Add some tests about range types.

test/cctest/test-types.cc

 // Copyright 2013 the V8 project authors. All rights reserved.
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
 #include <vector>
 
 #include "src/hydrogen-types.h"
 #include "src/isolate-inl.h"
 #include "src/types.h"
 #include "test/cctest/cctest.h"
 
 using namespace v8::internal;
 
+
 // Testing auxiliaries (breaking the Type abstraction).
+
+
+static bool IsInteger(double x) {
+  return nearbyint(x) == x && !i::IsMinusZero(x);  // Allows for infinities.
+}
+
+
+static bool IsInteger(i::Object* x) {
+  return x->IsNumber() && IsInteger(x->Number());
+}
+
+
 typedef uint32_t bitset;
 
+
 struct ZoneRep {
   typedef void* Struct;
 
   static bool IsStruct(Type* t, int tag) {
     return !IsBitset(t) && reinterpret_cast<intptr_t>(AsStruct(t)[0]) == tag;
   }
   static bool IsBitset(Type* t) { return reinterpret_cast<uintptr_t>(t) & 1; }
   static bool IsUnion(Type* t) { return IsStruct(t, 6); }
 
   static Struct* AsStruct(Type* t) {
@@ skipping 585 matching lines @@
             if (min2->Number() > max2->Number()) std::swap(min2, max2);
             TypeHandle type1 = T.Range(min1, max1);
             TypeHandle type2 = T.Range(min2, max2);
             CHECK(Equal(type1, type2) == (*min1 == *min2 && *max1 == *max2));
           }
         }
       }
     }
   }
 
+  void Context() {
+    // Constructor
+    for (int i = 0; i < 20; ++i) {
+      TypeHandle type = T.Random();
+      TypeHandle context = T.Context(type);
+      CHECK(context->Iscontext());
+    }
+
+    // Attributes
+    for (int i = 0; i < 20; ++i) {
+      TypeHandle type = T.Random();
+      TypeHandle context = T.Context(type);
+      CheckEqual(type, context->AsContext()->Outer());
+    }
+
+    // Functionality & Injectivity: Context(T1) = Context(T2) iff T1 = T2
+    for (int i = 0; i < 20; ++i) {
+      for (int j = 0; j < 20; ++j) {
+        TypeHandle type1 = T.Random();
+        TypeHandle type2 = T.Random();
+        TypeHandle context1 = T.Context(type1);
+        TypeHandle context2 = T.Context(type2);
+        CHECK(Equal(context1, context2) == Equal(type1, type2));
+      }
+    }
+  }
+
   void Array() {
     // Constructor
     for (int i = 0; i < 20; ++i) {
       TypeHandle type = T.Random();
       TypeHandle array = T.Array1(type);
       CHECK(array->IsArray());
     }
 
     // Attributes
     for (int i = 0; i < 20; ++i) {
@@ skipping 164 matching lines @@
         Handle<i::Object> value = *vt;
         TypeHandle type = *it;
         TypeHandle const_type = T.Constant(value);
         TypeHandle nowof_type = T.NowOf(value);
         CHECK(!const_type->Is(type) ||
               nowof_type->Is(type) || type->Maybe(const_type));
       }
     }
   }
 
+  void MinMax() {
+    // If b is regular numeric bitset, then Range(b->Min(), b->Max())->Is(b).
+    // TODO(neis): Need to ignore representation for this to be true.
+    /*
+    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
+      TypeHandle type = *it;
+      if (this->IsBitset(type) && type->Is(T.Number) &&
+          !type->Is(T.None) && !type->Is(T.NaN)) {
+        TypeHandle range = T.Range(
+            isolate->factory()->NewNumber(type->Min()),
+            isolate->factory()->NewNumber(type->Max()));
+        CHECK(range->Is(type));
+      }
+    }
+    */
+
+    // If b is regular numeric bitset, then b->Min() and b->Max() are integers.
+    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
+      TypeHandle type = *it;
+      if (this->IsBitset(type) && type->Is(T.Number) &&
+          !type->Is(T.None) && !type->Is(T.NaN)) {
+        CHECK(IsInteger(type->Min()) && IsInteger(type->Max()));
+      }
+    }
+
+    // If b1 and b2 are regular numeric bitsets with b1->Is(b2), then
+    // b1->Min() >= b2->Min() and b1->Max() <= b2->Max().
+    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
+      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
+        TypeHandle type1 = *it1;
+        TypeHandle type2 = *it2;
+        if (this->IsBitset(type1) && type1->Is(type2) && type2->Is(T.Number) &&
+            !type1->Is(T.NaN) && !type2->Is(T.NaN)) {
+          CHECK(type1->Min() >= type2->Min());
+          CHECK(type1->Max() <= type2->Max());
+        }
+      }
+    }
+
+    // Lub(Range(x,y))->Min() <= x and y <= Lub(Range(x,y))->Max()
+    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
+      TypeHandle type = *it;
+      if (type->IsRange()) {
+        TypeHandle lub = Rep::BitsetType::New(
+            Rep::BitsetType::Lub(type), T.region());
+        CHECK(lub->Min() <= type->Min() && type->Max() <= lub->Max());
+      }
+    }
+  }
+
   void BitsetGlb() {
     // Lower: (T->BitsetGlb())->Is(T)
     for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
       TypeHandle type = *it;
       TypeHandle glb =
           Rep::BitsetType::New(Rep::BitsetType::Glb(type), T.region());
       CHECK(glb->Is(type));
     }
 
     // Greatest: If T1->IsBitset() and T1->Is(T2), then T1->Is(T2->BitsetGlb())
@@ skipping 48 matching lines @@
         TypeHandle type2 = *it2;
         TypeHandle lub1 =
             Rep::BitsetType::New(Rep::BitsetType::Lub(type1), T.region());
         TypeHandle lub2 =
             Rep::BitsetType::New(Rep::BitsetType::Lub(type2), T.region());
         CHECK(!type1->Is(type2) || lub1->Is(lub2));
       }
     }
   }
 
-  void Is() {
+  void Is1() {
     // Least Element (Bottom): None->Is(T)
     for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
       TypeHandle type = *it;
       CHECK(T.None->Is(type));
     }
 
     // Greatest Element (Top): T->Is(Any)
     for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
       TypeHandle type = *it;
       CHECK(type->Is(T.Any));
@@ skipping 31 matching lines @@
 
     // Antisymmetry: T1->Is(T2) and T2->Is(T1) iff T1 = T2
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         TypeHandle type1 = *it1;
         TypeHandle type2 = *it2;
         CHECK((type1->Is(type2) && type2->Is(type1)) == Equal(type1, type2));
       }
     }
 
+    // (In-)Compatibilities.
+    for (TypeIterator i = T.types.begin(); i != T.types.end(); ++i) {
+      for (TypeIterator j = T.types.begin(); j != T.types.end(); ++j) {
+        TypeHandle type1 = *i;
+        TypeHandle type2 = *j;
+        CHECK(!type1->Is(type2) || this->IsBitset(type2) ||
+              this->IsUnion(type2) || this->IsUnion(type1) ||
+              (type1->IsClass() && type2->IsClass()) ||
+              (type1->IsConstant() && type2->IsConstant()) ||
+              (type1->IsConstant() && type2->IsRange()) ||
+              (type1->IsRange() && type2->IsRange()) ||
+              (type1->IsContext() && type2->IsContext()) ||
+              (type1->IsArray() && type2->IsArray()) ||
+              (type1->IsFunction() && type2->IsFunction()) ||
+              type1->Equals(T.None));
+      }
+    }
+  }
+
+  void Is2() {
     // Class(M1)->Is(Class(M2)) iff M1 = M2
     for (MapIterator mt1 = T.maps.begin(); mt1 != T.maps.end(); ++mt1) {
       for (MapIterator mt2 = T.maps.begin(); mt2 != T.maps.end(); ++mt2) {
         Handle<i::Map> map1 = *mt1;
         Handle<i::Map> map2 = *mt2;
         TypeHandle class_type1 = T.Class(map1);
         TypeHandle class_type2 = T.Class(map2);
         CHECK(class_type1->Is(class_type2) == (*map1 == *map2));
       }
     }
 
-    // Constant(V1)->Is(Constant(V2)) iff V1 = V2
-    for (ValueIterator vt1 = T.values.begin(); vt1 != T.values.end(); ++vt1) {
-      for (ValueIterator vt2 = T.values.begin(); vt2 != T.values.end(); ++vt2) {
-        Handle<i::Object> value1 = *vt1;
-        Handle<i::Object> value2 = *vt2;
-        TypeHandle const_type1 = T.Constant(value1);
-        TypeHandle const_type2 = T.Constant(value2);
-        CHECK(const_type1->Is(const_type2) == (*value1 == *value2));
-      }
-    }
-
-    // Range(min1, max1)->Is(Range(min2, max2)) iff
-    // min1 >= min2 /\ max1 <= max2
+    // Range(X1, Y1)->Is(Range(X2, Y2)) iff X1 >= X2 /\ Y1 <= Y2
     for (ValueIterator i1 = T.integers.begin();
         i1 != T.integers.end(); ++i1) {
-      for (ValueIterator j1 = T.integers.begin();
+      for (ValueIterator j1 = i1;
           j1 != T.integers.end(); ++j1) {
         for (ValueIterator i2 = T.integers.begin();
              i2 != T.integers.end(); ++i2) {
-          for (ValueIterator j2 = T.integers.begin();
+          for (ValueIterator j2 = i2;
                j2 != T.integers.end(); ++j2) {
             i::Handle<i::Object> min1 = *i1;
             i::Handle<i::Object> max1 = *j1;
             i::Handle<i::Object> min2 = *i2;
             i::Handle<i::Object> max2 = *j2;
             if (min1->Number() > max1->Number()) std::swap(min1, max1);
             if (min2->Number() > max2->Number()) std::swap(min2, max2);
             TypeHandle type1 = T.Range(min1, max1);
             TypeHandle type2 = T.Range(min2, max2);
             CHECK(type1->Is(type2) ==
-                (min2->Number() <= min1->Number() &&
+                (min1->Number() >= min2->Number() &&
                  max1->Number() <= max2->Number()));
           }
         }
       }
     }
 
+    // Constant(V1)->Is(Constant(V2)) iff V1 = V2
+    for (ValueIterator vt1 = T.values.begin(); vt1 != T.values.end(); ++vt1) {
+      for (ValueIterator vt2 = T.values.begin(); vt2 != T.values.end(); ++vt2) {
+        Handle<i::Object> value1 = *vt1;
+        Handle<i::Object> value2 = *vt2;
+        TypeHandle const_type1 = T.Constant(value1);
+        TypeHandle const_type2 = T.Constant(value2);
+        CHECK(const_type1->Is(const_type2) == (*value1 == *value2));
+      }
+    }
+
     // Context(T1)->Is(Context(T2)) iff T1 = T2
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         TypeHandle outer1 = *it1;
         TypeHandle outer2 = *it2;
         TypeHandle type1 = T.Context(outer1);
         TypeHandle type2 = T.Context(outer2);
         CHECK(type1->Is(type2) == outer1->Equals(outer2));
       }
     }
@@ skipping 16 matching lines @@
         TypeHandle receiver1 = *j;
         TypeHandle type1 = T.Function0(result1, receiver1);
         TypeHandle result2 = T.Random();
         TypeHandle receiver2 = T.Random();
         TypeHandle type2 = T.Function0(result2, receiver2);
         CHECK(type1->Is(type2) ==
             (result1->Equals(result2) && receiver1->Equals(receiver2)));
       }
     }
 
-    // (In-)Compatibilities.
-    for (TypeIterator i = T.types.begin(); i != T.types.end(); ++i) {
-      for (TypeIterator j = T.types.begin(); j != T.types.end(); ++j) {
-        TypeHandle type1 = *i;
-        TypeHandle type2 = *j;
-        CHECK(!type1->Is(type2) || this->IsBitset(type2) ||
-              this->IsUnion(type2) || this->IsUnion(type1) ||
-              (type1->IsClass() && type2->IsClass()) ||
-              (type1->IsConstant() && type2->IsConstant()) ||
-              (type1->IsConstant() && type2->IsRange()) ||
-              (type1->IsRange() && type2->IsRange()) ||
-              (type1->IsContext() && type2->IsContext()) ||
-              (type1->IsArray() && type2->IsArray()) ||
-              (type1->IsFunction() && type2->IsFunction()) ||
-              type1->Equals(T.None));
+
+    // Range-specific subtyping
+
+    // If IsInteger(v) then Constant(v)->Is(Range(v, v)).
+    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
+      TypeHandle type = *it;
+      if (type->IsConstant() && IsInteger(*type->AsConstant()->Value())) {
+        CHECK(type->Is(
+            T.Range(type->AsConstant()->Value(), type->AsConstant()->Value())));
       }
     }
 
-    // Basic types
+    // If Constant(x)->Is(Range(min,max)) then IsInteger(v) and min <= x <= max.
+    for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
+      for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
+        TypeHandle type1 = *it1;
+        TypeHandle type2 = *it2;
+        if (type1->IsConstant() && type2->IsRange() && type1->Is(type2)) {
+          double x = type1->AsConstant()->Value()->Number();
+          double min = type2->AsRange()->Min()->Number();
+          double max = type2->AsRange()->Max()->Number();
+          CHECK(IsInteger(x) && min <= x && x <= max);
+        }
+      }
+    }
+
+    // Lub(Range(x,y))->Is(T.Union(T.Integral32, T.OtherNumber))
+    for (TypeIterator it = T.types.begin(); it != T.types.end(); ++it) {
+      TypeHandle type = *it;
+      if (type->IsRange()) {
+        TypeHandle lub = Rep::BitsetType::New(
+            Rep::BitsetType::Lub(type), T.region());
+        CHECK(lub->Is(T.Union(T.Integral32, T.OtherNumber)));
+      }
+    }
+
+
+    // Subtyping between concrete basic types
+
     CheckUnordered(T.Boolean, T.Null);
     CheckUnordered(T.Undefined, T.Null);
     CheckUnordered(T.Boolean, T.Undefined);
 
     CheckSub(T.SignedSmall, T.Number);
     CheckSub(T.Signed32, T.Number);
     CheckSub(T.SignedSmall, T.Signed32);
     CheckUnordered(T.SignedSmall, T.MinusZero);
     CheckUnordered(T.Signed32, T.Unsigned32);
 
     CheckSub(T.UniqueName, T.Name);
     CheckSub(T.String, T.Name);
     CheckSub(T.InternalizedString, T.String);
     CheckSub(T.InternalizedString, T.UniqueName);
     CheckSub(T.InternalizedString, T.Name);
     CheckSub(T.Symbol, T.UniqueName);
     CheckSub(T.Symbol, T.Name);
     CheckUnordered(T.String, T.UniqueName);
     CheckUnordered(T.String, T.Symbol);
     CheckUnordered(T.InternalizedString, T.Symbol);
 
     CheckSub(T.Object, T.Receiver);
     CheckSub(T.Array, T.Object);
     CheckSub(T.Function, T.Object);
     CheckSub(T.Proxy, T.Receiver);
     CheckUnordered(T.Object, T.Proxy);
     CheckUnordered(T.Array, T.Function);
 
-    // Structural types
+
+    // Subtyping between concrete structural types
+
     CheckSub(T.ObjectClass, T.Object);
     CheckSub(T.ArrayClass, T.Object);
     CheckSub(T.ArrayClass, T.Array);
     CheckSub(T.UninitializedClass, T.Internal);
     CheckUnordered(T.ObjectClass, T.ArrayClass);
     CheckUnordered(T.UninitializedClass, T.Null);
     CheckUnordered(T.UninitializedClass, T.Undefined);
 
     CheckSub(T.SmiConstant, T.SignedSmall);
     CheckSub(T.SmiConstant, T.Signed32);
@@ skipping 368 matching lines @@
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         TypeHandle type1 = *it1;
         TypeHandle type2 = *it2;
         TypeHandle union12 = T.Union(type1, type2);
         TypeHandle union21 = T.Union(type2, type1);
         CheckEqual(union12, union21);
       }
     }
 
     // Associativity: Union(T1, Union(T2, T3)) = Union(Union(T1, T2), T3)
-    // This does NOT hold!
+    // This does NOT hold!  For example:
+    // (Unsigned32 \/ Range(0,5)) \/ Range(-5,0) = Unsigned32 \/ Range(-5,0)
+    // Unsigned32 \/ (Range(0,5) \/ Range(-5,0)) = Unsigned32 \/ Range(-5,5)
     /*
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
           TypeHandle type1 = *it1;
           TypeHandle type2 = *it2;
           TypeHandle type3 = *it3;
           TypeHandle union12 = T.Union(type1, type2);
           TypeHandle union23 = T.Union(type2, type3);
           TypeHandle union1_23 = T.Union(type1, union23);
@@ skipping 19 matching lines @@
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         TypeHandle type1 = *it1;
         TypeHandle type2 = *it2;
         TypeHandle union12 = T.Union(type1, type2);
         if (type1->Is(type2)) CheckEqual(union12, type2);
       }
     }
 
     // Monotonicity: T1->Is(T2) implies Union(T1, T3)->Is(Union(T2, T3))
-    // This does NOT hold.
+    // This does NOT hold.  For example:
+    // Range(-5,-1) <= Signed32
+    // Range(-5,-1) \/ Range(1,5) = Range(-5,5) </= Signed32 \/ Range(1,5)
     /*
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
           TypeHandle type1 = *it1;
           TypeHandle type2 = *it2;
           TypeHandle type3 = *it3;
           TypeHandle union13 = T.Union(type1, type3);
           TypeHandle union23 = T.Union(type2, type3);
           CHECK(!type1->Is(type2) || union13->Is(union23));
         }
       }
     }
     */
   }
 
   void Union2() {
     // Monotonicity: T1->Is(T3) and T2->Is(T3) implies Union(T1, T2)->Is(T3)
-    // This does NOT hold.  TODO(neis): Could fix this by splitting
-    // OtherNumber into a negative and a positive part.
+    // This does NOT hold.  For example:
+    // Range(-2^33, -2^33) <= OtherNumber
+    // Range(2^33, 2^33) <= OtherNumber
+    // Range(-2^33, 2^33) </= OtherNumber
     /*
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
           TypeHandle type1 = *it1;
           TypeHandle type2 = *it2;
           TypeHandle type3 = *it3;
           TypeHandle union12 = T.Union(type1, type2);
           CHECK(!(type1->Is(type3) && type2->Is(type3)) || union12->Is(type3));
         }
@@ skipping 161 matching lines @@
         TypeHandle type1 = *it1;
         TypeHandle type2 = *it2;
         TypeHandle intersect12 = T.Intersect(type1, type2);
         TypeHandle intersect21 = T.Intersect(type2, type1);
         CheckEqual(intersect12, intersect21);
       }
     }
 
     // Associativity:
     // Intersect(T1, Intersect(T2, T3)) = Intersect(Intersect(T1, T2), T3)
-    // This does NOT hold.
+    // This does NOT hold.  For example:
+    // (Class(..stringy1..) /\ Class(..stringy2..)) /\ Constant(..string..) =
+    // None
+    // Class(..stringy1..) /\ (Class(..stringy2..) /\ Constant(..string..)) =
+    // Constant(..string..)
     /*
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
           TypeHandle type1 = *it1;
           TypeHandle type2 = *it2;
           TypeHandle type3 = *it3;
           TypeHandle intersect12 = T.Intersect(type1, type2);
           TypeHandle intersect23 = T.Intersect(type2, type3);
           TypeHandle intersect1_23 = T.Intersect(type1, intersect23);
           TypeHandle intersect12_3 = T.Intersect(intersect12, type3);
           CheckEqual(intersect1_23, intersect12_3);
         }
       }
     }
     */
 
     // Join: Intersect(T1, T2)->Is(T1) and Intersect(T1, T2)->Is(T2)
-    // This does NOT hold.  Not even the disjunction.
+    // This does NOT hold.  For example:
+    // Class(..stringy..) /\ Constant(..string..) = Constant(..string..)
+    // Currently, not even the disjunction holds:
+    // Class(Internal/TaggedPtr) /\ (Any/Untagged \/ Context(..)) =
+    // Class(Internal/TaggedPtr) \/ Context(..)
     /*
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         TypeHandle type1 = *it1;
         TypeHandle type2 = *it2;
         TypeHandle intersect12 = T.Intersect(type1, type2);
         CHECK(intersect12->Is(type1));
         CHECK(intersect12->Is(type2));
       }
     }
     */
 
     // Lower Boundedness: T1->Is(T2) implies Intersect(T1, T2) = T1
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         TypeHandle type1 = *it1;
         TypeHandle type2 = *it2;
         TypeHandle intersect12 = T.Intersect(type1, type2);
         if (type1->Is(type2)) CheckEqual(intersect12, type1);
       }
     }
 
     // Monotonicity: T1->Is(T2) implies Intersect(T1, T3)->Is(Intersect(T2, T3))
-    // This does NOT hold.
+    // This does NOT hold.  For example:
+    // Class(OtherObject/TaggedPtr) <= Any/TaggedPtr
+    // Class(OtherObject/TaggedPtr) /\ Any/UntaggedInt1 = Class(..)
+    // Any/TaggedPtr /\ Any/UntaggedInt1 = None
     /*
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
           TypeHandle type1 = *it1;
           TypeHandle type2 = *it2;
           TypeHandle type3 = *it3;
           TypeHandle intersect13 = T.Intersect(type1, type3);
           TypeHandle intersect23 = T.Intersect(type2, type3);
           CHECK(!type1->Is(type2) || intersect13->Is(intersect23));
         }
       }
     }
     */
 
     // Monotonicity: T1->Is(T3) or T2->Is(T3) implies Intersect(T1, T2)->Is(T3)
-    // This does NOT hold.
+    // This does NOT hold.  For example:
+    // Class(..stringy..) <= Class(..stringy..)
+    // Class(..stringy..) /\ Constant(..string..) = Constant(..string..)
+    // Constant(..string..) </= Class(..stringy..)
     /*
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
           TypeHandle type1 = *it1;
           TypeHandle type2 = *it2;
           TypeHandle type3 = *it3;
           TypeHandle intersect12 = T.Intersect(type1, type2);
           CHECK(!(type1->Is(type3) || type2->Is(type3)) ||
                 intersect12->Is(type3));
         }
       }
     }
     */
 
     // Monotonicity: T1->Is(T2) and T1->Is(T3) implies T1->Is(Intersect(T2, T3))
-    // This does NOT hold.
-    /*
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
           TypeHandle type1 = *it1;
           TypeHandle type2 = *it2;
           TypeHandle type3 = *it3;
           TypeHandle intersect23 = T.Intersect(type2, type3);
           CHECK(!(type1->Is(type2) && type1->Is(type3)) ||
                 type1->Is(intersect23));
         }
       }
     }
-    */
 
     // Bitset-class
     CheckEqual(T.Intersect(T.ObjectClass, T.Object), T.ObjectClass);
     CheckEqual(T.Intersect(T.ObjectClass, T.Array), T.None);
     CheckEqual(T.Intersect(T.ObjectClass, T.Number), T.None);
 
     // Bitset-array
     CheckEqual(T.Intersect(T.NumberArray, T.Object), T.NumberArray);
     CheckEqual(T.Intersect(T.AnyArray, T.Function), T.None);
 
@@ skipping 83 matching lines @@
             T.Union(
                 T.ObjectConstant1,
                 T.Union(T.ArrayConstant, T.ObjectConstant2))),
         T.Union(
             T.ArrayConstant,
             T.Union(T.ObjectConstant2, T.ObjectConstant1)));  // !!!
   }
 
   void Distributivity() {
     // Union(T1, Intersect(T2, T3)) = Intersect(Union(T1, T2), Union(T1, T3))
-    // This does NOT hold.
+    // This does NOT hold.  For example:
+    // Untagged \/ (Untagged /\ Class(../Tagged)) = Untagged \/ Class(../Tagged)
+    // (Untagged \/ Untagged) /\ (Untagged \/ Class(../Tagged)) =
+    // Untagged /\ (Untagged \/ Class(../Tagged)) = Untagged
+    // because Untagged <= Untagged \/ Class(../Tagged)
     /*
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
           TypeHandle type1 = *it1;
           TypeHandle type2 = *it2;
           TypeHandle type3 = *it3;
           TypeHandle union12 = T.Union(type1, type2);
           TypeHandle union13 = T.Union(type1, type3);
           TypeHandle intersect23 = T.Intersect(type2, type3);
           TypeHandle union1_23 = T.Union(type1, intersect23);
           TypeHandle intersect12_13 = T.Intersect(union12, union13);
           CHECK(Equal(union1_23, intersect12_13));
         }
       }
     }
     */
 
     // Intersect(T1, Union(T2, T3)) = Union(Intersect(T1, T2), Intersect(T1,T3))
-    // This does NOT hold.
+    // This does NOT hold.  For example:
+    // Untagged /\ (Untagged \/ Class(../Tagged)) = Untagged
+    // (Untagged /\ Untagged) \/ (Untagged /\ Class(../Tagged)) =
+    // Untagged \/ Class(../Tagged)
     /*
     for (TypeIterator it1 = T.types.begin(); it1 != T.types.end(); ++it1) {
       for (TypeIterator it2 = T.types.begin(); it2 != T.types.end(); ++it2) {
         for (TypeIterator it3 = T.types.begin(); it3 != T.types.end(); ++it3) {
           TypeHandle type1 = *it1;
           TypeHandle type2 = *it2;
           TypeHandle type3 = *it3;
           TypeHandle intersect12 = T.Intersect(type1, type2);
           TypeHandle intersect13 = T.Intersect(type1, type3);
           TypeHandle union23 = T.Union(type2, type3);
@@ skipping 105 matching lines @@
 }
 
 
 TEST(BitsetLub) {
   CcTest::InitializeVM();
   ZoneTests().BitsetLub();
   HeapTests().BitsetLub();
 }
 
 
-TEST(Is) {
+TEST(Is1) {
   CcTest::InitializeVM();
-  ZoneTests().Is();
-  HeapTests().Is();
+  ZoneTests().Is1();
+  HeapTests().Is1();
 }
 
 
+TEST(Is2) {
+  CcTest::InitializeVM();
+  ZoneTests().Is2();
+  HeapTests().Is2();
+}
+
+
 TEST(NowIs) {
   CcTest::InitializeVM();
   ZoneTests().NowIs();
   HeapTests().NowIs();
 }
 
 
 TEST(Contains) {
   CcTest::InitializeVM();
   ZoneTests().Contains();
@@ skipping 45 matching lines @@
 }
 
 
 TEST(Intersect) {
   CcTest::InitializeVM();
   ZoneTests().Intersect();
   HeapTests().Intersect();
 }
 
 
-/*
 TEST(Distributivity) {
   CcTest::InitializeVM();
   ZoneTests().Distributivity();
   HeapTests().Distributivity();
 }
-*/
 
 
 TEST(Convert) {
   CcTest::InitializeVM();
   ZoneTests().Convert<HeapType, Handle<HeapType>, Isolate, HeapRep>();
   HeapTests().Convert<Type, Type*, Zone, ZoneRep>();
 }
 
 
 TEST(HTypeFromType) {
   CcTest::InitializeVM();
   ZoneTests().HTypeFromType();
   HeapTests().HTypeFromType();
 }