is:
    ///
    /// ```text
    ///   OA -> OB [ -> OC]
    ///   '______'
    ///     Self
    /// ```
    ///
    /// If this method returns [`Some`],
    ///   that means that the target of this relation `OB` is an object
    ///   _that is capable of being related to_ an object of type `OC`.
    pub fn target_oi_rel_to_dyn<OC: ObjectRelatable>(
        &self,
    ) -> Option<ObjectIndexTo<OC>> {
        // TODO: A newtype ought to couple these in a way that we don't have
        //   to trust this assumption!
        // This requires assuming that the target is of the target type,
        //   which _should_ certainly be the case if originating from the graph,
        //   but if it's not,
        //     then later resolving the `ObjectIndex` with a mismatched type
        //     will result in a panic.
        self.target_ty()
            .assuming_oi_maybe_rel_to_dyn(*self.target())
    }

    /// Dynamically determine whether this edge represents a cross edge.
    ///
    /// This function is intended for _dynamic_ edge types,
    ///   which cannot be determined statically;
    ///     it should be used only in situations where the potential edge types
    ///     are unbounded,
    ///       e.g. on an iterator yielding generalized [`ObjectIndex`]es during
    ///       a full graph traversal.
    /// You should otherwise use [`ObjectRel::is_cross_edge`].
    ///
    /// For more information on cross edges,
    ///   see [`ObjectRel::is_cross_edge`].
    pub fn is_cross_edge(&self) -> bool {
        /// Generate cross-edge mappings between ObjectRelTy and the associated
        ///   ObjectRel.
        ///
        /// This is intended to both reduce boilerplate and to eliminate typos.
        ///
        /// This mess will be optimized away,
        ///   but exists so that cross edge definitions can exist alongside
        ///   other relationship definitions for each individual object type,
        ///     rather than having to maintain them in aggregate here.
        macro_rules! ty_cross_edge {
            ($($ty:ident),*) => {
                match self.source_ty() {
                    $(
                        ObjectRelTy::$ty => {
                            self.narrow_target::<$ty>().is_some_and(
                                |rel| rel.is_cross_edge(self)
                            )
                        },
                    )*
                }
            }
        }

        ty_cross_edge!(Root, Pkg, Ident, Expr, Tpl, Meta, Doc)
    }

    /// Dynamically determine whether this edge represents a permitted
    ///   cycle.
    ///
    /// A cycle is permitted in certain cases of recursion.
    /// See [`ObjectRel::can_recurse`] for more information.
    pub fn can_recurse(&self, asg: &Asg) -> bool {
        macro_rules! ty_can_recurse {
            ($($ty:ident),*) => {
                match self.source_ty() {
                    $(
                        ObjectRelTy::$ty => {
                            self.narrow_target::<$ty>().is_some_and(
                                |rel| rel.can_recurse(asg)
                            )
                        },
                    )*
                }
            }
        }

        ty_can_recurse!(Root, Pkg, Ident, Expr, Tpl, Meta, Doc)
    }
}

impl<T> DynObjectRel<ObjectIndex<Object>, T> {
    /// Pair the source [`ObjectIndex`] with its resolved [`Object`].
    ///
    /// This allows the [`ObjectIndex`] to be refined alongside the inner
    ///   [`ObjectKind`] so that callers can make use of the refined
    ///   [`ObjectIndex`] without having to explicitly narrow themselves.
    /// While isn't any more or less safe than the manual alternative,
    ///   it _does_ defend against logic bugs.
    pub fn resolve_source_oi_pair(
        self,
        asg: &Asg,
    ) -> DynObjectRel<Object<OiPairObjectInner>, T> {
        self.map(|(soi, toi)| (soi.resolve(asg).pair_oi(soi), toi))
    }
}

impl DynObjectRel<ObjectIndex<Object>, ObjectIndex<Object>> {
    /// Pair the source and target [`ObjectIndex`]es with their respective
    ///   resolved [`Object`]s.
    ///
    /// See [`Self::resolve_target_oi_pair`] and
    ///   [`Self::resolve_source_oi_pair`] for more information.
    pub fn resolve_oi_pairs(
        self,
        asg: &Asg,
    ) -> DynObjectRel<Object<OiPairObjectInner>, Object<OiPairObjectInner>>
    {
        self.resolve_source_oi_pair(asg).resolve_target_oi_pair(asg)
    }
}

impl<S, T, U, V> Functor<(S, T), (U, V)> for DynObjectRel<S, T> {
    type Target = DynObjectRel<U, V>;

    fn map(self, f: impl FnOnce((S, T)) -> (U, V)) -> Self::Target {
        match self {
            Self(tys, x, ctx_span) => DynObjectRel(tys, f(x), ctx_span),
        }
    }
}

impl<T: Display> Display for DynObjectRel<T> {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        let Self((from_ty, to_ty), (s, t), _) = self;

        write!(f, "dynamic edge {from_ty}->{to_ty} with {s}->{t}",)
    }
}

/// Indicate that an [`ObjectKind`] `Self` can be related to
///   [`ObjectKind`] `OB` by creating an edge from `Self` to `OB`.
///
/// This trait defines a portion of the graph ontology,
///   allowing [`Self`] to be related to `OB` by creating a directed edge
///   from [`Self`] _to_ `OB`, as in:
///
/// ```text
///   (Self) -> (OB)
/// ```
///
/// While the data on the graph itself is dynamic and provided at runtime,
///   the systems that _construct_ the graph using the runtime data can be
///   statically analyzed by the type system to ensure that they only
///   construct graphs that adhere to this schema.
pub trait ObjectRelTo<OB: ObjectKind + ObjectRelatable> =
    ObjectRelatable where <Self as ObjectRelatable>::Rel: From<ObjectIndex<OB>>;

/// Reverse of [`ObjectRelTo`].
///
/// This is primarily useful for avoiding `where` clauses,
///   or for use in `impl Trait` specifications.
pub trait ObjectRelFrom<OA: ObjectKind + ObjectRelatable> =
    ObjectRelatable where <OA as ObjectRelatable>::Rel: From<ObjectIndex<Self>>;

/// Indicate that an [`ObjectKind`] `Self` _could possibly take ownership
///   over_ an [`ObjectKind`] `OB`.
///
/// This is a stronger assertion than [`ObjectRelTo`];
///   see that trait for more information.
/// This trait is intended to be used in contexts where the distinction
///   between reference and ownership is important.
pub trait ObjectTreeRelTo<OB: ObjectKind + ObjectRelatable>:
    ObjectRelTo<OB>
{
}

/// Identify [`Self::Rel`] as a sum type consisting of the subset of
///   [`Object`] variants representing the valid _target_ edges of
///   [`Self`].
///
/// This is used to derive [`ObjectRelTo``],
///   which can be used as a trait bound to assert a valid relationship
///   between two [`Object`]s.
pub trait ObjectRelatable: ObjectKind {
    /// Sum type representing a subset of [`Object`] variants that are valid
    ///   targets for edges from [`Self`].
    ///
    /// See [`ObjectRel`] for more information.
    type Rel: ObjectRel<Self>;

    /// The [`ObjectRelTy`] tag used to identify this [`ObjectKind`] as a
    ///   target of a relation.
    fn rel_ty() -> ObjectRelTy;

    /// Represent a relation to another [`ObjectKind`] that cannot be
    ///   statically known and must be handled at runtime.
    ///
    /// A value of [`None`] means that the provided [`ObjectRelTy`] is not
    ///   valid for [`Self`].
    /// If the caller is utilizing edge data that is already present on the graph,
    ///   then this means that the system is not properly upholding edge
    ///   invariants
    ///     (the graph's ontology)
    ///     and the system ought to panic;
    ///       this is a significant bug representing a problem with the
    ///       correctness of the system.
    ///
    /// See [`ObjectRel`] for more information.
    fn new_rel_dyn(
        ty: ObjectRelTy,
        oi: ObjectIndex<Object>,
    ) -> Option<Self::Rel>;

    /// Cast the provided [`ObjectIndex`] into an [`ObjectIndexTo`] if it is
    ///   able to be related to the provided `OB`.
    ///
    /// This is intended to be used in a dynamic context,
    ///   where the caller is not aware statically of the [`ObjectKind`]s
    ///   involved.
    /// If it is _required_ that an object be relatable,
    ///   use [`ObjectRelTo`] to statically verify that assertion.
    ///
    /// If the type `OB` is not a valid target of a relation from this type,
    ///   [`None`] will be returned.
    fn oi_rel_to_dyn<OB: ObjectRelatable>(
        oi: ObjectIndex<Self>,
    ) -> Option<ObjectIndexTo<OB>>;
}

impl<O: ObjectKind + ObjectRelatable> ObjectIndex<O> {
    pub fn rel_ty(&self) -> ObjectRelTy {
        O::rel_ty()
    }
}

/// A relationship to another [`ObjectKind`].
///
/// This trait is intended to be implemented by enums that represent the
///   subset of [`ObjectKind`]s that are able to serve as edge targets for
///   the [`ObjectRelatable`] that utilizes it as its
///   [`ObjectRelatable::Rel`].
///
/// As described in the [module-level documentation](super),
///   the concrete [`ObjectKind`] of an edge is generally not able to be
///   determined statically outside of code paths that created the
///   [`Object`] anew.
/// But we _can_ at least narrow the types of [`ObjectKind`]s to those
///   [`ObjectRelTo`]s that we know are valid,
///     since the system is restricted (statically) to those edges when
///     performing operations on the graph.
///
/// This [`ObjectRel`] represents that subset of [`ObjectKind`]s.
/// A caller may decide to dispatch based on the type of edge it receives,
///   or it may filter edges with [`Self::narrow`] in conjunction with
///   [`Iterator::filter_map`]
///     (for example).
/// Since the wrapped value is an [`ObjectIndex`],
///   the system will eventually panic if it attempts to reference a node
///   that is not of the type expected by the edge,
///     which can only happen if the edge has an incorrect [`ObjectRelTy`],
///     meaning the graph is somehow corrupt
///       (because system invariants were not upheld).
///
/// This affords us both runtime memory safety and static guarantees that
///   the system is not able to generate an invalid graph that does not
///   adhere to the prescribed ontology,
///     provided that invariants are properly upheld by the
///     [`asg`](crate::asg) module.
pub trait ObjectRel<OA: ObjectKind + ObjectRelatable>:
    Sized + Into<ObjectIndex<Object>>
{
    /// Attempt to narrow into the [`ObjectKind`] `OB`.
    ///
    /// Unlike [`Object`] nodes,
    ///   _this operation does not panic_,
    ///   instead returning an [`Option`].
    /// If the relationship is of type `OB`,
    ///   then [`Some`] will be returned with an inner
    ///   [`ObjectIndex<OB>`](ObjectIndex).
    /// If the narrowing fails,
    ///   [`None`] will be returned instead.
    ///
    /// This return value is well-suited for [`Iterator::filter_map`] to
    ///   query for edges of particular kinds.
    fn narrow<OB: ObjectRelFrom<OA> + ObjectRelatable>(
        self,
    ) -> Option<ObjectIndex<OB>> {
        self.narrow_ref()
    }

    /// Attempt to narrow into the [`ObjectKind`] `OB`.
    ///
    /// This method is the same as [`Self::narrow`],
    ///   but taking a reference instead of ownership.
    fn narrow_ref<OB: ObjectRelFrom<OA> + ObjectRelatable>(
        &self,
    ) -> Option<ObjectIndex<OB>>;

    /// Attempt to narrow into the [`ObjectKind`] `OB`,
    ///   but rather than returning the narrowed type,
    ///   return `Option<Self>`.
    ///
    /// This can be used with [`Iterator::filter_map`].
    /// By not being a [`bool`] predicate,
    ///   we're able to provide a default trait implementation based on
    ///   [`Self::narrow`] without requiring that [`Self`] implement
    ///   [`Copy`].
    fn narrows_into<OB: ObjectRelFrom<OA> + ObjectRelatable>(
        self,
    ) -> Option<Self>
    where
        Self: From<ObjectIndex<OB>>,
    {
        self.narrow::<OB>().map(Into::into)
    }

    /// Widen into an [`ObjectIndex`],
    ///   discarding static type information.
    fn widen(self) -> ObjectIndex<Object> {
        self.into()
    }

    /// Whether this relationship represents an ontological cross edge.
    ///
    /// A _cross edge_ is an edge between two trees as described by the
    ///   graph's ontology.
    /// Many objects on the graph represent trees,
    ///   but contain references to other trees.
    /// Recognizing cross edges allows the system to understand when it is
    ///   following an edge between two trees,
    ///     which may require different behavior.
    ///
    /// This contrasts to cross edges in the context of a graph traversal,
    ///   where a tree is determined by a walk of the graph and may not take
    ///   into consideration the meaning of edges.
    ///
    /// _Because this is a property of the ontology rather than a structural
    ///   interpretation of the graph,
    ///     it must be manually verified by a human._
    /// An incorrect flagging of cross edges here will result in certain
    ///   traversals being incorrect.
    ///
    /// Implementation Context
    /// ======================
    /// It is important to understand why this method exists and how it may
    ///   be used so that implementations of this trait do the right thing
    ///   with regards to determining whether an edge ought to represent a
    ///   cross edge.
    ///
    /// For example,
    ///   when generating a representation of an [`Expr`],
    ///   a walk of the graph ought not consider an [`Ident`] reference to
    ///   be part of the expression tree,
    ///     otherwise the referenced expression would be inlined.
    /// Furthermore,
    ///   visiting the referenced [`Ident`] ought not inhibit a later walk,
    ///   since the walk must later traverse the [`Ident`] to reach the
    ///   [`Object`] that it represents.
    /// Similarly,
    ///   if the [`Ident`] has already been visited by a previous walk,
    ///   we want to _re-visit_ it to output a reference as part of the
    ///   referencing [`Expr`].
    ///
    /// However,
    ///   this behavior is not always desirable.
    /// In the case of a topological sort of the graph for linking,
    ///   cross edges ought to count as visitations since that dependency
    ///   must be calculated before the expression that needs it,
    ///     and we don't want to re-calculate it again later on.
    ///
    /// The cross-edge is therefore an ontological fact,
    ///   but its _interpretation_ is context-dependent.
    ///
    /// Note that the ontology is not intended to support back edges,
    ///   since they produce cycles,
    ///   except for exceptional situations
    ///     (e.g. function recursion which will hopefully be removed from
    ///       the language in the future).
    /// With that said,
    ///   if an edge could conceivably be a back edge and not be rejected
    ///   from circular dependency checks,
    ///     then do _not_ assume that it is a cross edge without further
    ///     analysis,
    ///       which may require introducing more context to this method.
    ///
    /// Dynamic Cross Edges
    /// ==================
    /// Sometimes a cross edge cannot be determined statically due to
    ///   ontological compromises.
    /// For example,
    ///   a [`Tpl`]->[`Ident`] edge could be a reference to another tree,
    ///     as in the case of template application,
    ///     or the template could be serving as a container for that
    ///       definition.
    /// The former case is a cross edge,
    ///   but the ladder is not.
    ///
    /// We could introduce a layer of indirection on the graph to
    ///   disambiguate,
    ///     but that adds complexity to the graph that many different
    ///     subsystems need to concern themselves with.
    /// But cross edge determination is fairly isolated,
    ///   needed only by traversals.
    ///
    /// Therefore,
    ///   this method also receives a [`DynObjectRel`] reference,
    ///     which contains edge information.
    /// The edge can be augmented with data that helps to determine,
    ///   at runtime,
    ///   whether that particular edge is a cross edge.
    ///
    /// The use of [`DynObjectRel`] is heavy and effectively makes this
    ///   method useless for callers that do not deal directly with raw
    ///   [`Asg`] data;
    ///     it may be useful to refine this further in the future to correct
    ///     that,
    ///       once all use cases are clear.
    fn is_cross_edge<S, T>(&self, rel: &DynObjectRel<S, T>) -> bool;

    /// Whether the provided relationship represents a valid recursive
    ///   target.
    ///
    /// It is expected that this method will be consulted only when the
    ///   provided [`ObjectIndex`] would produce a cycle when added to some
    ///   path.
    /// This means that the source and target object will be identical.
    ///
    /// It is expected that a cycle should be able to be "cut" at this point
    ///   while still producing a valid topological ordering of the graph.
    /// For example,
    ///   consider two mutually recursive functions `A` and `B`,
    ///   as shown here:
    ///
    /// ```text
    ///   A -> B
    ///   ^----'
    /// ```
    ///
    /// There are two cycles that might be encountered:
    ///
    ///   - `A -> B -> A`, which would cut to `A -> B`; and
    ///   - `B -> A -> B`, which would cut to `B -> A`.
    ///
    /// In both cases,
    ///   since both `A` and `B` are functions,
    ///   a valid ordering is produced.
    ///
    /// Failure to uphold this invariant when designing the graph's ontology
    ///   will result in an invalid ordering of the graph,
    ///     which will compile a program that does not behave according to
    ///     its specification.
    /// That is:
    ///   proper ordering is a requirement to uphold soundness.
    ///
    /// Recursion will continue to be limited as TAMER progresses,
    ///   migrating to a more APL-like alternative to solving
    ///   otherwise-recursive problems and restricting remaining recursion
    ///   to that which can provably terminate.
    fn can_recurse(&self, _asg: &Asg) -> bool {
        false
    }
}

/// An [`ObjectIndex`]-like object that is able to relate to
///   [`ObjectKind`] `OB`.
///
/// This serves primarily as an opaque [`ObjectIndex`] that we know can be
///   related to some other type of [`ObjectKind`] `OB`.
/// This allows for generic graph operations that operate on relationships
///   without having to know the type of the source object (`Self`).
pub trait ObjectIndexRelTo<OB: ObjectRelatable>: Sized + Clone + Copy {
    /// The [`ObjectRelTy`] of the inner [`ObjectIndex`] before widening.
    fn src_rel_ty(&self) -> ObjectRelTy;

    /// Widen this type into a generic [`ObjectIndex`] with no
    ///   [`ObjectKind`] information.
    ///
    /// See [`ObjectIndex::widen`] for more information.
    fn widen(&self) -> ObjectIndex<Object>;

    /// Add an edge from `self` to `to_oi` on the provided [`Asg`].
    ///
    /// Since the only invariant asserted by [`ObjectIndexRelTo`] is that
    ///   it may be related to `OB`,
    ///     this method will only permit edges to `OB`;
    ///       nothing else about the inner object is statically known.
    /// To create edges to other types of objects,
    ///   and for more information about this operation
    ///     (including `ctx_span`),
    ///   see [`ObjectIndex::add_edge_to`].
    fn add_edge_to(
        self,
        asg: &mut Asg,
        to_oi: ObjectIndex<OB>,
        ctx_span: Option<Span>,
    ) -> Self {
        asg.add_edge(self, to_oi, ctx_span);
        self
    }

    /// Check whether an edge exists from `self` to `to_oi`.
    fn has_edge_to(&self, asg: &Asg, to_oi: ObjectIndex<OB>) -> bool {
        asg.has_edge(*self, to_oi)
    }

    /// Indicate that the given identifier `oi` is defined by this object.
    fn defines(self, asg: &mut Asg, oi: ObjectIndex<Ident>) -> Self
    where
        Self: ObjectIndexRelTo<Ident>,
    {
        self.add_edge_to(asg, oi, None)
    }

    /// Iterate over the [`ObjectIndex`]es of the outgoing edges of `self`
    ///   that match the [`ObjectKind`] `OB`.
    ///
    /// Since this trait only guarantees edges to `OB`,
    ///   only edges targeting that type will be returned;
    ///     other types of edges may or may not exist.
    /// See also [`ObjectIndex::edges_filtered`].
    fn edges_rel_to<'a>(
        &self,
        asg: &'a Asg,
    ) -> impl Iterator<Item = ObjectIndex<OB>> + 'a {
        asg.edges_dyn(self.widen())
            .filter_map(|rel| rel.filter_into_target())
    }

    /// Attempt to look up a locally bound [`Ident`] via a linear search of
    ///   `self`'s edges.
    ///
    /// Performance
    /// ===========
    /// _This is a linear (O(1)) search of the edges of the node
    ///   corresponding to `self`!_
    /// At the time of writing,
    ///   edges are stored using index references in a manner similar to a
    ///   linked list (petgraph).
    /// And for each such edge,
    ///   the target object must be resolved so that its
    ///   [`SymbolId`](crate::sym::SymbolId) may be retrieved and compared
    ///   against the provided `name`.
    ///
    /// If the number of edges is small and the objects are fairly localized
    ///   in memory relative to `self`,
    ///     then this may not be a concern.
    /// However,
    ///   if you've arrived at this method while investigating unfavorable
    ///   circumstances during profiling,
    ///     then you should consider caching like the global environment
    ///       (see [`Asg::lookup`]).
    fn lookup_local_linear(
        &self,
        asg: &Asg,
        name: SPair,
    ) -> Option<ObjectIndex<Ident>>
    where
        Self: ObjectIndexRelTo<Ident>,
    {
        // Rust fails to infer OB with `self.edges_rel_to` as of 2023-03
        ObjectIndexRelTo::<Ident>::edges_rel_to(self, asg)
            .find(|oi| oi.resolve(asg).name().symbol() == name.symbol())
    }

    /// Declare a local identifier.
    ///
    /// A local identifier is lexically scoped to `self`.
    /// This operation is valid only for [`ObjectKind`]s that can contain
    ///   edges to [`Ident`]s.
    ///
    /// TODO: This allows for duplicate local identifiers!
    fn declare_local(&self, asg: &mut Asg, name: SPair) -> ObjectIndex<Ident>
    where
        Self: ObjectIndexRelTo<Ident>,
    {
        asg.create(Ident::declare(name))
            .add_edge_from(asg, *self, None)
    }
}

impl<O: ObjectRelatable, OB: ObjectRelatable> ObjectIndexRelTo<OB>
    for ObjectIndex<O>
where
    O: ObjectRelTo<OB>,
{
    fn src_rel_ty(&self) -> ObjectRelTy {
        O::rel_ty()
    }

    fn widen(&self) -> ObjectIndex<Object> {
        ObjectIndex::<O>::widen(*self)
    }
}

impl<OB: ObjectRelatable> ObjectIndexRelTo<OB> for ObjectIndexTo<OB> {
    fn src_rel_ty(&self) -> ObjectRelTy {
        match self {
            Self((_, ty), _) => *ty,
        }
    }

    fn widen(&self) -> ObjectIndex<Object> {
        *self.as_ref()
    }
}

impl<OB: ObjectRelatable> ObjectIndexRelTo<OB> for ObjectIndexToTree<OB> {
    fn src_rel_ty(&self) -> ObjectRelTy {
        match self {
            Self(oito) => oito.src_rel_ty(),
        }
    }

    fn widen(&self) -> ObjectIndex<Object> {
        match self {
            Self(oito) => oito.widen(),
        }
    }
}

impl<OB: ObjectRelatable> From<ObjectIndexTo<OB>> for ObjectIndex<Object> {
    fn from(oi_rel: ObjectIndexTo<OB>) -> Self {
        oi_rel.widen()
    }
}

impl<OB: ObjectRelatable> AsRef<ObjectIndex<Object>> for ObjectIndexTo<OB> {
    fn as_ref(&self) -> &ObjectIndex<Object> {
        match self {
            Self((oi, _), _) => oi,
        }
    }
}

/// An [`ObjectIndex`]-like object that is able to create a _tree_ edge to
///   [`ObjectKind`] `OB`.
///
/// This allows for generic graph operations that operate on ownership
///   relationships without having to know the type of the source
///   object (`Self`).
///
/// This is a specialization of [`ObjectIndexRelTo`].
pub trait ObjectIndexTreeRelTo<OB: ObjectRelatable>:
    ObjectIndexRelTo<OB> + Into<ObjectIndexToTree<OB>>
{
}

impl<OB: ObjectRelatable> ObjectIndexTreeRelTo<OB> for ObjectIndexToTree<OB> {}

impl<O: ObjectRelatable, OB: ObjectRelatable> ObjectIndexTreeRelTo<OB>
    for ObjectIndex<O>
where
    O: ObjectTreeRelTo<OB>,
{
}

pub use private::{ObjectIndexTo, ObjectIndexToTree};

/// Private inner module to ensure that nothing is able to bypass invariants
///   by constructing [`ObjectIndexTo`] manually.
mod private {
    use std::hash::{Hash, Hasher};

    use super::*;

    /// Some [`ObjectIndex`] that is able to [`ObjectRelTo`] `OB`.
    ///
    /// This type upholds the invariant that any [`ObjectIndex`] contained
    ///   within is [`ObjectRelTo`] `OB`.
    /// This allows this object to serve in place of a concrete
    ///   [`ObjectIndex`] for graph operations that need only know whether
    ///   an object is relatable to another,
    ///     such as when adding edges.
    ///
    /// This object is only needed when relations need to be manipulated on
    ///   a known target [`ObjectKind`] `OB`,
    ///     but the source [`ObjectKind`] is dynamic.
    /// This is necessary because a generic [`Object`] must first be
    ///   narrowed before being able to be used in any graph operation so
    ///   that the ontology can be statically enforced.
    ///
    /// See [`ObjectIndexRelTo`] for more information.
    ///
    /// Constructing [`ObjectIndexTo`]
    /// ==============================
    /// This object is intended to be constructed using [`From`].
    /// _Never construct this object in any other way;_
    ///   manually creating the struct will not uphold its invariants,
    ///     which can lead to an invalid graph construction,
    ///     which will in turn lead to internal system failures when trying
    ///       to operate on the graph data down the line.
    /// There are no memory safety concerns.
    #[derive(Debug)]
    pub struct ObjectIndexTo<OB: ObjectRelatable>(
        (ObjectIndex<Object>, ObjectRelTy),
        PhantomData<OB>,
    );

    impl<OB: ObjectRelatable, O: ObjectRelatable> From<ObjectIndex<O>>
        for ObjectIndexTo<OB>
    where
        O: ObjectRelTo<OB>,
    {
        fn from(oi: ObjectIndex<O>) -> Self {
            Self(oi.widen_dyn_ty(), PhantomData::default())
        }
    }

    impl<OB: ObjectRelatable> ObjectIndexTo<OB> {
        pub fn span(&self) -> Span {
            (*self).into()
        }

        /// Assert a reflexive relationship between `OB` and `OC`.
        ///
        /// The types `OB` and `OC` are equivalent (and therefore reflexive)
        ///   iff they have matching `ObjectRelTy`s.
        ///
        /// The sole purpose of this method is to satisfy Rust's type system
        ///   in dynamic situations where the type system is not able to
        ///   understand what we're doing,
        ///     where the type `OC` is more general than the type `OB`.
        /// This method is always safe;
        ///   it will return [`None`] if the two types differ in runtime
        ///   value.
        ///
        /// While the term "reflexive" is a binary relation in mathematics,
        ///   the term "reflexivity" originates from the Coq tactic.
        ///
        /// For an example of where this is needed,
        ///   see [`ObjectRelatable::oi_rel_to_dyn`].
        pub fn reflexivity<OC: ObjectRelatable>(
            self,
        ) -> Option<ObjectIndexTo<OC>> {
            let Self(parts, _) = self;
            (OB::rel_ty() == OC::rel_ty())
                .then_some(ObjectIndexTo(parts, PhantomData::default()))
        }
    }

    // Ignore metadata that should always be consistent with the underlying
    //   `ObjectIndex`.
    impl<OB: ObjectRelatable> PartialEq for ObjectIndexTo<OB> {
        fn eq(&self, other: &Self) -> bool {
            match (self, other) {
                (Self((oi, _), _), Self((oi_other, _), _)) => oi == oi_other,
            }
        }
    }

    impl<OB: ObjectRelatable> Eq for ObjectIndexTo<OB> {}

    // Ignore metadata that should always be consistent with the underlying
    //   `ObjectIndex`.
    impl<OB: ObjectRelatable> Hash for ObjectIndexTo<OB> {
        fn hash<H: Hasher>(&self, state: &mut H) {
            match self {
                Self((oi, _), _) => oi.hash(state),
            }
        }
    }

    // Deriving `Clone`/`Copy` as of 2023-03 was introducing a
    //   `Clone`/`Copy` bound on `OB`.
    impl<OB: ObjectRelatable> Clone for ObjectIndexTo<OB> {
        fn clone(&self) -> Self {
            Self(self.0, self.1)
        }
    }

    impl<OB: ObjectRelatable> Copy for ObjectIndexTo<OB> {}

    impl<OB: ObjectRelatable> From<ObjectIndexTo<OB>> for Span {
        fn from(oi: ObjectIndexTo<OB>) -> Self {
            match oi {
                ObjectIndexTo((oi, _), _) => oi.span(),
            }
        }
    }

    impl<OB: ObjectRelatable> From<ObjectIndexToTree<OB>> for ObjectIndexTo<OB> {
        fn from(value: ObjectIndexToTree<OB>) -> Self {
            match value {
                ObjectIndexToTree(oit) => oit,
            }
        }
    }

    /// Some [`ObjectIndex`] that can create a _tree_ edge to `OB`.
    ///
    /// This is a specialization of
    ///   (and contains)
    ///   [`ObjectIndexTo`];
    ///     see that for more information.
    ///
    /// See also [`ObjectIndexTreeRelTo`].
    #[derive(Debug)]
    pub struct ObjectIndexToTree<OB: ObjectRelatable>(ObjectIndexTo<OB>);

    impl<OB: ObjectRelatable, O: ObjectRelatable> From<ObjectIndex<O>>
        for ObjectIndexToTree<OB>
    where
        O: ObjectTreeRelTo<OB>,
    {
        fn from(oi: ObjectIndex<O>) -> Self {
            Self(oi.into())
        }
    }

    // Deriving any of the below were introducing trait bounds on `OB`.

    impl<OB: ObjectRelatable> PartialEq for ObjectIndexToTree<OB> {
        fn eq(&self, other: &Self) -> bool {
            match (self, other) {
                (Self(oi), Self(oi_other)) => oi == oi_other,
            }
        }
    }

    impl<OB: ObjectRelatable> Eq for ObjectIndexToTree<OB> {}

    impl<OB: ObjectRelatable> Hash for ObjectIndexToTree<OB> {
        fn hash<H: Hasher>(&self, state: &mut H) {
            match self {
                Self(oi) => oi.hash(state),
            }
        }
    }

    impl<OB: ObjectRelatable> Clone for ObjectIndexToTree<OB> {
        fn clone(&self) -> Self {
            Self(self.0)
        }
    }

    impl<OB: ObjectRelatable> Copy for ObjectIndexToTree<OB> {}

    impl<OB: ObjectRelatable> From<ObjectIndexToTree<OB>> for Span {
        fn from(oi: ObjectIndexToTree<OB>) -> Self {
            match oi {
                ObjectIndexToTree(inner) => inner.span(),
            }
        }
    }
}