[red-knot] add IntersectionBuilder (#12791)

For type narrowing, we'll need intersections (since applying type
narrowing is just a type intersection.)

Add `IntersectionBuilder`, along with some tests for it and
`UnionBuilder` (renamed from `UnionTypeBuilder`).

We use smart builders to ensure that we always keep these types in
disjunctive normal form (DNF). That means that we never have deeply
nested trees of unions and intersections: unions flatten into unions,
intersections flatten into intersections, and intersections distribute
over unions, so the most complex tree we can ever have is a union of
intersections. We also never have a single-element union or a
single-positive-element intersection; these both just simplify to the
contained type.

Maintaining these invariants means that `UnionBuilder` doesn't
necessarily end up building a `Type::Union` (e.g. if you only add a
single type to the union, it'll just return that type instead), and
`IntersectionBuilder` doesn't necessarily build a `Type::Intersection`
(if you add a union to the intersection, we distribute the intersection
over that union, and `IntersectionBuilder` will end up returning a
`Type::Union` of intersections).

We also simplify intersections by ensuring that if a type and its
negation are both in an intersection, they simplify out. (In future this
should also respect subtyping, not just type identity, but we don't have
subtyping yet.) We do implement subtyping of `Never` as a special case
for now.

Most of this PR is unused for now until type narrowing lands; I'm just
breaking it out to reduce the review fatigue of a single massive PR.

crates/red_knot_python_semantic/src/types.rs

@@ -7,9 +7,11 @@ use crate::semantic_index::symbol::{ScopeId, ScopedSymbolId};
 use crate::semantic_index::{global_scope, symbol_table, use_def_map};
 use crate::{Db, FxOrderSet};
 
+mod builder;
 mod display;
 mod infer;
 
+pub(crate) use self::builder::UnionBuilder;
 pub(crate) use self::infer::{infer_definition_types, infer_scope_types};
 
 /// Infer the public type of a symbol (its type as seen from outside its scope).
@@ -91,14 +93,14 @@ pub(crate) fn definitions_ty<'db>(
     };
 
     if let Some(second) = all_types.next() {
-        let mut builder = UnionTypeBuilder::new(db);
+        let mut builder = UnionBuilder::new(db);
         builder = builder.add(first).add(second);
 
         for variant in all_types {
             builder = builder.add(variant);
         }
 
-        Type::Union(builder.build())
+        builder.build()
     } else {
         first
     }
@@ -117,7 +119,7 @@ pub enum Type<'db> {
     /// name does not exist or is not bound to any value (this represents an error, but with some
     /// leniency options it could be silently resolved to Unknown in some cases)
     Unbound,
-    /// the None object (TODO remove this in favor of Instance(types.NoneType)
+    /// the None object -- TODO remove this in favor of Instance(types.NoneType)
     None,
     /// a specific function object
     Function(FunctionType<'db>),
@@ -127,8 +129,11 @@ pub enum Type<'db> {
     Class(ClassType<'db>),
     /// the set of Python objects with the given class in their __class__'s method resolution order
     Instance(ClassType<'db>),
+    /// the set of objects in any of the types in the union
     Union(UnionType<'db>),
+    /// the set of objects in all of the types in the intersection
     Intersection(IntersectionType<'db>),
+    /// An integer literal
     IntLiteral(i64),
     /// A boolean literal, either `True` or `False`.
     BooleanLiteral(bool),
@@ -159,15 +164,13 @@ impl<'db> Type<'db> {
                 // TODO MRO? get_own_instance_member, get_instance_member
                 todo!("attribute lookup on Instance type")
             }
-            Type::Union(union) => Type::Union(
-                union
-                    .elements(db)
-                    .iter()
-                    .fold(UnionTypeBuilder::new(db), |builder, element_ty| {
-                        builder.add(element_ty.member(db, name))
-                    })
-                    .build(),
-            ),
+            Type::Union(union) => union
+                .elements(db)
+                .iter()
+                .fold(UnionBuilder::new(db), |builder, element_ty| {
+                    builder.add(element_ty.member(db, name))
+                })
+                .build(),
             Type::Intersection(_) => {
                 // TODO perform the get_member on each type in the intersection
                 // TODO return the intersection of those results
@@ -251,7 +254,7 @@ impl<'db> ClassType<'db> {
 
 #[salsa::interned]
 pub struct UnionType<'db> {
-    /// the union type includes values in any of these types
+    /// The union type includes values in any of these types.
     elements: FxOrderSet<Type<'db>>,
 }
 
@@ -261,48 +264,15 @@ impl<'db> UnionType<'db> {
     }
 }
 
-struct UnionTypeBuilder<'db> {
-    elements: FxOrderSet<Type<'db>>,
-    db: &'db dyn Db,
-}
-
-impl<'db> UnionTypeBuilder<'db> {
-    fn new(db: &'db dyn Db) -> Self {
-        Self {
-            db,
-            elements: FxOrderSet::default(),
-        }
-    }
-
-    /// Adds a type to this union.
-    fn add(mut self, ty: Type<'db>) -> Self {
-        match ty {
-            Type::Union(union) => {
-                self.elements.extend(&union.elements(self.db));
-            }
-            _ => {
-                self.elements.insert(ty);
-            }
-        }
-
-        self
-    }
-
-    fn build(self) -> UnionType<'db> {
-        UnionType::new(self.db, self.elements)
-    }
-}
-
-// Negation types aren't expressible in annotations, and are most likely to arise from type
-// narrowing along with intersections (e.g. `if not isinstance(...)`), so we represent them
-// directly in intersections rather than as a separate type. This sacrifices some efficiency in the
-// case where a Not appears outside an intersection (unclear when that could even happen, but we'd
-// have to represent it as a single-element intersection if it did) in exchange for better
-// efficiency in the within-intersection case.
 #[salsa::interned]
 pub struct IntersectionType<'db> {
-    // the intersection type includes only values in all of these types
+    /// The intersection type includes only values in all of these types.
     positive: FxOrderSet<Type<'db>>,
-    // the intersection type does not include any value in any of these types
+
+    /// The intersection type does not include any value in any of these types.
+    ///
+    /// Negation types aren't expressible in annotations, and are most likely to arise from type
+    /// narrowing along with intersections (e.g. `if not isinstance(...)`), so we represent them
+    /// directly in intersections rather than as a separate type.
     negative: FxOrderSet<Type<'db>>,
 }

crates/red_knot_python_semantic/src/types/builder.rs

@@ -0,0 +1,429 @@
+//! Smart builders for union and intersection types.
+//!
+//! Invariants we maintain here:
+//!   * No single-element union types (should just be the contained type instead.)
+//!   * No single-positive-element intersection types. Single-negative-element are OK, we don't
+//!     have a standalone negation type so there's no other representation for this.
+//!   * The same type should never appear more than once in a union or intersection. (This should
+//!     be expanded to cover subtyping -- see below -- but for now we only implement it for type
+//!     identity.)
+//!   * Disjunctive normal form (DNF): the tree of unions and intersections can never be deeper
+//!     than a union-of-intersections. Unions cannot contain other unions (the inner union just
+//!     flattens into the outer one), intersections cannot contain other intersections (also
+//!     flattens), and intersections cannot contain unions (the intersection distributes over the
+//!     union, inverting it into a union-of-intersections).
+//!
+//! The implication of these invariants is that a [`UnionBuilder`] does not necessarily build a
+//! [`Type::Union`]. For example, if only one type is added to the [`UnionBuilder`], `build()` will
+//! just return that type directly. The same is true for [`IntersectionBuilder`]; for example, if a
+//! union type is added to the intersection, it will distribute and [`IntersectionBuilder::build`]
+//! may end up returning a [`Type::Union`] of intersections.
+//!
+//! In the future we should have these additional invariants, but they aren't implemented yet:
+//!   * No type in a union can be a subtype of any other type in the union (just eliminate the
+//!     subtype from the union).
+//!   * No type in an intersection can be a supertype of any other type in the intersection (just
+//!     eliminate the supertype from the intersection).
+//!   * An intersection containing two non-overlapping types should simplify to [`Type::Never`].
+use crate::types::{IntersectionType, Type, UnionType};
+use crate::{Db, FxOrderSet};
+
+pub(crate) struct UnionBuilder<'db> {
+    elements: FxOrderSet<Type<'db>>,
+    db: &'db dyn Db,
+}
+
+impl<'db> UnionBuilder<'db> {
+    pub(crate) fn new(db: &'db dyn Db) -> Self {
+        Self {
+            db,
+            elements: FxOrderSet::default(),
+        }
+    }
+
+    /// Adds a type to this union.
+    pub(crate) fn add(mut self, ty: Type<'db>) -> Self {
+        match ty {
+            Type::Union(union) => {
+                self.elements.extend(&union.elements(self.db));
+            }
+            Type::Never => {}
+            _ => {
+                self.elements.insert(ty);
+            }
+        }
+
+        self
+    }
+
+    pub(crate) fn build(self) -> Type<'db> {
+        match self.elements.len() {
+            0 => Type::Never,
+            1 => self.elements[0],
+            _ => Type::Union(UnionType::new(self.db, self.elements)),
+        }
+    }
+}
+
+#[allow(unused)]
+#[derive(Clone)]
+pub(crate) struct IntersectionBuilder<'db> {
+    // Really this builds a union-of-intersections, because we always keep our set-theoretic types
+    // in disjunctive normal form (DNF), a union of intersections. In the simplest case there's
+    // just a single intersection in this vector, and we are building a single intersection type,
+    // but if a union is added to the intersection, we'll distribute ourselves over that union and
+    // create a union of intersections.
+    intersections: Vec<InnerIntersectionBuilder<'db>>,
+    db: &'db dyn Db,
+}
+
+impl<'db> IntersectionBuilder<'db> {
+    #[allow(dead_code)]
+    fn new(db: &'db dyn Db) -> Self {
+        Self {
+            db,
+            intersections: vec![InnerIntersectionBuilder::new()],
+        }
+    }
+
+    fn empty(db: &'db dyn Db) -> Self {
+        Self {
+            db,
+            intersections: vec![],
+        }
+    }
+
+    #[allow(dead_code)]
+    fn add_positive(mut self, ty: Type<'db>) -> Self {
+        if let Type::Union(union) = ty {
+            // Distribute ourself over this union: for each union element, clone ourself and
+            // intersect with that union element, then create a new union-of-intersections with all
+            // of those sub-intersections in it. E.g. if `self` is a simple intersection `T1 & T2`
+            // and we add `T3 | T4` to the intersection, we don't get `T1 & T2 & (T3 | T4)` (that's
+            // not in DNF), we distribute the union and get `(T1 & T3) | (T2 & T3) | (T1 & T4) |
+            // (T2 & T4)`. If `self` is already a union-of-intersections `(T1 & T2) | (T3 & T4)`
+            // and we add `T5 | T6` to it, that flattens all the way out to `(T1 & T2 & T5) | (T1 &
+            // T2 & T6) | (T3 & T4 & T5) ...` -- you get the idea.
+            union
+                .elements(self.db)
+                .iter()
+                .map(|elem| self.clone().add_positive(*elem))
+                .fold(IntersectionBuilder::empty(self.db), |mut builder, sub| {
+                    builder.intersections.extend(sub.intersections);
+                    builder
+                })
+        } else {
+            // If we are already a union-of-intersections, distribute the new intersected element
+            // across all of those intersections.
+            for inner in &mut self.intersections {
+                inner.add_positive(self.db, ty);
+            }
+            self
+        }
+    }
+
+    #[allow(dead_code)]
+    fn add_negative(mut self, ty: Type<'db>) -> Self {
+        // See comments above in `add_positive`; this is just the negated version.
+        if let Type::Union(union) = ty {
+            union
+                .elements(self.db)
+                .iter()
+                .map(|elem| self.clone().add_negative(*elem))
+                .fold(IntersectionBuilder::empty(self.db), |mut builder, sub| {
+                    builder.intersections.extend(sub.intersections);
+                    builder
+                })
+        } else {
+            for inner in &mut self.intersections {
+                inner.add_negative(self.db, ty);
+            }
+            self
+        }
+    }
+
+    #[allow(dead_code)]
+    fn build(mut self) -> Type<'db> {
+        // Avoid allocating the UnionBuilder unnecessarily if we have just one intersection:
+        if self.intersections.len() == 1 {
+            self.intersections.pop().unwrap().build(self.db)
+        } else {
+            let mut builder = UnionBuilder::new(self.db);
+            for inner in self.intersections {
+                builder = builder.add(inner.build(self.db));
+            }
+            builder.build()
+        }
+    }
+}
+
+#[allow(unused)]
+#[derive(Debug, Clone, Default)]
+struct InnerIntersectionBuilder<'db> {
+    positive: FxOrderSet<Type<'db>>,
+    negative: FxOrderSet<Type<'db>>,
+}
+
+impl<'db> InnerIntersectionBuilder<'db> {
+    fn new() -> Self {
+        Self::default()
+    }
+
+    /// Adds a positive type to this intersection.
+    fn add_positive(&mut self, db: &'db dyn Db, ty: Type<'db>) {
+        match ty {
+            Type::Intersection(inter) => {
+                let pos = inter.positive(db);
+                let neg = inter.negative(db);
+                self.positive.extend(pos.difference(&self.negative));
+                self.negative.extend(neg.difference(&self.positive));
+                self.positive.retain(|elem| !neg.contains(elem));
+                self.negative.retain(|elem| !pos.contains(elem));
+            }
+            _ => {
+                if !self.negative.remove(&ty) {
+                    self.positive.insert(ty);
+                };
+            }
+        }
+    }
+
+    /// Adds a negative type to this intersection.
+    fn add_negative(&mut self, db: &'db dyn Db, ty: Type<'db>) {
+        // TODO Any/Unknown actually should not self-cancel
+        match ty {
+            Type::Intersection(intersection) => {
+                let pos = intersection.negative(db);
+                let neg = intersection.positive(db);
+                self.positive.extend(pos.difference(&self.negative));
+                self.negative.extend(neg.difference(&self.positive));
+                self.positive.retain(|elem| !neg.contains(elem));
+                self.negative.retain(|elem| !pos.contains(elem));
+            }
+            Type::Never => {}
+            _ => {
+                if !self.positive.remove(&ty) {
+                    self.negative.insert(ty);
+                };
+            }
+        }
+    }
+
+    fn simplify(&mut self) {
+        // TODO this should be generalized based on subtyping, for now we just handle a few cases
+
+        // Never is a subtype of all types
+        if self.positive.contains(&Type::Never) {
+            self.positive.clear();
+            self.negative.clear();
+            self.positive.insert(Type::Never);
+        }
+    }
+
+    fn build(mut self, db: &'db dyn Db) -> Type<'db> {
+        self.simplify();
+        match (self.positive.len(), self.negative.len()) {
+            (0, 0) => Type::Never,
+            (1, 0) => self.positive[0],
+            _ => {
+                self.positive.shrink_to_fit();
+                self.negative.shrink_to_fit();
+                Type::Intersection(IntersectionType::new(db, self.positive, self.negative))
+            }
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::{IntersectionBuilder, IntersectionType, Type, UnionBuilder, UnionType};
+    use crate::db::tests::TestDb;
+
+    fn setup_db() -> TestDb {
+        TestDb::new()
+    }
+
+    impl<'db> UnionType<'db> {
+        fn elements_vec(self, db: &'db TestDb) -> Vec<Type<'db>> {
+            self.elements(db).into_iter().collect()
+        }
+    }
+
+    #[test]
+    fn build_union() {
+        let db = setup_db();
+        let t0 = Type::IntLiteral(0);
+        let t1 = Type::IntLiteral(1);
+        let Type::Union(union) = UnionBuilder::new(&db).add(t0).add(t1).build() else {
+            panic!("expected a union");
+        };
+
+        assert_eq!(union.elements_vec(&db), &[t0, t1]);
+    }
+
+    #[test]
+    fn build_union_single() {
+        let db = setup_db();
+        let t0 = Type::IntLiteral(0);
+        let ty = UnionBuilder::new(&db).add(t0).build();
+
+        assert_eq!(ty, t0);
+    }
+
+    #[test]
+    fn build_union_empty() {
+        let db = setup_db();
+        let ty = UnionBuilder::new(&db).build();
+
+        assert_eq!(ty, Type::Never);
+    }
+
+    #[test]
+    fn build_union_never() {
+        let db = setup_db();
+        let t0 = Type::IntLiteral(0);
+        let ty = UnionBuilder::new(&db).add(t0).add(Type::Never).build();
+
+        assert_eq!(ty, t0);
+    }
+
+    #[test]
+    fn build_union_flatten() {
+        let db = setup_db();
+        let t0 = Type::IntLiteral(0);
+        let t1 = Type::IntLiteral(1);
+        let t2 = Type::IntLiteral(2);
+        let u1 = UnionBuilder::new(&db).add(t0).add(t1).build();
+        let Type::Union(union) = UnionBuilder::new(&db).add(u1).add(t2).build() else {
+            panic!("expected a union");
+        };
+
+        assert_eq!(union.elements_vec(&db), &[t0, t1, t2]);
+    }
+
+    impl<'db> IntersectionType<'db> {
+        fn pos_vec(self, db: &'db TestDb) -> Vec<Type<'db>> {
+            self.positive(db).into_iter().collect()
+        }
+
+        fn neg_vec(self, db: &'db TestDb) -> Vec<Type<'db>> {
+            self.negative(db).into_iter().collect()
+        }
+    }
+
+    #[test]
+    fn build_intersection() {
+        let db = setup_db();
+        let t0 = Type::IntLiteral(0);
+        let ta = Type::Any;
+        let Type::Intersection(inter) = IntersectionBuilder::new(&db)
+            .add_positive(ta)
+            .add_negative(t0)
+            .build()
+        else {
+            panic!("expected to be an intersection");
+        };
+
+        assert_eq!(inter.pos_vec(&db), &[ta]);
+        assert_eq!(inter.neg_vec(&db), &[t0]);
+    }
+
+    #[test]
+    fn build_intersection_flatten_positive() {
+        let db = setup_db();
+        let ta = Type::Any;
+        let t1 = Type::IntLiteral(1);
+        let t2 = Type::IntLiteral(2);
+        let i0 = IntersectionBuilder::new(&db)
+            .add_positive(ta)
+            .add_negative(t1)
+            .build();
+        let Type::Intersection(inter) = IntersectionBuilder::new(&db)
+            .add_positive(t2)
+            .add_positive(i0)
+            .build()
+        else {
+            panic!("expected to be an intersection");
+        };
+
+        assert_eq!(inter.pos_vec(&db), &[t2, ta]);
+        assert_eq!(inter.neg_vec(&db), &[t1]);
+    }
+
+    #[test]
+    fn build_intersection_flatten_negative() {
+        let db = setup_db();
+        let ta = Type::Any;
+        let t1 = Type::IntLiteral(1);
+        let t2 = Type::IntLiteral(2);
+        let i0 = IntersectionBuilder::new(&db)
+            .add_positive(ta)
+            .add_negative(t1)
+            .build();
+        let Type::Intersection(inter) = IntersectionBuilder::new(&db)
+            .add_positive(t2)
+            .add_negative(i0)
+            .build()
+        else {
+            panic!("expected to be an intersection");
+        };
+
+        assert_eq!(inter.pos_vec(&db), &[t2, t1]);
+        assert_eq!(inter.neg_vec(&db), &[ta]);
+    }
+
+    #[test]
+    fn intersection_distributes_over_union() {
+        let db = setup_db();
+        let t0 = Type::IntLiteral(0);
+        let t1 = Type::IntLiteral(1);
+        let ta = Type::Any;
+        let u0 = UnionBuilder::new(&db).add(t0).add(t1).build();
+
+        let Type::Union(union) = IntersectionBuilder::new(&db)
+            .add_positive(ta)
+            .add_positive(u0)
+            .build()
+        else {
+            panic!("expected a union");
+        };
+        let [Type::Intersection(i0), Type::Intersection(i1)] = union.elements_vec(&db)[..] else {
+            panic!("expected a union of two intersections");
+        };
+        assert_eq!(i0.pos_vec(&db), &[ta, t0]);
+        assert_eq!(i1.pos_vec(&db), &[ta, t1]);
+    }
+
+    #[test]
+    fn build_intersection_self_negation() {
+        let db = setup_db();
+        let ty = IntersectionBuilder::new(&db)
+            .add_positive(Type::None)
+            .add_negative(Type::None)
+            .build();
+
+        assert_eq!(ty, Type::Never);
+    }
+
+    #[test]
+    fn build_intersection_simplify_negative_never() {
+        let db = setup_db();
+        let ty = IntersectionBuilder::new(&db)
+            .add_positive(Type::None)
+            .add_negative(Type::Never)
+            .build();
+
+        assert_eq!(ty, Type::None);
+    }
+
+    #[test]
+    fn build_intersection_simplify_positive_never() {
+        let db = setup_db();
+        let ty = IntersectionBuilder::new(&db)
+            .add_positive(Type::None)
+            .add_positive(Type::Never)
+            .build();
+
+        assert_eq!(ty, Type::Never);
+    }
+}

crates/red_knot_python_semantic/src/types/infer.rs

@@ -40,7 +40,7 @@ use crate::semantic_index::symbol::{FileScopeId, NodeWithScopeKind, NodeWithScop
 use crate::semantic_index::SemanticIndex;
 use crate::types::{
     builtins_symbol_ty_by_name, definitions_ty, global_symbol_ty_by_name, ClassType, FunctionType,
-    Name, Type, UnionTypeBuilder,
+    Name, Type, UnionBuilder,
 };
 use crate::Db;
 
@@ -1179,12 +1179,10 @@ impl<'db> TypeInferenceBuilder<'db> {
         let body_ty = self.infer_expression(body);
         let orelse_ty = self.infer_expression(orelse);
 
-        let union = UnionTypeBuilder::new(self.db)
+        UnionBuilder::new(self.db)
             .add(body_ty)
             .add(orelse_ty)
-            .build();
-
-        Type::Union(union)
+            .build()
     }
 
     fn infer_lambda_body(&mut self, lambda_expression: &ast::ExprLambda) {