[ty] Fix negation upper bounds in constraint sets (#21897)

This fixes the logic error that @sharkdp
[found](https://github.com/astral-sh/ruff/pull/21871#discussion_r2605755588)
in the constraint set upper bound normalization logic I introduced in
#21871.

I had originally claimed that `(T ≤ α & ~β)` should simplify into `(T ≤
α) ∧ ¬(T ≤ β)`. But that also suggests that `T ≤ ~β` should simplify to
`¬(T ≤ β)` on its own, and that's not correct.

The correct simplification is that `~α` is an "atomic" type, not an
"intersection" for the purposes of our upper bound simplifcation. So `(T
≤ α & ~β)` should simplify to `(T ≤ α) ∧ (T ≤ ~β)`. That is, break apart
the elements of a (proper) intersection, regardless of whether each
element is negated or not.

This PR fixes the logic, adds a test case, and updates the comments to
be hopefully more clear and accurate.

crates/ty_python_semantic/resources/mdtest/type_properties/constraints.md

@@ -126,7 +126,7 @@ strict subtype of the lower bound, a strict supertype of the upper bound, or inc
 
 ```py
 from typing import Any, final, Never, Sequence
-from ty_extensions import ConstraintSet, static_assert
+from ty_extensions import ConstraintSet, Not, static_assert
 
 class Super: ...
 class Base(Super): ...
@@ -207,6 +207,15 @@ def _[T]() -> None:
     static_assert(constraints == expected)
 ```
 
+A negated _type_ is not the same thing as a negated _range_.
+
+```py
+def _[T]() -> None:
+    negated_type = ConstraintSet.range(Never, T, Not[int])
+    negated_constraint = ~ConstraintSet.range(Never, T, int)
+    static_assert(negated_type != negated_constraint)
+```
+
 ## Intersection
 
 The intersection of two constraint sets requires that the constraints in both sets hold. In many

crates/ty_python_semantic/src/types.rs

@@ -1268,8 +1268,14 @@ impl<'db> Type<'db> {
         self.as_union().expect("Expected a Type::Union variant")
     }
 
-    pub(crate) const fn is_intersection(self) -> bool {
-        matches!(self, Type::Intersection(_))
+    /// Returns whether this is a "real" intersection type. (Negated types are represented by an
+    /// intersection containing a single negative branch, which this method does _not_ consider a
+    /// "real" intersection.)
+    pub(crate) fn is_nontrivial_intersection(self, db: &'db dyn Db) -> bool {
+        match self {
+            Type::Intersection(intersection) => !intersection.is_simple_negation(db),
+            _ => false,
+        }
     }
 
     pub(crate) const fn as_function_literal(self) -> Option<FunctionType<'db>> {
@@ -14151,6 +14157,10 @@ impl<'db> IntersectionType<'db> {
         (self.positive(db).len() + self.negative(db).len()) == 1
     }
 
+    pub(crate) fn is_simple_negation(self, db: &'db dyn Db) -> bool {
+        self.positive(db).is_empty() && self.negative(db).len() == 1
+    }
+
     fn heap_size((positive, negative): &(FxOrderSet<Type<'db>>, FxOrderSet<Type<'db>>)) -> usize {
         ruff_memory_usage::order_set_heap_size(positive)
             + ruff_memory_usage::order_set_heap_size(negative)

crates/ty_python_semantic/src/types/constraints.rs

@@ -435,6 +435,11 @@ impl<'db> ConstraintSet<'db> {
     pub(crate) fn display(self, db: &'db dyn Db) -> impl Display {
         self.node.simplify_for_display(db).display(db)
     }
+
+    #[expect(dead_code)] // Keep this around for debugging purposes
+    pub(crate) fn display_graph(self, db: &'db dyn Db, prefix: &dyn Display) -> impl Display {
+        self.node.display_graph(db, prefix)
+    }
 }
 
 impl From<bool> for ConstraintSet<'_> {
@@ -498,11 +503,13 @@ impl<'db> ConstrainedTypeVar<'db> {
         debug_assert_eq!(upper, upper.top_materialization(db));
 
         // It's not useful for an upper bound to be an intersection type, or for a lower bound to
-        // be a union type. Both of those can be rewritten as simpler BDDs:
+        // be a union type. Because the following equivalences hold, we can break these bounds
+        // apart and create an equivalent BDD with more nodes but simpler constraints. (Fewer,
+        // simpler constraints mean that our sequent maps won't grow pathologically large.)
         //
-        //   T ≤ α & β  ⇒ (T ≤ α) ∧ (T ≤ β)
-        //   T ≤ α & ¬β ⇒ (T ≤ α) ∧ ¬(T ≤ β)
-        //   α | β ≤ T  ⇒ (α ≤ T) ∧ (β ≤ T)
+        //   T ≤ (α & β)   ⇔ (T ≤ α) ∧ (T ≤ β)
+        //   T ≤ (¬α & ¬β) ⇔ (T ≤ ¬α) ∧ (T ≤ ¬β)
+        //   (α | β) ≤ T   ⇔ (α ≤ T) ∧ (β ≤ T)
         if let Type::Union(lower_union) = lower {
             let mut result = Node::AlwaysTrue;
             for lower_element in lower_union.elements(db) {
@@ -513,7 +520,12 @@ impl<'db> ConstrainedTypeVar<'db> {
             }
             return result;
         }
-        if let Type::Intersection(upper_intersection) = upper {
+        // A negated type ¬α is represented as an intersection with no positive elements, and a
+        // single negative element. We _don't_ want to treat that an "intersection" for the
+        // purposes of simplifying upper bounds.
+        if let Type::Intersection(upper_intersection) = upper
+            && !upper_intersection.is_simple_negation(db)
+        {
             let mut result = Node::AlwaysTrue;
             for upper_element in upper_intersection.iter_positive(db) {
                 result = result.and(
@@ -524,7 +536,7 @@ impl<'db> ConstrainedTypeVar<'db> {
             for upper_element in upper_intersection.iter_negative(db) {
                 result = result.and(
                     db,
-                    ConstrainedTypeVar::new_node(db, typevar, lower, upper_element).negate(db),
+                    ConstrainedTypeVar::new_node(db, typevar, lower, upper_element.negate(db)),
                 );
             }
             return result;
@@ -716,7 +728,7 @@ impl<'db> ConstrainedTypeVar<'db> {
             return IntersectionResult::Disjoint;
         }
 
-        if lower.is_union() || upper.is_intersection() {
+        if lower.is_union() || upper.is_nontrivial_intersection(db) {
             return IntersectionResult::CannotSimplify;
         }
 
@@ -1579,7 +1591,6 @@ impl<'db> Node<'db> {
     ///     │       └─₀ never
     ///     └─₀ never
     /// ```
-    #[cfg_attr(not(test), expect(dead_code))] // Keep this around for debugging purposes
     fn display_graph(self, db: &'db dyn Db, prefix: &dyn Display) -> impl Display {
         struct DisplayNode<'a, 'db> {
             db: &'db dyn Db,

crates/ty_python_semantic/src/types/infer/builder.rs

@@ -10844,19 +10844,14 @@ impl<'db, 'ast> TypeInferenceBuilder<'db, 'ast> {
             (
                 Type::KnownInstance(KnownInstanceType::ConstraintSet(left)),
                 Type::KnownInstance(KnownInstanceType::ConstraintSet(right)),
-            ) => {
-                let result = match op {
-                    ast::CmpOp::Eq => Some(
-                        left.constraints(self.db()).iff(self.db(), right.constraints(self.db()))
-                    ),
-                    ast::CmpOp::NotEq => Some(
-                        left.constraints(self.db()).iff(self.db(), right.constraints(self.db())).negate(self.db())
-                    ),
-                    _ => None,
-                };
-                result.map(|constraints| Ok(Type::KnownInstance(KnownInstanceType::ConstraintSet(
-                    TrackedConstraintSet::new(self.db(), constraints)
-                ))))
+            ) => match op {
+                ast::CmpOp::Eq => Some(Ok(Type::BooleanLiteral(
+                    left.constraints(self.db()).iff(self.db(), right.constraints(self.db())).is_always_satisfied(self.db()),
+                ))),
+                ast::CmpOp::NotEq => Some(Ok(Type::BooleanLiteral(
+                    !left.constraints(self.db()).iff(self.db(), right.constraints(self.db())).is_always_satisfied(self.db()),
+                ))),
+                _ => None,
             }
 
             (