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``````//! # Lattice variables
//!
//! Generic code for operating on [lattices] of inference variables
//! that are characterized by an upper- and lower-bound.
//!
//! The code is defined quite generically so that it can be
//! applied both to type variables, which represent types being inferred,
//! and fn variables, which represent function types being inferred.
//! (It may eventually be applied to their types as well.)
//! In some cases, the functions are also generic with respect to the
//! operation on the lattice (GLB vs LUB).
//!
//! ## Note
//!
//! Although all the functions are generic, for simplicity, comments in the source code
//! generally refer to type variables and the LUB operation.
//!
//! [lattices]: https://en.wikipedia.org/wiki/Lattice_(order)

use super::combine::PredicateEmittingRelation;
use crate::infer::{DefineOpaqueTypes, InferCtxt};
use crate::traits::ObligationCause;

use rustc_middle::ty::relate::RelateResult;
use rustc_middle::ty::TyVar;
use rustc_middle::ty::{self, Ty};

/// Trait for returning data about a lattice, and for abstracting
/// over the "direction" of the lattice operation (LUB/GLB).
///
/// GLB moves "down" the lattice (to smaller values); LUB moves
/// "up" the lattice (to bigger values).
pub trait LatticeDir<'f, 'tcx>: PredicateEmittingRelation<'tcx> {
fn infcx(&self) -> &'f InferCtxt<'tcx>;

fn cause(&self) -> &ObligationCause<'tcx>;

fn define_opaque_types(&self) -> DefineOpaqueTypes;

// Relates the type `v` to `a` and `b` such that `v` represents
// the LUB/GLB of `a` and `b` as appropriate.
//
// Subtle hack: ordering *may* be significant here. This method
// relates `v` to `a` first, which may help us to avoid unnecessary
// type variable obligations. See caller for details.
fn relate_bound(&mut self, v: Ty<'tcx>, a: Ty<'tcx>, b: Ty<'tcx>) -> RelateResult<'tcx, ()>;
}

/// Relates two types using a given lattice.
#[instrument(skip(this), level = "debug")]
pub fn super_lattice_tys<'a, 'tcx: 'a, L>(
this: &mut L,
a: Ty<'tcx>,
b: Ty<'tcx>,
) -> RelateResult<'tcx, Ty<'tcx>>
where
L: LatticeDir<'a, 'tcx>,
{
debug!("{}", this.tag());

if a == b {
return Ok(a);
}

let infcx = this.infcx();

let a = infcx.shallow_resolve(a);
let b = infcx.shallow_resolve(b);

match (a.kind(), b.kind()) {
// If one side is known to be a variable and one is not,
// create a variable (`v`) to represent the LUB. Make sure to
// relate `v` to the non-type-variable first (by passing it
// first to `relate_bound`). Otherwise, we would produce a
// subtype obligation that must then be processed.
//
// Example: if the LHS is a type variable, and RHS is
// `Box<i32>`, then we current compare `v` to the RHS first,
// which will instantiate `v` with `Box<i32>`. Then when `v`
// is compared to the LHS, we instantiate LHS with `Box<i32>`.
// But if we did in reverse order, we would create a `v <:
// LHS` (or vice versa) constraint and then instantiate
// `v`. This would require further processing to achieve same
// end-result; in particular, this screws up some of the logic
// in coercion, which expects LUB to figure out that the LHS
// is (e.g.) `Box<i32>`. A more obvious solution might be to
// iterate on the subtype obligations that are returned, but I
// think this suffices. -nmatsakis
(&ty::Infer(TyVar(..)), _) => {
let v = infcx.next_ty_var(this.cause().span);
this.relate_bound(v, b, a)?;
Ok(v)
}
(_, &ty::Infer(TyVar(..))) => {
let v = infcx.next_ty_var(this.cause().span);
this.relate_bound(v, a, b)?;
Ok(v)
}

(
&ty::Alias(ty::Opaque, ty::AliasTy { def_id: a_def_id, .. }),
&ty::Alias(ty::Opaque, ty::AliasTy { def_id: b_def_id, .. }),
) if a_def_id == b_def_id => infcx.super_combine_tys(this, a, b),

(&ty::Alias(ty::Opaque, ty::AliasTy { def_id, .. }), _)
| (_, &ty::Alias(ty::Opaque, ty::AliasTy { def_id, .. }))
if this.define_opaque_types() == DefineOpaqueTypes::Yes
&& def_id.is_local()
&& !this.infcx().next_trait_solver() =>
{
this.register_goals(infcx.handle_opaque_type(a, b, this.span(), this.param_env())?);
Ok(a)
}

_ => infcx.super_combine_tys(this, a, b),
}
}
``````