rust/src/librustc/middle/infer/combine.rs

// Copyright 2012 The Rust Project Developers. See the COPYRIGHT
// file at the top-level directory of this distribution and at
// http://rust-lang.org/COPYRIGHT.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.

///////////////////////////////////////////////////////////////////////////
// # Type combining
//
// There are four type combiners: equate, sub, lub, and glb.  Each
// implements the trait `Combine` and contains methods for combining
// two instances of various things and yielding a new instance.  These
// combiner methods always yield a `Result<T>`.  There is a lot of
// common code for these operations, implemented as default methods on
// the `Combine` trait.
//
// Each operation may have side-effects on the inference context,
// though these can be unrolled using snapshots. On success, the
// LUB/GLB operations return the appropriate bound. The Eq and Sub
// operations generally return the first operand.
//
// ## Contravariance
//
// When you are relating two things which have a contravariant
// relationship, you should use `contratys()` or `contraregions()`,
// rather than inversing the order of arguments!  This is necessary
// because the order of arguments is not relevant for LUB and GLB.  It
// is also useful to track which value is the "expected" value in
// terms of error reporting.

use super::bivariate::Bivariate;
use super::equate::Equate;
use super::glb::Glb;
use super::lub::Lub;
use super::sub::Sub;
use super::unify::InferCtxtMethodsForSimplyUnifiableTypes;
use super::{InferCtxt, cres};
use super::{MiscVariable, TypeTrace};
use super::type_variable::{RelationDir, BiTo, EqTo, SubtypeOf, SupertypeOf};

use middle::subst;
use middle::subst::{ErasedRegions, NonerasedRegions, Substs};
use middle::ty::{FloatVar, FnSig, IntVar, TyVar};
use middle::ty::{IntType, UintType};
use middle::ty::BuiltinBounds;
use middle::ty::{self, Ty};
use middle::ty_fold;
use middle::ty_fold::{TypeFolder, TypeFoldable};
use util::ppaux::Repr;

use std::rc::Rc;
use syntax::ast::Unsafety;
use syntax::ast;
use syntax::abi;
use syntax::codemap::Span;

pub trait Combine<'tcx> : Sized {
    fn tcx<'a>(&'a self) -> &'a ty::ctxt<'tcx> { self.infcx().tcx }
    fn tag(&self) -> String;

    fn fields<'a>(&'a self) -> &'a CombineFields<'a, 'tcx>;

    fn infcx<'a>(&'a self) -> &'a InferCtxt<'a, 'tcx> { self.fields().infcx }
    fn a_is_expected(&self) -> bool { self.fields().a_is_expected }
    fn trace(&self) -> TypeTrace<'tcx> { self.fields().trace.clone() }
    fn equate<'a>(&'a self) -> Equate<'a, 'tcx> { self.fields().equate() }
    fn bivariate<'a>(&'a self) -> Bivariate<'a, 'tcx> { self.fields().bivariate() }

    fn sub<'a>(&'a self) -> Sub<'a, 'tcx> { self.fields().sub() }
    fn lub<'a>(&'a self) -> Lub<'a, 'tcx> { Lub(self.fields().clone()) }
    fn glb<'a>(&'a self) -> Glb<'a, 'tcx> { Glb(self.fields().clone()) }

    fn mts(&self, a: &ty::mt<'tcx>, b: &ty::mt<'tcx>) -> cres<'tcx, ty::mt<'tcx>> {
        debug!("{}.mts({}, {})",
               self.tag(),
               a.repr(self.tcx()),
               b.repr(self.tcx()));

        if a.mutbl != b.mutbl {
            Err(ty::terr_mutability)
        } else {
            let mutbl = a.mutbl;
            let variance = match mutbl {
                ast::MutImmutable => ty::Covariant,
                ast::MutMutable => ty::Invariant,
            };
            let ty = try!(self.tys_with_variance(variance, a.ty, b.ty));
            Ok(ty::mt {ty: ty, mutbl: mutbl})
        }
    }

    fn tys_with_variance(&self, variance: ty::Variance, a: Ty<'tcx>, b: Ty<'tcx>)
                         -> cres<'tcx, Ty<'tcx>>;

    fn tys(&self, a: Ty<'tcx>, b: Ty<'tcx>) -> cres<'tcx, Ty<'tcx>>;

    fn regions_with_variance(&self, variance: ty::Variance, a: ty::Region, b: ty::Region)
                             -> cres<'tcx, ty::Region>;

    fn regions(&self, a: ty::Region, b: ty::Region) -> cres<'tcx, ty::Region>;

    fn substs(&self,
              item_def_id: ast::DefId,
              a_subst: &subst::Substs<'tcx>,
              b_subst: &subst::Substs<'tcx>)
              -> cres<'tcx, subst::Substs<'tcx>>
    {
        debug!("substs: item_def_id={} a_subst={} b_subst={}",
               item_def_id.repr(self.infcx().tcx),
               a_subst.repr(self.infcx().tcx),
               b_subst.repr(self.infcx().tcx));

        let variances = if self.infcx().tcx.variance_computed.get() {
            Some(ty::item_variances(self.infcx().tcx, item_def_id))
        } else {
            None
        };
        self.substs_variances(variances.as_ref().map(|v| &**v), a_subst, b_subst)
    }

    fn substs_variances(&self,
                        variances: Option<&ty::ItemVariances>,
                        a_subst: &subst::Substs<'tcx>,
                        b_subst: &subst::Substs<'tcx>)
                        -> cres<'tcx, subst::Substs<'tcx>>
    {
        let mut substs = subst::Substs::empty();

        for &space in &subst::ParamSpace::all() {
            let a_tps = a_subst.types.get_slice(space);
            let b_tps = b_subst.types.get_slice(space);
            let t_variances = variances.map(|v| v.types.get_slice(space));
            let tps = try!(relate_type_params(self, t_variances, a_tps, b_tps));
            substs.types.replace(space, tps);
        }

        match (&a_subst.regions, &b_subst.regions) {
            (&ErasedRegions, _) | (_, &ErasedRegions) => {
                substs.regions = ErasedRegions;
            }

            (&NonerasedRegions(ref a), &NonerasedRegions(ref b)) => {
                for &space in &subst::ParamSpace::all() {
                    let a_regions = a.get_slice(space);
                    let b_regions = b.get_slice(space);
                    let r_variances = variances.map(|v| v.regions.get_slice(space));
                    let regions = try!(relate_region_params(self,
                                                            r_variances,
                                                            a_regions,
                                                            b_regions));
                    substs.mut_regions().replace(space, regions);
                }
            }
        }

        return Ok(substs);

        fn relate_type_params<'tcx, C: Combine<'tcx>>(this: &C,
                                                      variances: Option<&[ty::Variance]>,
                                                      a_tys: &[Ty<'tcx>],
                                                      b_tys: &[Ty<'tcx>])
                                                      -> cres<'tcx, Vec<Ty<'tcx>>>
        {
            if a_tys.len() != b_tys.len() {
                return Err(ty::terr_ty_param_size(expected_found(this,
                                                                 a_tys.len(),
                                                                 b_tys.len())));
            }

            (0.. a_tys.len()).map(|i| {
                let a_ty = a_tys[i];
                let b_ty = b_tys[i];
                let v = variances.map_or(ty::Invariant, |v| v[i]);
                this.tys_with_variance(v, a_ty, b_ty)
            }).collect()
        }

        fn relate_region_params<'tcx, C: Combine<'tcx>>(this: &C,
                                                        variances: Option<&[ty::Variance]>,
                                                        a_rs: &[ty::Region],
                                                        b_rs: &[ty::Region])
                                                        -> cres<'tcx, Vec<ty::Region>>
        {
            let tcx = this.infcx().tcx;
            let num_region_params = a_rs.len();

            debug!("relate_region_params(\
                   a_rs={}, \
                   b_rs={},
                   variances={})",
                   a_rs.repr(tcx),
                   b_rs.repr(tcx),
                   variances.repr(tcx));

            assert_eq!(num_region_params,
                       variances.map_or(num_region_params,
                                        |v| v.len()));

            assert_eq!(num_region_params, b_rs.len());

            (0..a_rs.len()).map(|i| {
                let a_r = a_rs[i];
                let b_r = b_rs[i];
                let variance = variances.map_or(ty::Invariant, |v| v[i]);
                this.regions_with_variance(variance, a_r, b_r)
            }).collect()
        }
    }

    fn bare_fn_tys(&self, a: &ty::BareFnTy<'tcx>,
                   b: &ty::BareFnTy<'tcx>) -> cres<'tcx, ty::BareFnTy<'tcx>> {
        let unsafety = try!(self.unsafeties(a.unsafety, b.unsafety));
        let abi = try!(self.abi(a.abi, b.abi));
        let sig = try!(self.binders(&a.sig, &b.sig));
        Ok(ty::BareFnTy {unsafety: unsafety,
                         abi: abi,
                         sig: sig})
    }

    fn fn_sigs(&self, a: &ty::FnSig<'tcx>, b: &ty::FnSig<'tcx>) -> cres<'tcx, ty::FnSig<'tcx>> {
        if a.variadic != b.variadic {
            return Err(ty::terr_variadic_mismatch(expected_found(self, a.variadic, b.variadic)));
        }

        let inputs = try!(argvecs(self,
                                  &a.inputs,
                                  &b.inputs));

        let output = try!(match (a.output, b.output) {
            (ty::FnConverging(a_ty), ty::FnConverging(b_ty)) =>
                Ok(ty::FnConverging(try!(self.tys(a_ty, b_ty)))),
            (ty::FnDiverging, ty::FnDiverging) =>
                Ok(ty::FnDiverging),
            (a, b) =>
                Err(ty::terr_convergence_mismatch(
                    expected_found(self, a != ty::FnDiverging, b != ty::FnDiverging))),
        });

        return Ok(ty::FnSig {inputs: inputs,
                             output: output,
                             variadic: a.variadic});


        fn argvecs<'tcx, C>(combiner: &C,
                            a_args: &[Ty<'tcx>],
                            b_args: &[Ty<'tcx>])
                            -> cres<'tcx, Vec<Ty<'tcx>>>
                            where C: Combine<'tcx> {
            if a_args.len() == b_args.len() {
                a_args.iter().zip(b_args.iter())
                    .map(|(a, b)| combiner.args(*a, *b)).collect()
            } else {
                Err(ty::terr_arg_count)
            }
        }
    }

    fn args(&self, a: Ty<'tcx>, b: Ty<'tcx>) -> cres<'tcx, Ty<'tcx>> {
        self.tys_with_variance(ty::Contravariant, a, b).and_then(|t| Ok(t))
    }

    fn unsafeties(&self, a: Unsafety, b: Unsafety) -> cres<'tcx, Unsafety> {
        if a != b {
            Err(ty::terr_unsafety_mismatch(expected_found(self, a, b)))
        } else {
            Ok(a)
        }
    }

    fn abi(&self, a: abi::Abi, b: abi::Abi) -> cres<'tcx, abi::Abi> {
        if a == b {
            Ok(a)
        } else {
            Err(ty::terr_abi_mismatch(expected_found(self, a, b)))
        }
    }

    fn projection_tys(&self,
                      a: &ty::ProjectionTy<'tcx>,
                      b: &ty::ProjectionTy<'tcx>)
                      -> cres<'tcx, ty::ProjectionTy<'tcx>>
    {
        if a.item_name != b.item_name {
            Err(ty::terr_projection_name_mismatched(
                expected_found(self, a.item_name, b.item_name)))
        } else {
            let trait_ref = try!(self.trait_refs(&*a.trait_ref, &*b.trait_ref));
            Ok(ty::ProjectionTy { trait_ref: Rc::new(trait_ref), item_name: a.item_name })
        }
    }

    fn projection_predicates(&self,
                             a: &ty::ProjectionPredicate<'tcx>,
                             b: &ty::ProjectionPredicate<'tcx>)
                             -> cres<'tcx, ty::ProjectionPredicate<'tcx>>
    {
        let projection_ty = try!(self.projection_tys(&a.projection_ty, &b.projection_ty));
        let ty = try!(self.tys(a.ty, b.ty));
        Ok(ty::ProjectionPredicate { projection_ty: projection_ty, ty: ty })
    }

    fn projection_bounds(&self,
                         a: &Vec<ty::PolyProjectionPredicate<'tcx>>,
                         b: &Vec<ty::PolyProjectionPredicate<'tcx>>)
                         -> cres<'tcx, Vec<ty::PolyProjectionPredicate<'tcx>>>
    {
        // To be compatible, `a` and `b` must be for precisely the
        // same set of traits and item names. We always require that
        // projection bounds lists are sorted by trait-def-id and item-name,
        // so we can just iterate through the lists pairwise, so long as they are the
        // same length.
        if a.len() != b.len() {
            Err(ty::terr_projection_bounds_length(expected_found(self, a.len(), b.len())))
        } else {
            a.iter()
                .zip(b.iter())
                .map(|(a, b)| self.binders(a, b))
                .collect()
        }
    }

    fn existential_bounds(&self,
                          a: &ty::ExistentialBounds<'tcx>,
                          b: &ty::ExistentialBounds<'tcx>)
                          -> cres<'tcx, ty::ExistentialBounds<'tcx>>
    {
        let r = try!(self.regions_with_variance(ty::Contravariant, a.region_bound, b.region_bound));
        let nb = try!(self.builtin_bounds(a.builtin_bounds, b.builtin_bounds));
        let pb = try!(self.projection_bounds(&a.projection_bounds, &b.projection_bounds));
        Ok(ty::ExistentialBounds { region_bound: r,
                                   builtin_bounds: nb,
                                   projection_bounds: pb })
    }

    fn builtin_bounds(&self,
                      a: BuiltinBounds,
                      b: BuiltinBounds)
                      -> cres<'tcx, BuiltinBounds>
    {
        // Two sets of builtin bounds are only relatable if they are
        // precisely the same (but see the coercion code).
        if a != b {
            Err(ty::terr_builtin_bounds(expected_found(self, a, b)))
        } else {
            Ok(a)
        }
    }

    fn trait_refs(&self,
                  a: &ty::TraitRef<'tcx>,
                  b: &ty::TraitRef<'tcx>)
                  -> cres<'tcx, ty::TraitRef<'tcx>>
    {
        // Different traits cannot be related
        if a.def_id != b.def_id {
            Err(ty::terr_traits(expected_found(self, a.def_id, b.def_id)))
        } else {
            let substs = try!(self.substs(a.def_id, a.substs, b.substs));
            Ok(ty::TraitRef { def_id: a.def_id, substs: self.tcx().mk_substs(substs) })
        }
    }

    fn binders<T>(&self, a: &ty::Binder<T>, b: &ty::Binder<T>) -> cres<'tcx, ty::Binder<T>>
        where T : Combineable<'tcx>;
    // this must be overridden to do correctly, so as to account for higher-ranked
    // behavior
}

pub trait Combineable<'tcx> : Repr<'tcx> + TypeFoldable<'tcx> {
    fn combine<C:Combine<'tcx>>(combiner: &C, a: &Self, b: &Self) -> cres<'tcx, Self>;
}

impl<'tcx,T> Combineable<'tcx> for Rc<T>
    where T : Combineable<'tcx>
{
    fn combine<C>(combiner: &C,
                  a: &Rc<T>,
                  b: &Rc<T>)
                  -> cres<'tcx, Rc<T>>
                  where C: Combine<'tcx> {
        Ok(Rc::new(try!(Combineable::combine(combiner, &**a, &**b))))
    }
}

impl<'tcx> Combineable<'tcx> for ty::TraitRef<'tcx> {
    fn combine<C>(combiner: &C,
                  a: &ty::TraitRef<'tcx>,
                  b: &ty::TraitRef<'tcx>)
                  -> cres<'tcx, ty::TraitRef<'tcx>>
                  where C: Combine<'tcx> {
        combiner.trait_refs(a, b)
    }
}

impl<'tcx> Combineable<'tcx> for Ty<'tcx> {
    fn combine<C>(combiner: &C,
                  a: &Ty<'tcx>,
                  b: &Ty<'tcx>)
                  -> cres<'tcx, Ty<'tcx>>
                  where C: Combine<'tcx> {
        combiner.tys(*a, *b)
    }
}

impl<'tcx> Combineable<'tcx> for ty::ProjectionPredicate<'tcx> {
    fn combine<C>(combiner: &C,
                  a: &ty::ProjectionPredicate<'tcx>,
                  b: &ty::ProjectionPredicate<'tcx>)
                  -> cres<'tcx, ty::ProjectionPredicate<'tcx>>
                  where C: Combine<'tcx> {
        combiner.projection_predicates(a, b)
    }
}

impl<'tcx> Combineable<'tcx> for ty::FnSig<'tcx> {
    fn combine<C>(combiner: &C,
                  a: &ty::FnSig<'tcx>,
                  b: &ty::FnSig<'tcx>)
                  -> cres<'tcx, ty::FnSig<'tcx>>
                  where C: Combine<'tcx> {
        combiner.fn_sigs(a, b)
    }
}

#[derive(Clone)]
pub struct CombineFields<'a, 'tcx: 'a> {
    pub infcx: &'a InferCtxt<'a, 'tcx>,
    pub a_is_expected: bool,
    pub trace: TypeTrace<'tcx>,
}

pub fn expected_found<'tcx, C, T>(this: &C,
                                  a: T,
                                  b: T)
                                  -> ty::expected_found<T>
                                  where C: Combine<'tcx> {
    if this.a_is_expected() {
        ty::expected_found {expected: a, found: b}
    } else {
        ty::expected_found {expected: b, found: a}
    }
}

pub fn super_tys<'tcx, C>(this: &C,
                          a: Ty<'tcx>,
                          b: Ty<'tcx>)
                          -> cres<'tcx, Ty<'tcx>>
                          where C: Combine<'tcx> {
    let tcx = this.infcx().tcx;
    let a_sty = &a.sty;
    let b_sty = &b.sty;
    debug!("super_tys: a_sty={:?} b_sty={:?}", a_sty, b_sty);
    return match (a_sty, b_sty) {
        // The "subtype" ought to be handling cases involving var:
        (&ty::ty_infer(TyVar(_)), _)
        | (_, &ty::ty_infer(TyVar(_))) =>
            tcx.sess.bug(
                &format!("{}: bot and var types should have been handled ({},{})",
                this.tag(),
                a.repr(this.infcx().tcx),
                b.repr(this.infcx().tcx))),

        (&ty::ty_err, _) | (_, &ty::ty_err) => Ok(tcx.types.err),

        // Relate integral variables to other types
        (&ty::ty_infer(IntVar(a_id)), &ty::ty_infer(IntVar(b_id))) => {
            try!(this.infcx().simple_vars(this.a_is_expected(),
                                            a_id, b_id));
            Ok(a)
        }
        (&ty::ty_infer(IntVar(v_id)), &ty::ty_int(v)) => {
            unify_integral_variable(this, this.a_is_expected(),
                                    v_id, IntType(v))
        }
        (&ty::ty_int(v), &ty::ty_infer(IntVar(v_id))) => {
            unify_integral_variable(this, !this.a_is_expected(),
                                    v_id, IntType(v))
        }
        (&ty::ty_infer(IntVar(v_id)), &ty::ty_uint(v)) => {
            unify_integral_variable(this, this.a_is_expected(),
                                    v_id, UintType(v))
        }
        (&ty::ty_uint(v), &ty::ty_infer(IntVar(v_id))) => {
            unify_integral_variable(this, !this.a_is_expected(),
                                    v_id, UintType(v))
        }

        // Relate floating-point variables to other types
        (&ty::ty_infer(FloatVar(a_id)), &ty::ty_infer(FloatVar(b_id))) => {
            try!(this.infcx().simple_vars(this.a_is_expected(), a_id, b_id));
            Ok(a)
        }
        (&ty::ty_infer(FloatVar(v_id)), &ty::ty_float(v)) => {
            unify_float_variable(this, this.a_is_expected(), v_id, v)
        }
        (&ty::ty_float(v), &ty::ty_infer(FloatVar(v_id))) => {
            unify_float_variable(this, !this.a_is_expected(), v_id, v)
        }

        (&ty::ty_char, _)
        | (&ty::ty_bool, _)
        | (&ty::ty_int(_), _)
        | (&ty::ty_uint(_), _)
        | (&ty::ty_float(_), _) => {
            if a == b {
                Ok(a)
            } else {
                Err(ty::terr_sorts(expected_found(this, a, b)))
            }
        }

        (&ty::ty_param(ref a_p), &ty::ty_param(ref b_p)) if
          a_p.idx == b_p.idx && a_p.space == b_p.space => Ok(a),

        (&ty::ty_enum(a_id, a_substs), &ty::ty_enum(b_id, b_substs))
          if a_id == b_id => {
            let substs = try!(this.substs(a_id, a_substs, b_substs));
            Ok(ty::mk_enum(tcx, a_id, tcx.mk_substs(substs)))
        }

        (&ty::ty_trait(ref a_), &ty::ty_trait(ref b_)) => {
            debug!("Trying to match traits {:?} and {:?}", a, b);
            let principal = try!(this.binders(&a_.principal, &b_.principal));
            let bounds = try!(this.existential_bounds(&a_.bounds, &b_.bounds));
            Ok(ty::mk_trait(tcx, principal, bounds))
        }

        (&ty::ty_struct(a_id, a_substs), &ty::ty_struct(b_id, b_substs))
          if a_id == b_id => {
            let substs = try!(this.substs(a_id, a_substs, b_substs));
            Ok(ty::mk_struct(tcx, a_id, tcx.mk_substs(substs)))
        }

        (&ty::ty_closure(a_id, a_substs),
         &ty::ty_closure(b_id, b_substs))
          if a_id == b_id => {
            // All ty_closure types with the same id represent
            // the (anonymous) type of the same closure expression. So
            // all of their regions should be equated.
            let substs = try!(this.substs_variances(None, a_substs, b_substs));
            Ok(ty::mk_closure(tcx, a_id, tcx.mk_substs(substs)))
        }

        (&ty::ty_uniq(a_inner), &ty::ty_uniq(b_inner)) => {
            let typ = try!(this.tys(a_inner, b_inner));
            Ok(ty::mk_uniq(tcx, typ))
        }

        (&ty::ty_ptr(ref a_mt), &ty::ty_ptr(ref b_mt)) => {
            let mt = try!(this.mts(a_mt, b_mt));
            Ok(ty::mk_ptr(tcx, mt))
        }

        (&ty::ty_rptr(a_r, ref a_mt), &ty::ty_rptr(b_r, ref b_mt)) => {
            let r = try!(this.regions_with_variance(ty::Contravariant, *a_r, *b_r));
            let mt = try!(this.mts(a_mt, b_mt));
            Ok(ty::mk_rptr(tcx, tcx.mk_region(r), mt))
        }

        (&ty::ty_vec(a_t, Some(sz_a)), &ty::ty_vec(b_t, Some(sz_b))) => {
            this.tys(a_t, b_t).and_then(|t| {
                if sz_a == sz_b {
                    Ok(ty::mk_vec(tcx, t, Some(sz_a)))
                } else {
                    Err(ty::terr_fixed_array_size(expected_found(this, sz_a, sz_b)))
                }
            })
        }

        (&ty::ty_vec(a_t, sz_a), &ty::ty_vec(b_t, sz_b)) => {
            this.tys(a_t, b_t).and_then(|t| {
                if sz_a == sz_b {
                    Ok(ty::mk_vec(tcx, t, sz_a))
                } else {
                    Err(ty::terr_sorts(expected_found(this, a, b)))
                }
            })
        }

        (&ty::ty_str, &ty::ty_str) => Ok(ty::mk_str(tcx)),

        (&ty::ty_tup(ref as_), &ty::ty_tup(ref bs)) => {
            if as_.len() == bs.len() {
                as_.iter().zip(bs.iter())
                   .map(|(a, b)| this.tys(*a, *b))
                   .collect::<Result<_, _>>()
                   .map(|ts| ty::mk_tup(tcx, ts))
            } else if as_.len() != 0 && bs.len() != 0 {
                Err(ty::terr_tuple_size(
                    expected_found(this, as_.len(), bs.len())))
            } else {
                Err(ty::terr_sorts(expected_found(this, a, b)))
            }
        }

        (&ty::ty_bare_fn(a_opt_def_id, a_fty), &ty::ty_bare_fn(b_opt_def_id, b_fty))
            if a_opt_def_id == b_opt_def_id =>
        {
            let fty = try!(this.bare_fn_tys(a_fty, b_fty));
            Ok(ty::mk_bare_fn(tcx, a_opt_def_id, tcx.mk_bare_fn(fty)))
        }

        (&ty::ty_projection(ref a_data), &ty::ty_projection(ref b_data)) => {
            let projection_ty = try!(this.projection_tys(a_data, b_data));
            Ok(ty::mk_projection(tcx, projection_ty.trait_ref, projection_ty.item_name))
        }

        _ => Err(ty::terr_sorts(expected_found(this, a, b))),
    };

    fn unify_integral_variable<'tcx, C>(this: &C,
                                        vid_is_expected: bool,
                                        vid: ty::IntVid,
                                        val: ty::IntVarValue)
                                        -> cres<'tcx, Ty<'tcx>>
                                        where C: Combine<'tcx> {
        try!(this.infcx().simple_var_t(vid_is_expected, vid, val));
        match val {
            IntType(v) => Ok(ty::mk_mach_int(this.tcx(), v)),
            UintType(v) => Ok(ty::mk_mach_uint(this.tcx(), v)),
        }
    }

    fn unify_float_variable<'tcx, C>(this: &C,
                                     vid_is_expected: bool,
                                     vid: ty::FloatVid,
                                     val: ast::FloatTy)
                                     -> cres<'tcx, Ty<'tcx>>
                                     where C: Combine<'tcx> {
        try!(this.infcx().simple_var_t(vid_is_expected, vid, val));
        Ok(ty::mk_mach_float(this.tcx(), val))
    }
}

impl<'f, 'tcx> CombineFields<'f, 'tcx> {
    pub fn switch_expected(&self) -> CombineFields<'f, 'tcx> {
        CombineFields {
            a_is_expected: !self.a_is_expected,
            ..(*self).clone()
        }
    }

    fn equate(&self) -> Equate<'f, 'tcx> {
        Equate((*self).clone())
    }

    fn bivariate(&self) -> Bivariate<'f, 'tcx> {
        Bivariate((*self).clone())
    }

    fn sub(&self) -> Sub<'f, 'tcx> {
        Sub((*self).clone())
    }

    pub fn instantiate(&self,
                       a_ty: Ty<'tcx>,
                       dir: RelationDir,
                       b_vid: ty::TyVid)
                       -> cres<'tcx, ()>
    {
        let tcx = self.infcx.tcx;
        let mut stack = Vec::new();
        stack.push((a_ty, dir, b_vid));
        loop {
            // For each turn of the loop, we extract a tuple
            //
            //     (a_ty, dir, b_vid)
            //
            // to relate. Here dir is either SubtypeOf or
            // SupertypeOf. The idea is that we should ensure that
            // the type `a_ty` is a subtype or supertype (respectively) of the
            // type to which `b_vid` is bound.
            //
            // If `b_vid` has not yet been instantiated with a type
            // (which is always true on the first iteration, but not
            // necessarily true on later iterations), we will first
            // instantiate `b_vid` with a *generalized* version of
            // `a_ty`. Generalization introduces other inference
            // variables wherever subtyping could occur (at time of
            // this writing, this means replacing free regions with
            // region variables).
            let (a_ty, dir, b_vid) = match stack.pop() {
                None => break,
                Some(e) => e,
            };

            debug!("instantiate(a_ty={} dir={:?} b_vid={})",
                   a_ty.repr(tcx),
                   dir,
                   b_vid.repr(tcx));

            // Check whether `vid` has been instantiated yet.  If not,
            // make a generalized form of `ty` and instantiate with
            // that.
            let b_ty = self.infcx.type_variables.borrow().probe(b_vid);
            let b_ty = match b_ty {
                Some(t) => t, // ...already instantiated.
                None => {     // ...not yet instantiated:
                    // Generalize type if necessary.
                    let generalized_ty = try!(match dir {
                        EqTo => self.generalize(a_ty, b_vid, false),
                        BiTo | SupertypeOf | SubtypeOf => self.generalize(a_ty, b_vid, true),
                    });
                    debug!("instantiate(a_ty={}, dir={:?}, \
                                        b_vid={}, generalized_ty={})",
                           a_ty.repr(tcx), dir, b_vid.repr(tcx),
                           generalized_ty.repr(tcx));
                    self.infcx.type_variables
                        .borrow_mut()
                        .instantiate_and_push(
                            b_vid, generalized_ty, &mut stack);
                    generalized_ty
                }
            };

            // The original triple was `(a_ty, dir, b_vid)` -- now we have
            // resolved `b_vid` to `b_ty`, so apply `(a_ty, dir, b_ty)`:
            //
            // FIXME(#16847): This code is non-ideal because all these subtype
            // relations wind up attributed to the same spans. We need
            // to associate causes/spans with each of the relations in
            // the stack to get this right.
            match dir {
                BiTo => try!(self.bivariate().tys(a_ty, b_ty)),

                EqTo => try!(self.equate().tys(a_ty, b_ty)),

                SubtypeOf => try!(self.sub().tys(a_ty, b_ty)),

                SupertypeOf => try!(self.sub().tys_with_variance(ty::Contravariant, a_ty, b_ty)),
            };
        }

        Ok(())
    }

    /// Attempts to generalize `ty` for the type variable `for_vid`.  This checks for cycle -- that
    /// is, whether the type `ty` references `for_vid`. If `make_region_vars` is true, it will also
    /// replace all regions with fresh variables. Returns `ty_err` in the case of a cycle, `Ok`
    /// otherwise.
    fn generalize(&self,
                  ty: Ty<'tcx>,
                  for_vid: ty::TyVid,
                  make_region_vars: bool)
                  -> cres<'tcx, Ty<'tcx>>
    {
        let mut generalize = Generalizer {
            infcx: self.infcx,
            span: self.trace.origin.span(),
            for_vid: for_vid,
            make_region_vars: make_region_vars,
            cycle_detected: false
        };
        let u = ty.fold_with(&mut generalize);
        if generalize.cycle_detected {
            Err(ty::terr_cyclic_ty)
        } else {
            Ok(u)
        }
    }
}

struct Generalizer<'cx, 'tcx:'cx> {
    infcx: &'cx InferCtxt<'cx, 'tcx>,
    span: Span,
    for_vid: ty::TyVid,
    make_region_vars: bool,
    cycle_detected: bool,
}

impl<'cx, 'tcx> ty_fold::TypeFolder<'tcx> for Generalizer<'cx, 'tcx> {
    fn tcx(&self) -> &ty::ctxt<'tcx> {
        self.infcx.tcx
    }

    fn fold_ty(&mut self, t: Ty<'tcx>) -> Ty<'tcx> {
        // Check to see whether the type we are genealizing references
        // `vid`. At the same time, also update any type variables to
        // the values that they are bound to. This is needed to truly
        // check for cycles, but also just makes things readable.
        //
        // (In particular, you could have something like `$0 = Box<$1>`
        //  where `$1` has already been instantiated with `Box<$0>`)
        match t.sty {
            ty::ty_infer(ty::TyVar(vid)) => {
                if vid == self.for_vid {
                    self.cycle_detected = true;
                    self.tcx().types.err
                } else {
                    match self.infcx.type_variables.borrow().probe(vid) {
                        Some(u) => self.fold_ty(u),
                        None => t,
                    }
                }
            }
            _ => {
                ty_fold::super_fold_ty(self, t)
            }
        }
    }

    fn fold_region(&mut self, r: ty::Region) -> ty::Region {
        match r {
            // Never make variables for regions bound within the type itself.
            ty::ReLateBound(..) => { return r; }

            // Early-bound regions should really have been substituted away before
            // we get to this point.
            ty::ReEarlyBound(..) => {
                self.tcx().sess.span_bug(
                    self.span,
                    &format!("Encountered early bound region when generalizing: {}",
                            r.repr(self.tcx())));
            }

            // Always make a fresh region variable for skolemized regions;
            // the higher-ranked decision procedures rely on this.
            ty::ReInfer(ty::ReSkolemized(..)) => { }

            // For anything else, we make a region variable, unless we
            // are *equating*, in which case it's just wasteful.
            ty::ReEmpty |
            ty::ReStatic |
            ty::ReScope(..) |
            ty::ReInfer(ty::ReVar(..)) |
            ty::ReFree(..) => {
                if !self.make_region_vars {
                    return r;
                }
            }
        }

        // FIXME: This is non-ideal because we don't give a
        // very descriptive origin for this region variable.
        self.infcx.next_region_var(MiscVariable(self.span))
    }
}