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

   1 // Copyright 2012 The Rust Project Developers. See the COPYRIGHT
   2 // file at the top-level directory of this distribution and at
   3 // http://rust-lang.org/COPYRIGHT.
   4 //
   5 // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
   6 // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
   7 // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
   8 // option. This file may not be copied, modified, or distributed
   9 // except according to those terms.
  10
  11 ///////////////////////////////////////////////////////////////////////////
  12 // # Type combining
  13 //
  14 // There are four type combiners: equate, sub, lub, and glb.  Each
  15 // implements the trait `Combine` and contains methods for combining
  16 // two instances of various things and yielding a new instance.  These
  17 // combiner methods always yield a `Result<T>`.  There is a lot of
  18 // common code for these operations, implemented as default methods on
  19 // the `Combine` trait.
  20 //
  21 // Each operation may have side-effects on the inference context,
  22 // though these can be unrolled using snapshots. On success, the
  23 // LUB/GLB operations return the appropriate bound. The Eq and Sub
  24 // operations generally return the first operand.
  25 //
  26 // ## Contravariance
  27 //
  28 // When you are relating two things which have a contravariant
  29 // relationship, you should use `contratys()` or `contraregions()`,
  30 // rather than inversing the order of arguments!  This is necessary
  31 // because the order of arguments is not relevant for LUB and GLB.  It
  32 // is also useful to track which value is the "expected" value in
  33 // terms of error reporting.
  34
  35
  36 use middle::subst;
  37 use middle::subst::{ErasedRegions, NonerasedRegions, Substs};
  38 use middle::ty::{FloatVar, FnSig, IntVar, TyVar};
  39 use middle::ty::{IntType, UintType};
  40 use middle::ty::{BuiltinBounds};
  41 use middle::ty::{mod, Ty};
  42 use middle::ty_fold;
  43 use middle::typeck::infer::equate::Equate;
  44 use middle::typeck::infer::glb::Glb;
  45 use middle::typeck::infer::lub::Lub;
  46 use middle::typeck::infer::sub::Sub;
  47 use middle::typeck::infer::unify::InferCtxtMethodsForSimplyUnifiableTypes;
  48 use middle::typeck::infer::{InferCtxt, cres};
  49 use middle::typeck::infer::{MiscVariable, TypeTrace};
  50 use middle::typeck::infer::type_variable::{RelationDir, EqTo,
  51                                            SubtypeOf, SupertypeOf};
  52 use middle::ty_fold::{TypeFoldable};
  53 use util::ppaux::Repr;
  54
  55 use syntax::ast::{Onceness, FnStyle};
  56 use syntax::ast;
  57 use syntax::abi;
  58 use syntax::codemap::Span;
  59
  60 pub trait Combine<'tcx> {
  61     fn infcx<'a>(&'a self) -> &'a InferCtxt<'a, 'tcx>;
  62     fn tcx<'a>(&'a self) -> &'a ty::ctxt<'tcx> { self.infcx().tcx }
  63     fn tag(&self) -> String;
  64     fn a_is_expected(&self) -> bool;
  65     fn trace(&self) -> TypeTrace<'tcx>;
  66
  67     fn equate<'a>(&'a self) -> Equate<'a, 'tcx>;
  68     fn sub<'a>(&'a self) -> Sub<'a, 'tcx>;
  69     fn lub<'a>(&'a self) -> Lub<'a, 'tcx>;
  70     fn glb<'a>(&'a self) -> Glb<'a, 'tcx>;
  71
  72     fn mts(&self, a: &ty::mt<'tcx>, b: &ty::mt<'tcx>) -> cres<'tcx, ty::mt<'tcx>>;
  73     fn contratys(&self, a: Ty<'tcx>, b: Ty<'tcx>) -> cres<'tcx, Ty<'tcx>>;
  74     fn tys(&self, a: Ty<'tcx>, b: Ty<'tcx>) -> cres<'tcx, Ty<'tcx>>;
  75
  76     fn tps(&self,
  77            _: subst::ParamSpace,
  78            as_: &[Ty<'tcx>],
  79            bs: &[Ty<'tcx>])
  80            -> cres<'tcx, Vec<Ty<'tcx>>> {
  81         // FIXME -- In general, we treat variance a bit wrong
  82         // here. For historical reasons, we treat tps and Self
  83         // as invariant. This is overly conservative.
  84
  85         if as_.len() != bs.len() {
  86             return Err(ty::terr_ty_param_size(expected_found(self,
  87                                                              as_.len(),
  88                                                              bs.len())));
  89         }
  90
  91         try!(as_.iter().zip(bs.iter())
  92                 .map(|(a, b)| self.equate().tys(*a, *b))
  93                 .collect::<cres<Vec<Ty>>>());
  94         Ok(as_.to_vec())
  95     }
  96
  97     fn substs(&self,
  98               item_def_id: ast::DefId,
  99               a_subst: &subst::Substs<'tcx>,
 100               b_subst: &subst::Substs<'tcx>)
 101               -> cres<'tcx, subst::Substs<'tcx>>
 102     {
 103         let variances = if self.infcx().tcx.variance_computed.get() {
 104             Some(ty::item_variances(self.infcx().tcx, item_def_id))
 105         } else {
 106             None
 107         };
 108         self.substs_variances(variances.as_ref().map(|v| &**v), a_subst, b_subst)
 109     }
 110
 111     fn substs_variances(&self,
 112                         variances: Option<&ty::ItemVariances>,
 113                         a_subst: &subst::Substs<'tcx>,
 114                         b_subst: &subst::Substs<'tcx>)
 115                         -> cres<'tcx, subst::Substs<'tcx>>
 116     {
 117         let mut substs = subst::Substs::empty();
 118
 119         for &space in subst::ParamSpace::all().iter() {
 120             let a_tps = a_subst.types.get_slice(space);
 121             let b_tps = b_subst.types.get_slice(space);
 122             let tps = try!(self.tps(space, a_tps, b_tps));
 123             substs.types.replace(space, tps);
 124         }
 125
 126         match (&a_subst.regions, &b_subst.regions) {
 127             (&ErasedRegions, _) | (_, &ErasedRegions) => {
 128                 substs.regions = ErasedRegions;
 129             }
 130
 131             (&NonerasedRegions(ref a), &NonerasedRegions(ref b)) => {
 132                 for &space in subst::ParamSpace::all().iter() {
 133                     let a_regions = a.get_slice(space);
 134                     let b_regions = b.get_slice(space);
 135
 136                     let mut invariance = Vec::new();
 137                     let r_variances = match variances {
 138                         Some(variances) => {
 139                             variances.regions.get_slice(space)
 140                         }
 141                         None => {
 142                             for _ in a_regions.iter() {
 143                                 invariance.push(ty::Invariant);
 144                             }
 145                             invariance.as_slice()
 146                         }
 147                     };
 148
 149                     let regions = try!(relate_region_params(self,
 150                                                             r_variances,
 151                                                             a_regions,
 152                                                             b_regions));
 153                     substs.mut_regions().replace(space, regions);
 154                 }
 155             }
 156         }
 157
 158         return Ok(substs);
 159
 160         fn relate_region_params<'tcx, C: Combine<'tcx>>(this: &C,
 161                                                         variances: &[ty::Variance],
 162                                                         a_rs: &[ty::Region],
 163                                                         b_rs: &[ty::Region])
 164                                                         -> cres<'tcx, Vec<ty::Region>> {
 165             let tcx = this.infcx().tcx;
 166             let num_region_params = variances.len();
 167
 168             debug!("relate_region_params(\
 169                    a_rs={}, \
 170                    b_rs={},
 171                    variances={})",
 172                    a_rs.repr(tcx),
 173                    b_rs.repr(tcx),
 174                    variances.repr(tcx));
 175
 176             assert_eq!(num_region_params, a_rs.len());
 177             assert_eq!(num_region_params, b_rs.len());
 178             let mut rs = vec!();
 179             for i in range(0, num_region_params) {
 180                 let a_r = a_rs[i];
 181                 let b_r = b_rs[i];
 182                 let variance = variances[i];
 183                 let r = match variance {
 184                     ty::Invariant => this.equate().regions(a_r, b_r),
 185                     ty::Covariant => this.regions(a_r, b_r),
 186                     ty::Contravariant => this.contraregions(a_r, b_r),
 187                     ty::Bivariant => Ok(a_r),
 188                 };
 189                 rs.push(try!(r));
 190             }
 191             Ok(rs)
 192         }
 193     }
 194
 195     fn bare_fn_tys(&self, a: &ty::BareFnTy<'tcx>,
 196                    b: &ty::BareFnTy<'tcx>) -> cres<'tcx, ty::BareFnTy<'tcx>> {
 197         let fn_style = try!(self.fn_styles(a.fn_style, b.fn_style));
 198         let abi = try!(self.abi(a.abi, b.abi));
 199         let sig = try!(self.fn_sigs(&a.sig, &b.sig));
 200         Ok(ty::BareFnTy {fn_style: fn_style,
 201                 abi: abi,
 202                 sig: sig})
 203     }
 204
 205     fn closure_tys(&self, a: &ty::ClosureTy<'tcx>,
 206                    b: &ty::ClosureTy<'tcx>) -> cres<'tcx, ty::ClosureTy<'tcx>> {
 207
 208         let store = match (a.store, b.store) {
 209             (ty::RegionTraitStore(a_r, a_m),
 210              ty::RegionTraitStore(b_r, b_m)) if a_m == b_m => {
 211                 let r = try!(self.contraregions(a_r, b_r));
 212                 ty::RegionTraitStore(r, a_m)
 213             }
 214
 215             _ if a.store == b.store => {
 216                 a.store
 217             }
 218
 219             _ => {
 220                 return Err(ty::terr_sigil_mismatch(expected_found(self, a.store, b.store)))
 221             }
 222         };
 223         let fn_style = try!(self.fn_styles(a.fn_style, b.fn_style));
 224         let onceness = try!(self.oncenesses(a.onceness, b.onceness));
 225         let bounds = try!(self.existential_bounds(a.bounds, b.bounds));
 226         let sig = try!(self.fn_sigs(&a.sig, &b.sig));
 227         let abi = try!(self.abi(a.abi, b.abi));
 228         Ok(ty::ClosureTy {
 229             fn_style: fn_style,
 230             onceness: onceness,
 231             store: store,
 232             bounds: bounds,
 233             sig: sig,
 234             abi: abi,
 235         })
 236     }
 237
 238     fn fn_sigs(&self, a: &ty::FnSig<'tcx>, b: &ty::FnSig<'tcx>) -> cres<'tcx, ty::FnSig<'tcx>>;
 239
 240     fn args(&self, a: Ty<'tcx>, b: Ty<'tcx>) -> cres<'tcx, Ty<'tcx>> {
 241         self.contratys(a, b).and_then(|t| Ok(t))
 242     }
 243
 244     fn fn_styles(&self, a: FnStyle, b: FnStyle) -> cres<'tcx, FnStyle>;
 245
 246     fn abi(&self, a: abi::Abi, b: abi::Abi) -> cres<'tcx, abi::Abi> {
 247         if a == b {
 248             Ok(a)
 249         } else {
 250             Err(ty::terr_abi_mismatch(expected_found(self, a, b)))
 251         }
 252     }
 253
 254     fn oncenesses(&self, a: Onceness, b: Onceness) -> cres<'tcx, Onceness>;
 255
 256     fn existential_bounds(&self,
 257                           a: ty::ExistentialBounds,
 258                           b: ty::ExistentialBounds)
 259                           -> cres<'tcx, ty::ExistentialBounds>
 260     {
 261         let r = try!(self.contraregions(a.region_bound, b.region_bound));
 262         let nb = try!(self.builtin_bounds(a.builtin_bounds, b.builtin_bounds));
 263         Ok(ty::ExistentialBounds { region_bound: r,
 264                                    builtin_bounds: nb })
 265     }
 266
 267     fn builtin_bounds(&self,
 268                       a: ty::BuiltinBounds,
 269                       b: ty::BuiltinBounds)
 270                       -> cres<'tcx, ty::BuiltinBounds>;
 271
 272     fn contraregions(&self, a: ty::Region, b: ty::Region)
 273                   -> cres<'tcx, ty::Region>;
 274
 275     fn regions(&self, a: ty::Region, b: ty::Region) -> cres<'tcx, ty::Region>;
 276
 277     fn trait_stores(&self,
 278                     vk: ty::terr_vstore_kind,
 279                     a: ty::TraitStore,
 280                     b: ty::TraitStore)
 281                     -> cres<'tcx, ty::TraitStore> {
 282         debug!("{}.trait_stores(a={}, b={})", self.tag(), a, b);
 283
 284         match (a, b) {
 285             (ty::RegionTraitStore(a_r, a_m),
 286              ty::RegionTraitStore(b_r, b_m)) if a_m == b_m => {
 287                 self.contraregions(a_r, b_r).and_then(|r| {
 288                     Ok(ty::RegionTraitStore(r, a_m))
 289                 })
 290             }
 291
 292             _ if a == b => {
 293                 Ok(a)
 294             }
 295
 296             _ => {
 297                 Err(ty::terr_trait_stores_differ(vk, expected_found(self, a, b)))
 298             }
 299         }
 300     }
 301
 302     fn trait_refs(&self,
 303                   a: &ty::TraitRef<'tcx>,
 304                   b: &ty::TraitRef<'tcx>)
 305                   -> cres<'tcx, ty::TraitRef<'tcx>>;
 306     // this must be overridden to do correctly, so as to account for higher-ranked
 307     // behavior
 308 }
 309
 310 #[deriving(Clone)]
 311 pub struct CombineFields<'a, 'tcx: 'a> {
 312     pub infcx: &'a InferCtxt<'a, 'tcx>,
 313     pub a_is_expected: bool,
 314     pub trace: TypeTrace<'tcx>,
 315 }
 316
 317 pub fn expected_found<'tcx, C: Combine<'tcx>, T>(
 318         this: &C, a: T, b: T) -> ty::expected_found<T> {
 319     if this.a_is_expected() {
 320         ty::expected_found {expected: a, found: b}
 321     } else {
 322         ty::expected_found {expected: b, found: a}
 323     }
 324 }
 325
 326 pub fn super_tys<'tcx, C: Combine<'tcx>>(this: &C,
 327                                          a: Ty<'tcx>,
 328                                          b: Ty<'tcx>)
 329                                          -> cres<'tcx, Ty<'tcx>> {
 330
 331     let tcx = this.infcx().tcx;
 332     let a_sty = &a.sty;
 333     let b_sty = &b.sty;
 334     debug!("super_tys: a_sty={} b_sty={}", a_sty, b_sty);
 335     return match (a_sty, b_sty) {
 336       // The "subtype" ought to be handling cases involving var:
 337       (&ty::ty_infer(TyVar(_)), _) |
 338       (_, &ty::ty_infer(TyVar(_))) => {
 339         tcx.sess.bug(
 340             format!("{}: bot and var types should have been handled ({},{})",
 341                     this.tag(),
 342                     a.repr(this.infcx().tcx),
 343                     b.repr(this.infcx().tcx)).as_slice());
 344       }
 345
 346       (&ty::ty_err, _) | (_, &ty::ty_err) => {
 347           Ok(ty::mk_err())
 348       }
 349
 350         // Relate integral variables to other types
 351         (&ty::ty_infer(IntVar(a_id)), &ty::ty_infer(IntVar(b_id))) => {
 352             try!(this.infcx().simple_vars(this.a_is_expected(),
 353                                             a_id, b_id));
 354             Ok(a)
 355         }
 356         (&ty::ty_infer(IntVar(v_id)), &ty::ty_int(v)) => {
 357             unify_integral_variable(this, this.a_is_expected(),
 358                                     v_id, IntType(v))
 359         }
 360         (&ty::ty_int(v), &ty::ty_infer(IntVar(v_id))) => {
 361             unify_integral_variable(this, !this.a_is_expected(),
 362                                     v_id, IntType(v))
 363         }
 364         (&ty::ty_infer(IntVar(v_id)), &ty::ty_uint(v)) => {
 365             unify_integral_variable(this, this.a_is_expected(),
 366                                     v_id, UintType(v))
 367         }
 368         (&ty::ty_uint(v), &ty::ty_infer(IntVar(v_id))) => {
 369             unify_integral_variable(this, !this.a_is_expected(),
 370                                     v_id, UintType(v))
 371         }
 372
 373         // Relate floating-point variables to other types
 374         (&ty::ty_infer(FloatVar(a_id)), &ty::ty_infer(FloatVar(b_id))) => {
 375             try!(this.infcx().simple_vars(this.a_is_expected(), a_id, b_id));
 376             Ok(a)
 377         }
 378         (&ty::ty_infer(FloatVar(v_id)), &ty::ty_float(v)) => {
 379             unify_float_variable(this, this.a_is_expected(), v_id, v)
 380         }
 381         (&ty::ty_float(v), &ty::ty_infer(FloatVar(v_id))) => {
 382             unify_float_variable(this, !this.a_is_expected(), v_id, v)
 383         }
 384
 385       (&ty::ty_char, _) |
 386       (&ty::ty_bool, _) |
 387       (&ty::ty_int(_), _) |
 388       (&ty::ty_uint(_), _) |
 389       (&ty::ty_float(_), _) => {
 390         if a == b {
 391             Ok(a)
 392         } else {
 393             Err(ty::terr_sorts(expected_found(this, a, b)))
 394         }
 395       }
 396
 397       (&ty::ty_param(ref a_p), &ty::ty_param(ref b_p)) if
 398           a_p.idx == b_p.idx && a_p.space == b_p.space => {
 399         Ok(a)
 400       }
 401
 402       (&ty::ty_enum(a_id, ref a_substs),
 403        &ty::ty_enum(b_id, ref b_substs))
 404       if a_id == b_id => {
 405           let substs = try!(this.substs(a_id,
 406                                           a_substs,
 407                                           b_substs));
 408           Ok(ty::mk_enum(tcx, a_id, substs))
 409       }
 410
 411       (&ty::ty_trait(ref a_),
 412        &ty::ty_trait(ref b_)) => {
 413           debug!("Trying to match traits {} and {}", a, b);
 414           let principal = try!(this.trait_refs(&a_.principal, &b_.principal));
 415           let bounds = try!(this.existential_bounds(a_.bounds, b_.bounds));
 416           Ok(ty::mk_trait(tcx, principal, bounds))
 417       }
 418
 419       (&ty::ty_struct(a_id, ref a_substs), &ty::ty_struct(b_id, ref b_substs))
 420       if a_id == b_id => {
 421             let substs = try!(this.substs(a_id, a_substs, b_substs));
 422             Ok(ty::mk_struct(tcx, a_id, substs))
 423       }
 424
 425       (&ty::ty_unboxed_closure(a_id, a_region, ref a_substs),
 426        &ty::ty_unboxed_closure(b_id, b_region, ref b_substs))
 427       if a_id == b_id => {
 428           // All ty_unboxed_closure types with the same id represent
 429           // the (anonymous) type of the same closure expression. So
 430           // all of their regions should be equated.
 431           let region = try!(this.equate().regions(a_region, b_region));
 432           let substs = try!(this.substs_variances(None, a_substs, b_substs));
 433           Ok(ty::mk_unboxed_closure(tcx, a_id, region, substs))
 434       }
 435
 436       (&ty::ty_uniq(a_inner), &ty::ty_uniq(b_inner)) => {
 437           let typ = try!(this.tys(a_inner, b_inner));
 438           Ok(ty::mk_uniq(tcx, typ))
 439       }
 440
 441       (&ty::ty_ptr(ref a_mt), &ty::ty_ptr(ref b_mt)) => {
 442           let mt = try!(this.mts(a_mt, b_mt));
 443           Ok(ty::mk_ptr(tcx, mt))
 444       }
 445
 446       (&ty::ty_rptr(a_r, ref a_mt), &ty::ty_rptr(b_r, ref b_mt)) => {
 447             let r = try!(this.contraregions(a_r, b_r));
 448             // FIXME(14985)  If we have mutable references to trait objects, we
 449             // used to use covariant subtyping. I have preserved this behaviour,
 450             // even though it is probably incorrect. So don't go down the usual
 451             // path which would require invariance.
 452             let mt = match (&a_mt.ty.sty, &b_mt.ty.sty) {
 453                 (&ty::ty_trait(..), &ty::ty_trait(..)) if a_mt.mutbl == b_mt.mutbl => {
 454                     let ty = try!(this.tys(a_mt.ty, b_mt.ty));
 455                     ty::mt { ty: ty, mutbl: a_mt.mutbl }
 456                 }
 457                 _ => try!(this.mts(a_mt, b_mt))
 458             };
 459             Ok(ty::mk_rptr(tcx, r, mt))
 460       }
 461
 462       (&ty::ty_vec(a_t, Some(sz_a)), &ty::ty_vec(b_t, Some(sz_b))) => {
 463         this.tys(a_t, b_t).and_then(|t| {
 464             if sz_a == sz_b {
 465                 Ok(ty::mk_vec(tcx, t, Some(sz_a)))
 466             } else {
 467                 Err(ty::terr_fixed_array_size(expected_found(this, sz_a, sz_b)))
 468             }
 469         })
 470       }
 471
 472       (&ty::ty_vec(a_t, sz_a), &ty::ty_vec(b_t, sz_b)) => {
 473         this.tys(a_t, b_t).and_then(|t| {
 474             if sz_a == sz_b {
 475                 Ok(ty::mk_vec(tcx, t, sz_a))
 476             } else {
 477                 Err(ty::terr_sorts(expected_found(this, a, b)))
 478             }
 479         })
 480       }
 481
 482       (&ty::ty_str, &ty::ty_str) => {
 483             Ok(ty::mk_str(tcx))
 484       }
 485
 486       (&ty::ty_tup(ref as_), &ty::ty_tup(ref bs)) => {
 487         if as_.len() == bs.len() {
 488             as_.iter().zip(bs.iter())
 489                .map(|(a, b)| this.tys(*a, *b))
 490                .collect::<Result<_, _>>()
 491                .map(|ts| ty::mk_tup(tcx, ts))
 492         } else if as_.len() != 0 && bs.len() != 0 {
 493             Err(ty::terr_tuple_size(
 494                 expected_found(this, as_.len(), bs.len())))
 495         } else {
 496             Err(ty::terr_sorts(expected_found(this, a, b)))
 497         }
 498       }
 499
 500       (&ty::ty_bare_fn(ref a_fty), &ty::ty_bare_fn(ref b_fty)) => {
 501         this.bare_fn_tys(a_fty, b_fty).and_then(|fty| {
 502             Ok(ty::mk_bare_fn(tcx, fty))
 503         })
 504       }
 505
 506       (&ty::ty_closure(ref a_fty), &ty::ty_closure(ref b_fty)) => {
 507         this.closure_tys(&**a_fty, &**b_fty).and_then(|fty| {
 508             Ok(ty::mk_closure(tcx, fty))
 509         })
 510       }
 511
 512       _ => Err(ty::terr_sorts(expected_found(this, a, b)))
 513     };
 514
 515     fn unify_integral_variable<'tcx, C: Combine<'tcx>>(
 516         this: &C,
 517         vid_is_expected: bool,
 518         vid: ty::IntVid,
 519         val: ty::IntVarValue) -> cres<'tcx, Ty<'tcx>>
 520     {
 521         try!(this.infcx().simple_var_t(vid_is_expected, vid, val));
 522         match val {
 523             IntType(v) => Ok(ty::mk_mach_int(v)),
 524             UintType(v) => Ok(ty::mk_mach_uint(v))
 525         }
 526     }
 527
 528     fn unify_float_variable<'tcx, C: Combine<'tcx>>(
 529         this: &C,
 530         vid_is_expected: bool,
 531         vid: ty::FloatVid,
 532         val: ast::FloatTy) -> cres<'tcx, Ty<'tcx>>
 533     {
 534         try!(this.infcx().simple_var_t(vid_is_expected, vid, val));
 535         Ok(ty::mk_mach_float(val))
 536     }
 537 }
 538
 539 impl<'f, 'tcx> CombineFields<'f, 'tcx> {
 540     pub fn switch_expected(&self) -> CombineFields<'f, 'tcx> {
 541         CombineFields {
 542             a_is_expected: !self.a_is_expected,
 543             ..(*self).clone()
 544         }
 545     }
 546
 547     fn equate(&self) -> Equate<'f, 'tcx> {
 548         Equate((*self).clone())
 549     }
 550
 551     fn sub(&self) -> Sub<'f, 'tcx> {
 552         Sub((*self).clone())
 553     }
 554
 555     pub fn instantiate(&self,
 556                        a_ty: Ty<'tcx>,
 557                        dir: RelationDir,
 558                        b_vid: ty::TyVid)
 559                        -> cres<'tcx, ()>
 560     {
 561         let tcx = self.infcx.tcx;
 562         let mut stack = Vec::new();
 563         stack.push((a_ty, dir, b_vid));
 564         loop {
 565             // For each turn of the loop, we extract a tuple
 566             //
 567             //     (a_ty, dir, b_vid)
 568             //
 569             // to relate. Here dir is either SubtypeOf or
 570             // SupertypeOf. The idea is that we should ensure that
 571             // the type `a_ty` is a subtype or supertype (respectively) of the
 572             // type to which `b_vid` is bound.
 573             //
 574             // If `b_vid` has not yet been instantiated with a type
 575             // (which is always true on the first iteration, but not
 576             // necessarily true on later iterations), we will first
 577             // instantiate `b_vid` with a *generalized* version of
 578             // `a_ty`. Generalization introduces other inference
 579             // variables wherever subtyping could occur (at time of
 580             // this writing, this means replacing free regions with
 581             // region variables).
 582             let (a_ty, dir, b_vid) = match stack.pop() {
 583                 None => break,
 584                 Some(e) => e,
 585             };
 586
 587             debug!("instantiate(a_ty={} dir={} b_vid={})",
 588                    a_ty.repr(tcx),
 589                    dir,
 590                    b_vid.repr(tcx));
 591
 592             // Check whether `vid` has been instantiated yet.  If not,
 593             // make a generalized form of `ty` and instantiate with
 594             // that.
 595             let b_ty = self.infcx.type_variables.borrow().probe(b_vid);
 596             let b_ty = match b_ty {
 597                 Some(t) => t, // ...already instantiated.
 598                 None => {     // ...not yet instantiated:
 599                     // Generalize type if necessary.
 600                     let generalized_ty = try!(match dir {
 601                         EqTo => {
 602                             self.generalize(a_ty, b_vid, false)
 603                         }
 604                         SupertypeOf | SubtypeOf => {
 605                             self.generalize(a_ty, b_vid, true)
 606                         }
 607                     });
 608                     debug!("instantiate(a_ty={}, dir={}, \
 609                                         b_vid={}, generalized_ty={})",
 610                            a_ty.repr(tcx), dir, b_vid.repr(tcx),
 611                            generalized_ty.repr(tcx));
 612                     self.infcx.type_variables
 613                         .borrow_mut()
 614                         .instantiate_and_push(
 615                             b_vid, generalized_ty, &mut stack);
 616                     generalized_ty
 617                 }
 618             };
 619
 620             // The original triple was `(a_ty, dir, b_vid)` -- now we have
 621             // resolved `b_vid` to `b_ty`, so apply `(a_ty, dir, b_ty)`:
 622             //
 623             // FIXME(#16847): This code is non-ideal because all these subtype
 624             // relations wind up attributed to the same spans. We need
 625             // to associate causes/spans with each of the relations in
 626             // the stack to get this right.
 627             match dir {
 628                 EqTo => {
 629                     try!(self.equate().tys(a_ty, b_ty));
 630                 }
 631
 632                 SubtypeOf => {
 633                     try!(self.sub().tys(a_ty, b_ty));
 634                 }
 635
 636                 SupertypeOf => {
 637                     try!(self.sub().contratys(a_ty, b_ty));
 638                 }
 639             }
 640         }
 641
 642         Ok(())
 643     }
 644
 645     /// Attempts to generalize `ty` for the type variable `for_vid`.  This checks for cycle -- that
 646     /// is, whether the type `ty` references `for_vid`. If `make_region_vars` is true, it will also
 647     /// replace all regions with fresh variables. Returns `ty_err` in the case of a cycle, `Ok`
 648     /// otherwise.
 649     fn generalize(&self,
 650                   ty: Ty<'tcx>,
 651                   for_vid: ty::TyVid,
 652                   make_region_vars: bool)
 653                   -> cres<'tcx, Ty<'tcx>>
 654     {
 655         let mut generalize = Generalizer { infcx: self.infcx,
 656                                            span: self.trace.origin.span(),
 657                                            for_vid: for_vid,
 658                                            make_region_vars: make_region_vars,
 659                                            cycle_detected: false };
 660         let u = ty.fold_with(&mut generalize);
 661         if generalize.cycle_detected {
 662             Err(ty::terr_cyclic_ty)
 663         } else {
 664             Ok(u)
 665         }
 666     }
 667 }
 668
 669 struct Generalizer<'cx, 'tcx:'cx> {
 670     infcx: &'cx InferCtxt<'cx, 'tcx>,
 671     span: Span,
 672     for_vid: ty::TyVid,
 673     make_region_vars: bool,
 674     cycle_detected: bool,
 675 }
 676
 677 impl<'cx, 'tcx> ty_fold::TypeFolder<'tcx> for Generalizer<'cx, 'tcx> {
 678     fn tcx(&self) -> &ty::ctxt<'tcx> {
 679         self.infcx.tcx
 680     }
 681
 682     fn fold_ty(&mut self, t: Ty<'tcx>) -> Ty<'tcx> {
 683         // Check to see whether the type we are genealizing references
 684         // `vid`. At the same time, also update any type variables to
 685         // the values that they are bound to. This is needed to truly
 686         // check for cycles, but also just makes things readable.
 687         //
 688         // (In particular, you could have something like `$0 = Box<$1>`
 689         //  where `$1` has already been instantiated with `Box<$0>`)
 690         match t.sty {
 691             ty::ty_infer(ty::TyVar(vid)) => {
 692                 if vid == self.for_vid {
 693                     self.cycle_detected = true;
 694                     ty::mk_err()
 695                 } else {
 696                     match self.infcx.type_variables.borrow().probe(vid) {
 697                         Some(u) => self.fold_ty(u),
 698                         None => t,
 699                     }
 700                 }
 701             }
 702             _ => {
 703                 ty_fold::super_fold_ty(self, t)
 704             }
 705         }
 706     }
 707
 708     fn fold_region(&mut self, r: ty::Region) -> ty::Region {
 709         match r {
 710             ty::ReLateBound(..) | ty::ReEarlyBound(..) => r,
 711             _ if self.make_region_vars => {
 712                 // FIXME: This is non-ideal because we don't give a
 713                 // very descriptive origin for this region variable.
 714                 self.infcx.next_region_var(MiscVariable(self.span))
 715             }
 716             _ => r,
 717         }
 718     }
 719 }
 720
 721