Auto merge of #32062 - Marwes:unification_table_for_eq_relations, r=nikomatsakis

Improve time complexity of equality relations

This PR adds a `UnificationTable` to the `TypeVariableTable` type which is used store information about variable equality instead of just storing them in a vector for later processing. By using a `UnificationTable` equality relations can be resolved in O(n) (for all realistic values of n) rather than O(n!) which can give massive speedups in certain cases (see combine as an example).

Link to combine: https://github.com/Marwes/combine

12 files changed, 183 insertions, 42 deletions

diff --git a/src/librustc/middle/infer/bivariate.rs b/src/librustc/middle/infer/bivariate.rs
index cb6542856be..485b7d2a9dd 100644
--- a/src/librustc/middle/infer/bivariate.rs
+++ b/src/librustc/middle/infer/bivariate.rs
@@ -77,8 +77,8 @@ impl<'a, 'tcx> TypeRelation<'a, 'tcx> for Bivariate<'a, 'tcx> {
         if a == b { return Ok(a); }
 
         let infcx = self.fields.infcx;
-        let a = infcx.type_variables.borrow().replace_if_possible(a);
-        let b = infcx.type_variables.borrow().replace_if_possible(b);
+        let a = infcx.type_variables.borrow_mut().replace_if_possible(a);
+        let b = infcx.type_variables.borrow_mut().replace_if_possible(b);
         match (&a.sty, &b.sty) {
             (&ty::TyInfer(TyVar(a_id)), &ty::TyInfer(TyVar(b_id))) => {
                 infcx.type_variables.borrow_mut().relate_vars(a_id, BiTo, b_id);
diff --git a/src/librustc/middle/infer/combine.rs b/src/librustc/middle/infer/combine.rs
index cd4a2eb2d93..1c2af961325 100644
--- a/src/librustc/middle/infer/combine.rs
+++ b/src/librustc/middle/infer/combine.rs
@@ -210,6 +210,12 @@ impl<'a, 'tcx> CombineFields<'a, 'tcx> {
                 None => break,
                 Some(e) => e,
             };
+            // Get the actual variable that b_vid has been inferred to
+            let (b_vid, b_ty) = {
+                let mut variables = self.infcx.type_variables.borrow_mut();
+                let b_vid = variables.root_var(b_vid);
+                (b_vid, variables.probe_root(b_vid))
+            };
 
             debug!("instantiate(a_ty={:?} dir={:?} b_vid={:?})",
                    a_ty,
@@ -219,7 +225,6 @@ impl<'a, 'tcx> CombineFields<'a, '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:
@@ -307,12 +312,17 @@ impl<'cx, 'tcx> ty::fold::TypeFolder<'tcx> for Generalizer<'cx, 'tcx> {
         //  where `$1` has already been instantiated with `Box<$0>`)
         match t.sty {
             ty::TyInfer(ty::TyVar(vid)) => {
+                let mut variables = self.infcx.type_variables.borrow_mut();
+                let vid = variables.root_var(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),
+                    match variables.probe_root(vid) {
+                        Some(u) => {
+                            drop(variables);
+                            self.fold_ty(u)
+                        }
                         None => t,
                     }
                 }
diff --git a/src/librustc/middle/infer/equate.rs b/src/librustc/middle/infer/equate.rs
index a10568d1fa3..92a419fec32 100644
--- a/src/librustc/middle/infer/equate.rs
+++ b/src/librustc/middle/infer/equate.rs
@@ -50,8 +50,8 @@ impl<'a, 'tcx> TypeRelation<'a,'tcx> for Equate<'a, 'tcx> {
         if a == b { return Ok(a); }
 
         let infcx = self.fields.infcx;
-        let a = infcx.type_variables.borrow().replace_if_possible(a);
-        let b = infcx.type_variables.borrow().replace_if_possible(b);
+        let a = infcx.type_variables.borrow_mut().replace_if_possible(a);
+        let b = infcx.type_variables.borrow_mut().replace_if_possible(b);
         match (&a.sty, &b.sty) {
             (&ty::TyInfer(TyVar(a_id)), &ty::TyInfer(TyVar(b_id))) => {
                 infcx.type_variables.borrow_mut().relate_vars(a_id, EqTo, b_id);
diff --git a/src/librustc/middle/infer/freshen.rs b/src/librustc/middle/infer/freshen.rs
index 6c0dd9b608d..b0f6d45dc53 100644
--- a/src/librustc/middle/infer/freshen.rs
+++ b/src/librustc/middle/infer/freshen.rs
@@ -111,8 +111,9 @@ impl<'a, 'tcx> TypeFolder<'tcx> for TypeFreshener<'a, 'tcx> {
 
         match t.sty {
             ty::TyInfer(ty::TyVar(v)) => {
+                let opt_ty = self.infcx.type_variables.borrow_mut().probe(v);
                 self.freshen(
-                    self.infcx.type_variables.borrow().probe(v),
+                    opt_ty,
                     ty::TyVar(v),
                     ty::FreshTy)
             }
diff --git a/src/librustc/middle/infer/higher_ranked/mod.rs b/src/librustc/middle/infer/higher_ranked/mod.rs
index 9b6625886a4..6cb91438ec3 100644
--- a/src/librustc/middle/infer/higher_ranked/mod.rs
+++ b/src/librustc/middle/infer/higher_ranked/mod.rs
@@ -434,7 +434,7 @@ impl<'a,'tcx> InferCtxtExt for InferCtxt<'a,'tcx> {
             self.region_vars.vars_created_since_snapshot(&snapshot.region_vars_snapshot);
 
         let escaping_types =
-            self.type_variables.borrow().types_escaping_snapshot(&snapshot.type_snapshot);
+            self.type_variables.borrow_mut().types_escaping_snapshot(&snapshot.type_snapshot);
 
         let mut escaping_region_vars = FnvHashSet();
         for ty in &escaping_types {
diff --git a/src/librustc/middle/infer/lattice.rs b/src/librustc/middle/infer/lattice.rs
index 2a560ec8a1d..6b5f2c74a69 100644
--- a/src/librustc/middle/infer/lattice.rs
+++ b/src/librustc/middle/infer/lattice.rs
@@ -60,8 +60,8 @@ pub fn super_lattice_tys<'a,'tcx,L:LatticeDir<'a,'tcx>>(this: &mut L,
     }
 
     let infcx = this.infcx();
-    let a = infcx.type_variables.borrow().replace_if_possible(a);
-    let b = infcx.type_variables.borrow().replace_if_possible(b);
+    let a = infcx.type_variables.borrow_mut().replace_if_possible(a);
+    let b = infcx.type_variables.borrow_mut().replace_if_possible(b);
     match (&a.sty, &b.sty) {
         (&ty::TyInfer(TyVar(..)), &ty::TyInfer(TyVar(..)))
             if infcx.type_var_diverges(a) && infcx.type_var_diverges(b) => {
diff --git a/src/librustc/middle/infer/mod.rs b/src/librustc/middle/infer/mod.rs
index 290d9afa449..829cb763c4f 100644
--- a/src/librustc/middle/infer/mod.rs
+++ b/src/librustc/middle/infer/mod.rs
@@ -663,7 +663,7 @@ impl<'a, 'tcx> InferCtxt<'a, 'tcx> {
         let mut variables = Vec::new();
 
         let unbound_ty_vars = self.type_variables
-                                  .borrow()
+                                  .borrow_mut()
                                   .unsolved_variables()
                                   .into_iter()
                                   .map(|t| self.tcx.mk_var(t));
@@ -1196,7 +1196,7 @@ impl<'a, 'tcx> InferCtxt<'a, 'tcx> {
                 // structurally), and we prevent cycles in any case,
                 // so this recursion should always be of very limited
                 // depth.
-                self.type_variables.borrow()
+                self.type_variables.borrow_mut()
                     .probe(v)
                     .map(|t| self.shallow_resolve(t))
                     .unwrap_or(typ)
diff --git a/src/librustc/middle/infer/sub.rs b/src/librustc/middle/infer/sub.rs
index e13d29b8b42..918a8c362da 100644
--- a/src/librustc/middle/infer/sub.rs
+++ b/src/librustc/middle/infer/sub.rs
@@ -65,8 +65,8 @@ impl<'a, 'tcx> TypeRelation<'a, 'tcx> for Sub<'a, 'tcx> {
         if a == b { return Ok(a); }
 
         let infcx = self.fields.infcx;
-        let a = infcx.type_variables.borrow().replace_if_possible(a);
-        let b = infcx.type_variables.borrow().replace_if_possible(b);
+        let a = infcx.type_variables.borrow_mut().replace_if_possible(a);
+        let b = infcx.type_variables.borrow_mut().replace_if_possible(b);
         match (&a.sty, &b.sty) {
             (&ty::TyInfer(TyVar(a_id)), &ty::TyInfer(TyVar(b_id))) => {
                 infcx.type_variables
diff --git a/src/librustc/middle/infer/type_variable.rs b/src/librustc/middle/infer/type_variable.rs
index e4af098c2a4..fe66ea5a1ea 100644
--- a/src/librustc/middle/infer/type_variable.rs
+++ b/src/librustc/middle/infer/type_variable.rs
@@ -20,9 +20,11 @@ use std::marker::PhantomData;
 use std::mem;
 use std::u32;
 use rustc_data_structures::snapshot_vec as sv;
+use rustc_data_structures::unify as ut;
 
 pub struct TypeVariableTable<'tcx> {
     values: sv::SnapshotVec<Delegate<'tcx>>,
+    eq_relations: ut::UnificationTable<ty::TyVid>,
 }
 
 struct TypeVariableData<'tcx> {
@@ -50,20 +52,22 @@ pub struct Default<'tcx> {
 }
 
 pub struct Snapshot {
-    snapshot: sv::Snapshot
+    snapshot: sv::Snapshot,
+    eq_snapshot: ut::Snapshot<ty::TyVid>,
 }
 
 enum UndoEntry<'tcx> {
     // The type of the var was specified.
     SpecifyVar(ty::TyVid, Vec<Relation>, Option<Default<'tcx>>),
     Relate(ty::TyVid, ty::TyVid),
+    RelateRange(ty::TyVid, usize),
 }
 
 struct Delegate<'tcx>(PhantomData<&'tcx ()>);
 
 type Relation = (RelationDir, ty::TyVid);
 
-#[derive(Copy, Clone, PartialEq, Debug)]
+#[derive(Copy, Clone, Eq, PartialEq, Hash, Debug)]
 pub enum RelationDir {
     SubtypeOf, SupertypeOf, EqTo, BiTo
 }
@@ -81,7 +85,10 @@ impl RelationDir {
 
 impl<'tcx> TypeVariableTable<'tcx> {
     pub fn new() -> TypeVariableTable<'tcx> {
-        TypeVariableTable { values: sv::SnapshotVec::new() }
+        TypeVariableTable {
+            values: sv::SnapshotVec::new(),
+            eq_relations: ut::UnificationTable::new(),
+        }
     }
 
     fn relations<'a>(&'a mut self, a: ty::TyVid) -> &'a mut Vec<Relation> {
@@ -103,22 +110,48 @@ impl<'tcx> TypeVariableTable<'tcx> {
     ///
     /// Precondition: neither `a` nor `b` are known.
     pub fn relate_vars(&mut self, a: ty::TyVid, dir: RelationDir, b: ty::TyVid) {
+        let a = self.root_var(a);
+        let b = self.root_var(b);
         if a != b {
-            self.relations(a).push((dir, b));
-            self.relations(b).push((dir.opposite(), a));
-            self.values.record(Relate(a, b));
+            if dir == EqTo {
+                // a and b must be equal which we mark in the unification table
+                let root = self.eq_relations.union(a, b);
+                // In addition to being equal, all relations from the variable which is no longer
+                // the root must be added to the root so they are not forgotten as the other
+                // variable should no longer be referenced (other than to get the root)
+                let other = if a == root { b } else { a };
+                let count = {
+                    let (relations, root_relations) = if other.index < root.index {
+                        let (pre, post) = self.values.split_at_mut(root.index as usize);
+                        (relations(&mut pre[other.index as usize]), relations(&mut post[0]))
+                    } else {
+                        let (pre, post) = self.values.split_at_mut(other.index as usize);
+                        (relations(&mut post[0]), relations(&mut pre[root.index as usize]))
+                    };
+                    root_relations.extend_from_slice(relations);
+                    relations.len()
+                };
+                self.values.record(RelateRange(root, count));
+            } else {
+                self.relations(a).push((dir, b));
+                self.relations(b).push((dir.opposite(), a));
+                self.values.record(Relate(a, b));
+            }
         }
     }
 
     /// Instantiates `vid` with the type `ty` and then pushes an entry onto `stack` for each of the
     /// relations of `vid` to other variables. The relations will have the form `(ty, dir, vid1)`
     /// where `vid1` is some other variable id.
+    ///
+    /// Precondition: `vid` must be a root in the unification table
     pub fn instantiate_and_push(
         &mut self,
         vid: ty::TyVid,
         ty: Ty<'tcx>,
         stack: &mut Vec<(Ty<'tcx>, RelationDir, ty::TyVid)>)
     {
+        debug_assert!(self.root_var(vid) == vid);
         let old_value = {
             let value_ptr = &mut self.values.get_mut(vid.index as usize).value;
             mem::replace(value_ptr, Known(ty))
@@ -140,6 +173,7 @@ impl<'tcx> TypeVariableTable<'tcx> {
     pub fn new_var(&mut self,
                    diverging: bool,
                    default: Option<Default<'tcx>>) -> ty::TyVid {
+        self.eq_relations.new_key(());
         let index = self.values.push(TypeVariableData {
             value: Bounded { relations: vec![], default: default },
             diverging: diverging
@@ -147,14 +181,25 @@ impl<'tcx> TypeVariableTable<'tcx> {
         ty::TyVid { index: index as u32 }
     }
 
-    pub fn probe(&self, vid: ty::TyVid) -> Option<Ty<'tcx>> {
+    pub fn root_var(&mut self, vid: ty::TyVid) -> ty::TyVid {
+        self.eq_relations.find(vid)
+    }
+
+    pub fn probe(&mut self, vid: ty::TyVid) -> Option<Ty<'tcx>> {
+        let vid = self.root_var(vid);
+        self.probe_root(vid)
+    }
+
+    /// Retrieves the type of `vid` given that it is currently a root in the unification table
+    pub fn probe_root(&mut self, vid: ty::TyVid) -> Option<Ty<'tcx>> {
+        debug_assert!(self.root_var(vid) == vid);
         match self.values.get(vid.index as usize).value {
             Bounded { .. } => None,
             Known(t) => Some(t)
         }
     }
 
-    pub fn replace_if_possible(&self, t: Ty<'tcx>) -> Ty<'tcx> {
+    pub fn replace_if_possible(&mut self, t: Ty<'tcx>) -> Ty<'tcx> {
         match t.sty {
             ty::TyInfer(ty::TyVar(v)) => {
                 match self.probe(v) {
@@ -167,18 +212,23 @@ impl<'tcx> TypeVariableTable<'tcx> {
     }
 
     pub fn snapshot(&mut self) -> Snapshot {
-        Snapshot { snapshot: self.values.start_snapshot() }
+        Snapshot {
+            snapshot: self.values.start_snapshot(),
+            eq_snapshot: self.eq_relations.snapshot(),
+        }
     }
 
     pub fn rollback_to(&mut self, s: Snapshot) {
         self.values.rollback_to(s.snapshot);
+        self.eq_relations.rollback_to(s.eq_snapshot);
     }
 
     pub fn commit(&mut self, s: Snapshot) {
         self.values.commit(s.snapshot);
+        self.eq_relations.commit(s.eq_snapshot);
     }
 
-    pub fn types_escaping_snapshot(&self, s: &Snapshot) -> Vec<Ty<'tcx>> {
+    pub fn types_escaping_snapshot(&mut self, s: &Snapshot) -> Vec<Ty<'tcx>> {
         /*!
          * Find the set of type variables that existed *before* `s`
          * but which have only been unified since `s` started, and
@@ -208,7 +258,10 @@ impl<'tcx> TypeVariableTable<'tcx> {
                     if vid.index < new_elem_threshold {
                         // quick check to see if this variable was
                         // created since the snapshot started or not.
-                        let escaping_type = self.probe(vid).unwrap();
+                        let escaping_type = match self.values.get(vid.index as usize).value {
+                            Bounded { .. } => unreachable!(),
+                            Known(ty) => ty,
+                        };
                         escaping_types.push(escaping_type);
                     }
                     debug!("SpecifyVar({:?}) new_elem_threshold={}", vid, new_elem_threshold);
@@ -221,13 +274,15 @@ impl<'tcx> TypeVariableTable<'tcx> {
         escaping_types
     }
 
-    pub fn unsolved_variables(&self) -> Vec<ty::TyVid> {
-        self.values
-            .iter()
-            .enumerate()
-            .filter_map(|(i, value)| match &value.value {
-                &TypeVariableValue::Known(_) => None,
-                &TypeVariableValue::Bounded { .. } => Some(ty::TyVid { index: i as u32 })
+    pub fn unsolved_variables(&mut self) -> Vec<ty::TyVid> {
+        (0..self.values.len())
+            .filter_map(|i| {
+                let vid = ty::TyVid { index: i as u32 };
+                if self.probe(vid).is_some() {
+                    None
+                } else {
+                    Some(vid)
+                }
             })
             .collect()
     }
@@ -250,6 +305,13 @@ impl<'tcx> sv::SnapshotVecDelegate for Delegate<'tcx> {
                 relations(&mut (*values)[a.index as usize]).pop();
                 relations(&mut (*values)[b.index as usize]).pop();
             }
+
+            RelateRange(i, n) => {
+                let relations = relations(&mut (*values)[i.index as usize]);
+                for _ in 0..n {
+                    relations.pop();
+                }
+            }
         }
     }
 }
diff --git a/src/librustc/middle/infer/unify_key.rs b/src/librustc/middle/infer/unify_key.rs
index 5008a92a4f5..3f8c3fbce04 100644
--- a/src/librustc/middle/infer/unify_key.rs
+++ b/src/librustc/middle/infer/unify_key.rs
@@ -73,3 +73,10 @@ impl<'tcx> ToType<'tcx> for ast::FloatTy {
         tcx.mk_mach_float(*self)
     }
 }
+
+impl UnifyKey for ty::TyVid {
+    type Value = ();
+    fn index(&self) -> u32 { self.index }
+    fn from_index(i: u32) -> ty::TyVid { ty::TyVid { index: i } }
+    fn tag(_: Option<ty::TyVid>) -> &'static str { "TyVid" }
+}
diff --git a/src/librustc_data_structures/unify/mod.rs b/src/librustc_data_structures/unify/mod.rs
index 7a1ac830b22..3feea3218d0 100644
--- a/src/librustc_data_structures/unify/mod.rs
+++ b/src/librustc_data_structures/unify/mod.rs
@@ -211,7 +211,7 @@ impl<K: UnifyKey> UnificationTable<K> {
     /// really more of a building block. If the values associated with
     /// your key are non-trivial, you would probably prefer to call
     /// `unify_var_var` below.
-    fn unify(&mut self, root_a: VarValue<K>, root_b: VarValue<K>, new_value: K::Value) {
+    fn unify(&mut self, root_a: VarValue<K>, root_b: VarValue<K>, new_value: K::Value) -> K {
         debug!("unify(root_a(id={:?}, rank={:?}), root_b(id={:?}, rank={:?}))",
                root_a.key(),
                root_a.rank,
@@ -221,14 +221,14 @@ impl<K: UnifyKey> UnificationTable<K> {
         if root_a.rank > root_b.rank {
             // a has greater rank, so a should become b's parent,
             // i.e., b should redirect to a.
-            self.redirect_root(root_a.rank, root_b, root_a, new_value);
+            self.redirect_root(root_a.rank, root_b, root_a, new_value)
         } else if root_a.rank < root_b.rank {
             // b has greater rank, so a should redirect to b.
-            self.redirect_root(root_b.rank, root_a, root_b, new_value);
+            self.redirect_root(root_b.rank, root_a, root_b, new_value)
         } else {
             // If equal, redirect one to the other and increment the
             // other's rank.
-            self.redirect_root(root_a.rank + 1, root_a, root_b, new_value);
+            self.redirect_root(root_a.rank + 1, root_a, root_b, new_value)
         }
     }
 
@@ -236,11 +236,12 @@ impl<K: UnifyKey> UnificationTable<K> {
                      new_rank: u32,
                      old_root: VarValue<K>,
                      new_root: VarValue<K>,
-                     new_value: K::Value) {
+                     new_value: K::Value) -> K {
         let old_root_key = old_root.key();
         let new_root_key = new_root.key();
         self.set(old_root_key, old_root.redirect(new_root_key));
         self.set(new_root_key, new_root.root(new_rank, new_value));
+        new_root_key
     }
 }
 
@@ -256,14 +257,16 @@ impl<K: UnifyKey> sv::SnapshotVecDelegate for Delegate<K> {
 impl<'tcx, K: UnifyKey> UnificationTable<K>
     where K::Value: Combine
 {
-    pub fn union(&mut self, a_id: K, b_id: K) {
+    pub fn union(&mut self, a_id: K, b_id: K) -> K {
         let node_a = self.get(a_id);
         let node_b = self.get(b_id);
         let a_id = node_a.key();
         let b_id = node_b.key();
         if a_id != b_id {
             let new_value = node_a.value.combine(&node_b.value);
-            self.unify(node_a, node_b, new_value);
+            self.unify(node_a, node_b, new_value)
+        } else {
+            a_id
         }
     }
 
@@ -290,14 +293,14 @@ impl<'tcx, K, V> UnificationTable<K>
     where K: UnifyKey<Value = Option<V>>,
           V: Clone + PartialEq + Debug
 {
-    pub fn unify_var_var(&mut self, a_id: K, b_id: K) -> Result<(), (V, V)> {
+    pub fn unify_var_var(&mut self, a_id: K, b_id: K) -> Result<K, (V, V)> {
         let node_a = self.get(a_id);
         let node_b = self.get(b_id);
         let a_id = node_a.key();
         let b_id = node_b.key();
 
         if a_id == b_id {
-            return Ok(());
+            return Ok(a_id);
         }
 
         let combined = {
diff --git a/src/test/run-pass/bench/issue-32062.rs b/src/test/run-pass/bench/issue-32062.rs
new file mode 100644
index 00000000000..8f6457d820a
--- /dev/null
+++ b/src/test/run-pass/bench/issue-32062.rs
@@ -0,0 +1,58 @@
+// Copyright 2016 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.
+
+// pretty-expanded FIXME #23616
+
+fn main() {
+    let _ = test(Some(0).into_iter());
+}
+
+trait Parser {
+    type Input: Iterator;
+    type Output;
+    fn parse(self, input: Self::Input) -> Result<(Self::Output, Self::Input), ()>;
+    fn chain<P>(self, p: P) -> Chain<Self, P> where Self: Sized {
+        Chain(self, p)
+    }
+}
+
+struct Token<T>(T::Item) where T: Iterator;
+
+impl<T> Parser for Token<T> where T: Iterator {
+    type Input = T;
+    type Output = T::Item;
+    fn parse(self, _input: Self::Input) -> Result<(Self::Output, Self::Input), ()> {
+        Err(())
+    }
+}
+
+struct Chain<L, R>(L, R);
+
+impl<L, R> Parser for Chain<L, R> where L: Parser, R: Parser<Input = L::Input> {
+    type Input = L::Input;
+    type Output = (L::Output, R::Output);
+    fn parse(self, _input: Self::Input) -> Result<(Self::Output, Self::Input), ()> {
+        Err(())
+    }
+}
+
+fn test<I>(i: I) -> Result<((), I), ()> where I: Iterator<Item = i32> {
+    Chain(Token(0), Token(1))
+        .chain(Chain(Token(0), Token(1)))
+        .chain(Chain(Token(0), Token(1)))
+        .chain(Chain(Token(0), Token(1)))
+        .chain(Chain(Token(0), Token(1)))
+        .chain(Chain(Token(0), Token(1)))
+        .chain(Chain(Token(0), Token(1)))
+        .chain(Chain(Token(0), Token(1)))
+        .chain(Chain(Token(0), Token(1)))
+        .parse(i)
+        .map(|(_, i)| ((), i))
+}