diff --git a/.github/workflows/sync_typeshed.yaml b/.github/workflows/sync_typeshed.yaml
index d1785034e1ca4..20925a523e370 100644
--- a/.github/workflows/sync_typeshed.yaml
+++ b/.github/workflows/sync_typeshed.yaml
@@ -46,6 +46,10 @@ jobs:
           cp -r typeshed/stdlib ruff/crates/red_knot_vendored/vendor/typeshed/stdlib
           rm -rf ruff/crates/red_knot_vendored/vendor/typeshed/stdlib/@tests
           git -C typeshed rev-parse HEAD > ruff/crates/red_knot_vendored/vendor/typeshed/source_commit.txt
+          # Patch the typeshed stubs to include `knot_extensions`
+          ln -s ../../../knot_extensions/knot_extensions.pyi ruff/crates/red_knot_vendored/vendor/typeshed/stdlib/
+          echo "# Patch applied for red_knot:" >> ruff/crates/red_knot_vendored/vendor/typeshed/stdlib/VERSIONS
+          echo "knot_extensions: 3.0-" >> ruff/crates/red_knot_vendored/vendor/typeshed/stdlib/VERSIONS
       - name: Commit the changes
         id: commit
         if: ${{ steps.sync.outcome == 'success' }}
diff --git a/crates/red_knot_python_semantic/resources/mdtest/call/function.md b/crates/red_knot_python_semantic/resources/mdtest/call/function.md
index 435c9bbe21e33..b68aaf6675de9 100644
--- a/crates/red_knot_python_semantic/resources/mdtest/call/function.md
+++ b/crates/red_knot_python_semantic/resources/mdtest/call/function.md
@@ -257,3 +257,67 @@ def f(x: int) -> int:
 # error: 18 [parameter-already-assigned] "Multiple values provided for parameter `x` of function `f`"
 reveal_type(f(1, x=2))  # revealed: int
 ```
+
+## Special functions
+
+Some functions require special handling in type inference. Here, we make sure that we still emit
+proper diagnostics in case of missing or superfluous arguments.
+
+### `reveal_type`
+
+```py
+from typing_extensions import reveal_type
+
+# error: [missing-argument] "No argument provided for required parameter `obj` of function `reveal_type`"
+reveal_type()  # revealed: Unknown
+
+# error: [too-many-positional-arguments] "Too many positional arguments to function `reveal_type`: expected 1, got 2"
+reveal_type(1, 2)  # revealed: Literal[1]
+```
+
+### `static_assert`
+
+```py
+from knot_extensions import static_assert
+
+# error: [missing-argument] "No argument provided for required parameter `condition` of function `static_assert`"
+# error: [static-assert-error]
+static_assert()
+
+# error: [too-many-positional-arguments] "Too many positional arguments to function `static_assert`: expected 2, got 3"
+static_assert(True, 2, 3)
+```
+
+### `len`
+
+```py
+# error: [missing-argument] "No argument provided for required parameter `obj` of function `len`"
+len()
+
+# error: [too-many-positional-arguments] "Too many positional arguments to function `len`: expected 1, got 2"
+len([], 1)
+```
+
+### Type API predicates
+
+```py
+from knot_extensions import is_subtype_of, is_fully_static
+
+# error: [missing-argument]
+is_subtype_of()
+
+# error: [missing-argument]
+is_subtype_of(int)
+
+# error: [too-many-positional-arguments]
+is_subtype_of(int, int, int)
+
+# error: [too-many-positional-arguments]
+is_subtype_of(int, int, int, int)
+
+# error: [missing-argument]
+is_fully_static()
+
+# error: [too-many-positional-arguments]
+is_fully_static(int, int)
+```
diff --git a/crates/red_knot_python_semantic/resources/mdtest/type_api.md b/crates/red_knot_python_semantic/resources/mdtest/type_api.md
new file mode 100644
index 0000000000000..c4e7aa1a1685a
--- /dev/null
+++ b/crates/red_knot_python_semantic/resources/mdtest/type_api.md
@@ -0,0 +1,352 @@
+# Type API (`knot_extensions`)
+
+This document describes the internal `knot_extensions` API for creating and manipulating types as
+well as testing various type system properties.
+
+## Type extensions
+
+The Python language itself allows us to perform a variety of operations on types. For example, we
+can build a union of types like `int | None`, or we can use type constructors such as `list[int]`
+and `type[int]` to create new types. But some type-level operations that we rely on in Red Knot,
+like intersections, cannot yet be expressed in Python. The `knot_extensions` module provides the
+`Intersection` and `Not` type constructors (special forms) which allow us to construct these types
+directly.
+
+### Negation
+
+```py
+from knot_extensions import Not, static_assert
+
+def negate(n1: Not[int], n2: Not[Not[int]], n3: Not[Not[Not[int]]]) -> None:
+    reveal_type(n1)  # revealed: ~int
+    reveal_type(n2)  # revealed: int
+    reveal_type(n3)  # revealed: ~int
+
+def static_truthiness(not_one: Not[Literal[1]]) -> None:
+    static_assert(not_one != 1)
+    static_assert(not (not_one == 1))
+
+# error: "Special form `knot_extensions.Not` expected exactly one type parameter"
+n: Not[int, str]
+```
+
+### Intersection
+
+```py
+from knot_extensions import Intersection, Not, is_subtype_of, static_assert
+from typing_extensions import Never
+
+class S: ...
+class T: ...
+
+def x(x1: Intersection[S, T], x2: Intersection[S, Not[T]]) -> None:
+    reveal_type(x1)  # revealed: S & T
+    reveal_type(x2)  # revealed: S & ~T
+
+def y(y1: Intersection[int, object], y2: Intersection[int, bool], y3: Intersection[int, Never]) -> None:
+    reveal_type(y1)  # revealed: int
+    reveal_type(y2)  # revealed: bool
+    reveal_type(y3)  # revealed: Never
+
+def z(z1: Intersection[int, Not[Literal[1]], Not[Literal[2]]]) -> None:
+    reveal_type(z1)  # revealed: int & ~Literal[1] & ~Literal[2]
+
+class A: ...
+class B: ...
+class C: ...
+
+type ABC = Intersection[A, B, C]
+
+static_assert(is_subtype_of(ABC, A))
+static_assert(is_subtype_of(ABC, B))
+static_assert(is_subtype_of(ABC, C))
+
+class D: ...
+
+static_assert(not is_subtype_of(ABC, D))
+```
+
+### Unknown type
+
+The `Unknown` type is a special type that we use to represent actually unknown types (no
+annotation), as opposed to `Any` which represents an explicitly unknown type.
+
+```py
+from knot_extensions import Unknown, static_assert, is_assignable_to, is_fully_static
+
+static_assert(is_assignable_to(Unknown, int))
+static_assert(is_assignable_to(int, Unknown))
+
+static_assert(not is_fully_static(Unknown))
+
+def explicit_unknown(x: Unknown, y: tuple[str, Unknown], z: Unknown = 1) -> None:
+    reveal_type(x)  # revealed: Unknown
+    reveal_type(y)  # revealed: tuple[str, Unknown]
+    reveal_type(z)  # revealed: Unknown | Literal[1]
+
+# Unknown can be subclassed, just like Any
+class C(Unknown): ...
+
+# revealed: tuple[Literal[C], Unknown, Literal[object]]
+reveal_type(C.__mro__)
+
+# error: "Special form `knot_extensions.Unknown` expected no type parameter"
+u: Unknown[str]
+```
+
+## Static assertions
+
+### Basics
+
+The `knot_extensions` module provides a `static_assert` function that can be used to enforce
+properties at type-check time. The function takes an arbitrary expression and raises a type error if
+the expression is not of statically known truthiness.
+
+```py
+from knot_extensions import static_assert
+from typing import TYPE_CHECKING
+import sys
+
+static_assert(True)
+static_assert(False)  # error: "Static assertion error: argument evaluates to `False`"
+
+static_assert(False or True)
+static_assert(True and True)
+static_assert(False or False)  # error: "Static assertion error: argument evaluates to `False`"
+static_assert(False and True)  # error: "Static assertion error: argument evaluates to `False`"
+
+static_assert(1 + 1 == 2)
+static_assert(1 + 1 == 3)  # error: "Static assertion error: argument evaluates to `False`"
+
+static_assert("a" in "abc")
+static_assert("d" in "abc")  # error: "Static assertion error: argument evaluates to `False`"
+
+n = None
+static_assert(n is None)
+
+static_assert(TYPE_CHECKING)
+
+static_assert(sys.version_info >= (3, 6))
+```
+
+### Narrowing constraints
+
+Static assertions can be used to enforce narrowing constraints:
+
+```py
+from knot_extensions import static_assert
+
+def f(x: int) -> None:
+    if x != 0:
+        static_assert(x != 0)
+    else:
+        # `int` can be subclassed, so we cannot assert that `x == 0` here:
+        # error: "Static assertion error: argument of type `bool` has an ambiguous static truthiness"
+        static_assert(x == 0)
+```
+
+### Truthy expressions
+
+See also: <https://docs.python.org/3/library/stdtypes.html#truth-value-testing>
+
+```py
+from knot_extensions import static_assert
+
+static_assert(True)
+static_assert(False)  # error: "Static assertion error: argument evaluates to `False`"
+
+static_assert(None)  # error: "Static assertion error: argument of type `None` is statically known to be falsy"
+
+static_assert(1)
+static_assert(0)  # error: "Static assertion error: argument of type `Literal[0]` is statically known to be falsy"
+
+static_assert((0,))
+static_assert(())  # error: "Static assertion error: argument of type `tuple[()]` is statically known to be falsy"
+
+static_assert("a")
+static_assert("")  # error: "Static assertion error: argument of type `Literal[""]` is statically known to be falsy"
+
+static_assert(b"a")
+static_assert(b"")  # error: "Static assertion error: argument of type `Literal[b""]` is statically known to be falsy"
+```
+
+### Error messages
+
+We provide various tailored error messages for wrong argument types to `static_assert`:
+
+```py
+from knot_extensions import static_assert
+
+static_assert(2 * 3 == 6)
+
+# error: "Static assertion error: argument evaluates to `False`"
+static_assert(2 * 3 == 7)
+
+# error: "Static assertion error: argument of type `bool` has an ambiguous static truthiness"
+static_assert(int(2.0 * 3.0) == 6)
+
+class InvalidBoolDunder:
+    def __bool__(self) -> int:
+        return 1
+
+# error: "Static assertion error: argument of type `InvalidBoolDunder` has an ambiguous static truthiness"
+static_assert(InvalidBoolDunder())
+```
+
+### Custom error messages
+
+Alternatively, users can provide custom error messages:
+
+```py
+from knot_extensions import static_assert
+
+# error: "Static assertion error: I really want this to be true"
+static_assert(1 + 1 == 3, "I really want this to be true")
+
+error_message = "A custom message "
+error_message += "constructed from multiple string literals"
+# error: "Static assertion error: A custom message constructed from multiple string literals"
+static_assert(False, error_message)
+
+# There are limitations to what we can still infer as a string literal. In those cases,
+# we simply fall back to the default message.
+shouted_message = "A custom message".upper()
+# error: "Static assertion error: argument evaluates to `False`"
+static_assert(False, shouted_message)
+```
+
+## Type predicates
+
+The `knot_extensions` module also provides predicates to test various properties of types. These are
+implemented as functions that return `Literal[True]` or `Literal[False]` depending on the result of
+the test.
+
+### Equivalence
+
+```py
+from knot_extensions import is_equivalent_to, static_assert
+from typing_extensions import Never, Union
+
+static_assert(is_equivalent_to(type, type[object]))
+static_assert(is_equivalent_to(tuple[int, Never], Never))
+static_assert(is_equivalent_to(int | str, Union[int, str]))
+
+static_assert(not is_equivalent_to(int, str))
+static_assert(not is_equivalent_to(int | str, int | str | bytes))
+```
+
+### Subtyping
+
+```py
+from knot_extensions import is_subtype_of, static_assert
+
+static_assert(is_subtype_of(bool, int))
+static_assert(not is_subtype_of(str, int))
+
+static_assert(is_subtype_of(bool, int | str))
+static_assert(is_subtype_of(str, int | str))
+static_assert(not is_subtype_of(bytes, int | str))
+
+class Base: ...
+class Derived(Base): ...
+class Unrelated: ...
+
+static_assert(is_subtype_of(Derived, Base))
+static_assert(not is_subtype_of(Base, Derived))
+static_assert(is_subtype_of(Base, Base))
+
+static_assert(not is_subtype_of(Unrelated, Base))
+static_assert(not is_subtype_of(Base, Unrelated))
+```
+
+### Assignability
+
+```py
+from knot_extensions import is_assignable_to, static_assert
+from typing import Any
+
+static_assert(is_assignable_to(int, Any))
+static_assert(is_assignable_to(Any, str))
+static_assert(not is_assignable_to(int, str))
+```
+
+### Disjointness
+
+```py
+from knot_extensions import is_disjoint_from, static_assert
+
+static_assert(is_disjoint_from(None, int))
+static_assert(not is_disjoint_from(Literal[2] | str, int))
+```
+
+### Fully static types
+
+```py
+from knot_extensions import is_fully_static, static_assert
+from typing import Any
+
+static_assert(is_fully_static(int | str))
+static_assert(is_fully_static(type[int]))
+
+static_assert(not is_fully_static(int | Any))
+static_assert(not is_fully_static(type[Any]))
+```
+
+### Singleton types
+
+```py
+from knot_extensions import is_singleton, static_assert
+
+static_assert(is_singleton(None))
+static_assert(is_singleton(Literal[True]))
+
+static_assert(not is_singleton(int))
+static_assert(not is_singleton(Literal["a"]))
+```
+
+### Single-valued types
+
+```py
+from knot_extensions import is_single_valued, static_assert
+
+static_assert(is_single_valued(None))
+static_assert(is_single_valued(Literal[True]))
+static_assert(is_single_valued(Literal["a"]))
+
+static_assert(not is_single_valued(int))
+static_assert(not is_single_valued(Literal["a"] | Literal["b"]))
+```
+
+## `TypeOf`
+
+We use `TypeOf` to get the inferred type of an expression. This is useful when we want to refer to
+it in a type expression. For example, if we want to make sure that the class literal type `str` is a
+subtype of `type[str]`, we can not use `is_subtype_of(str, type[str])`, as that would test if the
+type `str` itself is a subtype of `type[str]`. Instead, we can use `TypeOf[str]` to get the type of
+the expression `str`:
+
+```py
+from knot_extensions import TypeOf, is_subtype_of, static_assert
+
+# This is incorrect and therefore fails with ...
+# error: "Static assertion error: argument evaluates to `False`"
+static_assert(is_subtype_of(str, type[str]))
+
+# Correct, returns True:
+static_assert(is_subtype_of(TypeOf[str], type[str]))
+
+class Base: ...
+class Derived(Base): ...
+
+# `TypeOf` can be used in annotations:
+def type_of_annotation() -> None:
+    t1: TypeOf[Base] = Base
+    t2: TypeOf[Base] = Derived  # error: [invalid-assignment]
+
+    # Note how this is different from `type[…]` which includes subclasses:
+    s1: type[Base] = Base
+    s2: type[Base] = Derived  # no error here
+
+# error: "Special form `knot_extensions.TypeOf` expected exactly one type parameter"
+t: TypeOf[int, str, bytes]
+```
diff --git a/crates/red_knot_python_semantic/src/module_resolver/module.rs b/crates/red_knot_python_semantic/src/module_resolver/module.rs
index 140153674db92..7040ce8edc3cf 100644
--- a/crates/red_knot_python_semantic/src/module_resolver/module.rs
+++ b/crates/red_knot_python_semantic/src/module_resolver/module.rs
@@ -109,6 +109,7 @@ pub enum KnownModule {
     #[allow(dead_code)]
     Abc, // currently only used in tests
     Collections,
+    KnotExtensions,
 }
 
 impl KnownModule {
@@ -122,6 +123,7 @@ impl KnownModule {
             Self::Sys => "sys",
             Self::Abc => "abc",
             Self::Collections => "collections",
+            Self::KnotExtensions => "knot_extensions",
         }
     }
 
@@ -147,6 +149,7 @@ impl KnownModule {
             "sys" => Some(Self::Sys),
             "abc" => Some(Self::Abc),
             "collections" => Some(Self::Collections),
+            "knot_extensions" => Some(Self::KnotExtensions),
             _ => None,
         }
     }
@@ -154,4 +157,8 @@ impl KnownModule {
     pub const fn is_typing(self) -> bool {
         matches!(self, Self::Typing)
     }
+
+    pub const fn is_knot_extensions(self) -> bool {
+        matches!(self, Self::KnotExtensions)
+    }
 }
diff --git a/crates/red_knot_python_semantic/src/semantic_index/definition.rs b/crates/red_knot_python_semantic/src/semantic_index/definition.rs
index fc75d252dafef..d8d60d04873bd 100644
--- a/crates/red_knot_python_semantic/src/semantic_index/definition.rs
+++ b/crates/red_knot_python_semantic/src/semantic_index/definition.rs
@@ -74,6 +74,11 @@ impl<'db> Definition<'db> {
             Some(KnownModule::Typing | KnownModule::TypingExtensions)
         )
     }
+
+    pub(crate) fn is_knot_extensions_definition(self, db: &'db dyn Db) -> bool {
+        file_to_module(db, self.file(db))
+            .is_some_and(|module| module.is_known(KnownModule::KnotExtensions))
+    }
 }
 
 #[derive(Copy, Clone, Debug)]
diff --git a/crates/red_knot_python_semantic/src/types.rs b/crates/red_knot_python_semantic/src/types.rs
index 4597563b278e6..84b1e2ef025cb 100644
--- a/crates/red_knot_python_semantic/src/types.rs
+++ b/crates/red_knot_python_semantic/src/types.rs
@@ -31,7 +31,9 @@ use crate::semantic_index::{
 use crate::stdlib::{builtins_symbol, known_module_symbol, typing_extensions_symbol};
 use crate::suppression::check_suppressions;
 use crate::symbol::{Boundness, Symbol};
-use crate::types::call::{bind_call, CallArguments, CallBinding, CallDunderResult, CallOutcome};
+use crate::types::call::{
+    bind_call, CallArguments, CallBinding, CallDunderResult, CallOutcome, StaticAssertionErrorKind,
+};
 use crate::types::class_base::ClassBase;
 use crate::types::diagnostic::INVALID_TYPE_FORM;
 use crate::types::mro::{Mro, MroError, MroIterator};
@@ -657,6 +659,13 @@ impl<'db> Type<'db> {
         }
     }
 
+    pub fn into_string_literal(self) -> Option<StringLiteralType<'db>> {
+        match self {
+            Type::StringLiteral(string_literal) => Some(string_literal),
+            _ => None,
+        }
+    }
+
     #[track_caller]
     pub fn expect_int_literal(self) -> i64 {
         self.into_int_literal()
@@ -1824,12 +1833,88 @@ impl<'db> Type<'db> {
                 let mut binding = bind_call(db, arguments, function_type.signature(db), Some(self));
                 match function_type.known(db) {
                     Some(KnownFunction::RevealType) => {
-                        let revealed_ty = binding.first_parameter().unwrap_or(Type::Unknown);
+                        let revealed_ty = binding.one_parameter_ty().unwrap_or(Type::Unknown);
                         CallOutcome::revealed(binding, revealed_ty)
                     }
+                    Some(KnownFunction::StaticAssert) => {
+                        if let Some((parameter_ty, message)) = binding.two_parameter_tys() {
+                            let truthiness = parameter_ty.bool(db);
+
+                            if truthiness.is_always_true() {
+                                CallOutcome::callable(binding)
+                            } else {
+                                let error_kind = if let Some(message) =
+                                    message.into_string_literal().map(|s| &**s.value(db))
+                                {
+                                    StaticAssertionErrorKind::CustomError(message)
+                                } else if parameter_ty == Type::BooleanLiteral(false) {
+                                    StaticAssertionErrorKind::ArgumentIsFalse
+                                } else if truthiness.is_always_false() {
+                                    StaticAssertionErrorKind::ArgumentIsFalsy(parameter_ty)
+                                } else {
+                                    StaticAssertionErrorKind::ArgumentTruthinessIsAmbiguous(
+                                        parameter_ty,
+                                    )
+                                };
+
+                                CallOutcome::StaticAssertionError {
+                                    binding,
+                                    error_kind,
+                                }
+                            }
+                        } else {
+                            CallOutcome::callable(binding)
+                        }
+                    }
+                    Some(KnownFunction::IsEquivalentTo) => {
+                        let (ty_a, ty_b) = binding
+                            .two_parameter_tys()
+                            .unwrap_or((Type::Unknown, Type::Unknown));
+                        binding
+                            .set_return_ty(Type::BooleanLiteral(ty_a.is_equivalent_to(db, ty_b)));
+                        CallOutcome::callable(binding)
+                    }
+                    Some(KnownFunction::IsSubtypeOf) => {
+                        let (ty_a, ty_b) = binding
+                            .two_parameter_tys()
+                            .unwrap_or((Type::Unknown, Type::Unknown));
+                        binding.set_return_ty(Type::BooleanLiteral(ty_a.is_subtype_of(db, ty_b)));
+                        CallOutcome::callable(binding)
+                    }
+                    Some(KnownFunction::IsAssignableTo) => {
+                        let (ty_a, ty_b) = binding
+                            .two_parameter_tys()
+                            .unwrap_or((Type::Unknown, Type::Unknown));
+                        binding
+                            .set_return_ty(Type::BooleanLiteral(ty_a.is_assignable_to(db, ty_b)));
+                        CallOutcome::callable(binding)
+                    }
+                    Some(KnownFunction::IsDisjointFrom) => {
+                        let (ty_a, ty_b) = binding
+                            .two_parameter_tys()
+                            .unwrap_or((Type::Unknown, Type::Unknown));
+                        binding
+                            .set_return_ty(Type::BooleanLiteral(ty_a.is_disjoint_from(db, ty_b)));
+                        CallOutcome::callable(binding)
+                    }
+                    Some(KnownFunction::IsFullyStatic) => {
+                        let ty = binding.one_parameter_ty().unwrap_or(Type::Unknown);
+                        binding.set_return_ty(Type::BooleanLiteral(ty.is_fully_static(db)));
+                        CallOutcome::callable(binding)
+                    }
+                    Some(KnownFunction::IsSingleton) => {
+                        let ty = binding.one_parameter_ty().unwrap_or(Type::Unknown);
+                        binding.set_return_ty(Type::BooleanLiteral(ty.is_singleton(db)));
+                        CallOutcome::callable(binding)
+                    }
+                    Some(KnownFunction::IsSingleValued) => {
+                        let ty = binding.one_parameter_ty().unwrap_or(Type::Unknown);
+                        binding.set_return_ty(Type::BooleanLiteral(ty.is_single_valued(db)));
+                        CallOutcome::callable(binding)
+                    }
 
                     Some(KnownFunction::Len) => {
-                        if let Some(first_arg) = binding.first_parameter() {
+                        if let Some(first_arg) = binding.one_parameter_ty() {
                             if let Some(len_ty) = first_arg.len(db) {
                                 binding.set_return_ty(len_ty);
                             }
@@ -2107,6 +2192,7 @@ impl<'db> Type<'db> {
                 invalid_expressions: smallvec::smallvec![InvalidTypeExpression::BareLiteral],
                 fallback_type: Type::Unknown,
             }),
+            Type::KnownInstance(KnownInstanceType::Unknown) => Ok(Type::Unknown),
             Type::Todo(_) => Ok(*self),
             _ => Ok(todo_type!(
                 "Unsupported or invalid type in a type expression"
@@ -2613,6 +2699,14 @@ pub enum KnownInstanceType<'db> {
     TypeVar(TypeVarInstance<'db>),
     /// A single instance of `typing.TypeAliasType` (PEP 695 type alias)
     TypeAliasType(TypeAliasType<'db>),
+    /// The symbol `knot_extensions.Unknown`
+    Unknown,
+    /// The symbol `knot_extensions.Not`
+    Not,
+    /// The symbol `knot_extensions.Intersection`
+    Intersection,
+    /// The symbol `knot_extensions.TypeOf`
+    TypeOf,
 
     // Various special forms, special aliases and type qualifiers that we don't yet understand
     // (all currently inferred as TODO in most contexts):
@@ -2667,6 +2761,10 @@ impl<'db> KnownInstanceType<'db> {
             Self::ChainMap => "ChainMap",
             Self::OrderedDict => "OrderedDict",
             Self::ReadOnly => "ReadOnly",
+            Self::Unknown => "Unknown",
+            Self::Not => "Not",
+            Self::Intersection => "Intersection",
+            Self::TypeOf => "TypeOf",
         }
     }
 
@@ -2705,7 +2803,11 @@ impl<'db> KnownInstanceType<'db> {
             | Self::ChainMap
             | Self::OrderedDict
             | Self::ReadOnly
-            | Self::TypeAliasType(_) => Truthiness::AlwaysTrue,
+            | Self::TypeAliasType(_)
+            | Self::Unknown
+            | Self::Not
+            | Self::Intersection
+            | Self::TypeOf => Truthiness::AlwaysTrue,
         }
     }
 
@@ -2745,6 +2847,10 @@ impl<'db> KnownInstanceType<'db> {
             Self::ReadOnly => "typing.ReadOnly",
             Self::TypeVar(typevar) => typevar.name(db),
             Self::TypeAliasType(_) => "typing.TypeAliasType",
+            Self::Unknown => "knot_extensions.Unknown",
+            Self::Not => "knot_extensions.Not",
+            Self::Intersection => "knot_extensions.Intersection",
+            Self::TypeOf => "knot_extensions.TypeOf",
         }
     }
 
@@ -2784,6 +2890,10 @@ impl<'db> KnownInstanceType<'db> {
             Self::OrderedDict => KnownClass::StdlibAlias,
             Self::TypeVar(_) => KnownClass::TypeVar,
             Self::TypeAliasType(_) => KnownClass::TypeAliasType,
+            Self::TypeOf => KnownClass::SpecialForm,
+            Self::Not => KnownClass::SpecialForm,
+            Self::Intersection => KnownClass::SpecialForm,
+            Self::Unknown => KnownClass::Object,
         }
     }
 
@@ -2834,6 +2944,10 @@ impl<'db> KnownInstanceType<'db> {
             "Concatenate" => Self::Concatenate,
             "NotRequired" => Self::NotRequired,
             "LiteralString" => Self::LiteralString,
+            "Unknown" => Self::Unknown,
+            "Not" => Self::Not,
+            "Intersection" => Self::Intersection,
+            "TypeOf" => Self::TypeOf,
             _ => return None,
         };
 
@@ -2883,6 +2997,9 @@ impl<'db> KnownInstanceType<'db> {
             | Self::TypeVar(_) => {
                 matches!(module, KnownModule::Typing | KnownModule::TypingExtensions)
             }
+            Self::Unknown | Self::Not | Self::Intersection | Self::TypeOf => {
+                module.is_knot_extensions()
+            }
         }
     }
 
@@ -3121,13 +3238,41 @@ pub enum KnownFunction {
 
     /// [`typing(_extensions).no_type_check`](https://typing.readthedocs.io/en/latest/spec/directives.html#no-type-check)
     NoTypeCheck,
+
+    /// `knot_extensions.static_assert`
+    StaticAssert,
+    /// `knot_extensions.is_equivalent_to`
+    IsEquivalentTo,
+    /// `knot_extensions.is_subtype_of`
+    IsSubtypeOf,
+    /// `knot_extensions.is_assignable_to`
+    IsAssignableTo,
+    /// `knot_extensions.is_disjoint_from`
+    IsDisjointFrom,
+    /// `knot_extensions.is_fully_static`
+    IsFullyStatic,
+    /// `knot_extensions.is_singleton`
+    IsSingleton,
+    /// `knot_extensions.is_single_valued`
+    IsSingleValued,
 }
 
 impl KnownFunction {
     pub fn constraint_function(self) -> Option<KnownConstraintFunction> {
         match self {
             Self::ConstraintFunction(f) => Some(f),
-            Self::RevealType | Self::Len | Self::Final | Self::NoTypeCheck => None,
+            Self::RevealType
+            | Self::Len
+            | Self::Final
+            | Self::NoTypeCheck
+            | Self::StaticAssert
+            | Self::IsEquivalentTo
+            | Self::IsSubtypeOf
+            | Self::IsAssignableTo
+            | Self::IsDisjointFrom
+            | Self::IsFullyStatic
+            | Self::IsSingleton
+            | Self::IsSingleValued => None,
         }
     }
 
@@ -3149,9 +3294,50 @@ impl KnownFunction {
             "no_type_check" if definition.is_typing_definition(db) => {
                 Some(KnownFunction::NoTypeCheck)
             }
+            "static_assert" if definition.is_knot_extensions_definition(db) => {
+                Some(KnownFunction::StaticAssert)
+            }
+            "is_subtype_of" if definition.is_knot_extensions_definition(db) => {
+                Some(KnownFunction::IsSubtypeOf)
+            }
+            "is_disjoint_from" if definition.is_knot_extensions_definition(db) => {
+                Some(KnownFunction::IsDisjointFrom)
+            }
+            "is_equivalent_to" if definition.is_knot_extensions_definition(db) => {
+                Some(KnownFunction::IsEquivalentTo)
+            }
+            "is_assignable_to" if definition.is_knot_extensions_definition(db) => {
+                Some(KnownFunction::IsAssignableTo)
+            }
+            "is_fully_static" if definition.is_knot_extensions_definition(db) => {
+                Some(KnownFunction::IsFullyStatic)
+            }
+            "is_singleton" if definition.is_knot_extensions_definition(db) => {
+                Some(KnownFunction::IsSingleton)
+            }
+            "is_single_valued" if definition.is_knot_extensions_definition(db) => {
+                Some(KnownFunction::IsSingleValued)
+            }
+
             _ => None,
         }
     }
+
+    /// Whether or not a particular function takes type expression as arguments, i.e. should
+    /// the argument of a call like `f(int)` be interpreted as the type int (true) or as the
+    /// type of the expression `int`, i.e. `Literal[int]` (false).
+    const fn takes_type_expression_arguments(self) -> bool {
+        matches!(
+            self,
+            KnownFunction::IsEquivalentTo
+                | KnownFunction::IsSubtypeOf
+                | KnownFunction::IsAssignableTo
+                | KnownFunction::IsDisjointFrom
+                | KnownFunction::IsFullyStatic
+                | KnownFunction::IsSingleton
+                | KnownFunction::IsSingleValued
+        )
+    }
 }
 
 #[salsa::interned]
diff --git a/crates/red_knot_python_semantic/src/types/call.rs b/crates/red_knot_python_semantic/src/types/call.rs
index d803b6103d016..951fdb7858442 100644
--- a/crates/red_knot_python_semantic/src/types/call.rs
+++ b/crates/red_knot_python_semantic/src/types/call.rs
@@ -1,6 +1,7 @@
 use super::context::InferContext;
 use super::diagnostic::CALL_NON_CALLABLE;
 use super::{Severity, Signature, Type, TypeArrayDisplay, UnionBuilder};
+use crate::types::diagnostic::STATIC_ASSERT_ERROR;
 use crate::Db;
 use ruff_db::diagnostic::DiagnosticId;
 use ruff_python_ast as ast;
@@ -11,6 +12,14 @@ mod bind;
 pub(super) use arguments::{Argument, CallArguments};
 pub(super) use bind::{bind_call, CallBinding};
 
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub(super) enum StaticAssertionErrorKind<'db> {
+    ArgumentIsFalse,
+    ArgumentIsFalsy(Type<'db>),
+    ArgumentTruthinessIsAmbiguous(Type<'db>),
+    CustomError(&'db str),
+}
+
 #[derive(Debug, Clone, PartialEq, Eq)]
 pub(super) enum CallOutcome<'db> {
     Callable {
@@ -31,6 +40,10 @@ pub(super) enum CallOutcome<'db> {
         called_ty: Type<'db>,
         call_outcome: Box<CallOutcome<'db>>,
     },
+    StaticAssertionError {
+        binding: CallBinding<'db>,
+        error_kind: StaticAssertionErrorKind<'db>,
+    },
 }
 
 impl<'db> CallOutcome<'db> {
@@ -89,6 +102,7 @@ impl<'db> CallOutcome<'db> {
                 })
                 .map(UnionBuilder::build),
             Self::PossiblyUnboundDunderCall { call_outcome, .. } => call_outcome.return_ty(db),
+            Self::StaticAssertionError { .. } => Some(Type::none(db)),
         }
     }
 
@@ -181,6 +195,7 @@ impl<'db> CallOutcome<'db> {
                 binding,
                 revealed_ty,
             } => {
+                binding.report_diagnostics(context, node);
                 context.report_diagnostic(
                     node,
                     DiagnosticId::RevealedType,
@@ -249,6 +264,51 @@ impl<'db> CallOutcome<'db> {
                     }),
                 }
             }
+            CallOutcome::StaticAssertionError {
+                binding,
+                error_kind,
+            } => {
+                binding.report_diagnostics(context, node);
+
+                match error_kind {
+                    StaticAssertionErrorKind::ArgumentIsFalse => {
+                        context.report_lint(
+                            &STATIC_ASSERT_ERROR,
+                            node,
+                            format_args!("Static assertion error: argument evaluates to `False`"),
+                        );
+                    }
+                    StaticAssertionErrorKind::ArgumentIsFalsy(parameter_ty) => {
+                        context.report_lint(
+                            &STATIC_ASSERT_ERROR,
+                            node,
+                            format_args!(
+                                "Static assertion error: argument of type `{parameter_ty}` is statically known to be falsy",
+                                parameter_ty=parameter_ty.display(context.db())
+                            ),
+                        );
+                    }
+                    StaticAssertionErrorKind::ArgumentTruthinessIsAmbiguous(parameter_ty) => {
+                        context.report_lint(
+                            &STATIC_ASSERT_ERROR,
+                            node,
+                            format_args!(
+                                "Static assertion error: argument of type `{parameter_ty}` has an ambiguous static truthiness",
+                                parameter_ty=parameter_ty.display(context.db())
+                            ),
+                        );
+                    }
+                    StaticAssertionErrorKind::CustomError(message) => {
+                        context.report_lint(
+                            &STATIC_ASSERT_ERROR,
+                            node,
+                            format_args!("Static assertion error: {message}"),
+                        );
+                    }
+                }
+
+                Ok(Type::Unknown)
+            }
         }
     }
 }
diff --git a/crates/red_knot_python_semantic/src/types/call/bind.rs b/crates/red_knot_python_semantic/src/types/call/bind.rs
index 0fcb40140efcc..7e699d1f5d094 100644
--- a/crates/red_knot_python_semantic/src/types/call/bind.rs
+++ b/crates/red_knot_python_semantic/src/types/call/bind.rs
@@ -154,8 +154,18 @@ impl<'db> CallBinding<'db> {
         &self.parameter_tys
     }
 
-    pub(crate) fn first_parameter(&self) -> Option<Type<'db>> {
-        self.parameter_tys().first().copied()
+    pub(crate) fn one_parameter_ty(&self) -> Option<Type<'db>> {
+        match self.parameter_tys() {
+            [ty] => Some(*ty),
+            _ => None,
+        }
+    }
+
+    pub(crate) fn two_parameter_tys(&self) -> Option<(Type<'db>, Type<'db>)> {
+        match self.parameter_tys() {
+            [first, second] => Some((*first, *second)),
+            _ => None,
+        }
     }
 
     fn callable_name(&self, db: &'db dyn Db) -> Option<&ast::name::Name> {
diff --git a/crates/red_knot_python_semantic/src/types/class_base.rs b/crates/red_knot_python_semantic/src/types/class_base.rs
index f08e4de444ad1..7a441d3f9e263 100644
--- a/crates/red_knot_python_semantic/src/types/class_base.rs
+++ b/crates/red_knot_python_semantic/src/types/class_base.rs
@@ -100,7 +100,11 @@ impl<'db> ClassBase<'db> {
                 | KnownInstanceType::Required
                 | KnownInstanceType::TypeAlias
                 | KnownInstanceType::ReadOnly
-                | KnownInstanceType::Optional => None,
+                | KnownInstanceType::Optional
+                | KnownInstanceType::Not
+                | KnownInstanceType::Intersection
+                | KnownInstanceType::TypeOf => None,
+                KnownInstanceType::Unknown => Some(Self::Unknown),
                 KnownInstanceType::Any => Some(Self::Any),
                 // TODO: Classes inheriting from `typing.Type` et al. also have `Generic` in their MRO
                 KnownInstanceType::Dict => {
diff --git a/crates/red_knot_python_semantic/src/types/diagnostic.rs b/crates/red_knot_python_semantic/src/types/diagnostic.rs
index c2468e7847055..7fe097ce4eadd 100644
--- a/crates/red_knot_python_semantic/src/types/diagnostic.rs
+++ b/crates/red_knot_python_semantic/src/types/diagnostic.rs
@@ -56,6 +56,7 @@ pub(crate) fn register_lints(registry: &mut LintRegistryBuilder) {
     registry.register_lint(&UNRESOLVED_REFERENCE);
     registry.register_lint(&UNSUPPORTED_OPERATOR);
     registry.register_lint(&ZERO_STEPSIZE_IN_SLICE);
+    registry.register_lint(&STATIC_ASSERT_ERROR);
 
     // String annotations
     registry.register_lint(&BYTE_STRING_TYPE_ANNOTATION);
@@ -678,6 +679,25 @@ declare_lint! {
     }
 }
 
+declare_lint! {
+    /// ## What it does
+    /// Makes sure that the argument of `static_assert` is statically known to be true.
+    ///
+    /// ## Examples
+    /// ```python
+    /// from knot_extensions import static_assert
+    ///
+    /// static_assert(1 + 1 == 3)  # error: evaluates to `False`
+    ///
+    /// static_assert(int(2.0 * 3.0) == 6)  # error: does not have a statically known truthiness
+    /// ```
+    pub(crate) static STATIC_ASSERT_ERROR = {
+        summary: "Failed static assertion",
+        status: LintStatus::preview("1.0.0"),
+        default_level: Level::Error,
+    }
+}
+
 #[derive(Debug, Eq, PartialEq, Clone)]
 pub struct TypeCheckDiagnostic {
     pub(crate) id: DiagnosticId,
diff --git a/crates/red_knot_python_semantic/src/types/infer.rs b/crates/red_knot_python_semantic/src/types/infer.rs
index 3eb4f72c1de9b..e17041e84f3e9 100644
--- a/crates/red_knot_python_semantic/src/types/infer.rs
+++ b/crates/red_knot_python_semantic/src/types/infer.rs
@@ -28,7 +28,7 @@
 //! definitions once the rest of the types in the scope have been inferred.
 use std::num::NonZeroU32;
 
-use itertools::Itertools;
+use itertools::{Either, Itertools};
 use ruff_db::files::File;
 use ruff_db::parsed::parsed_module;
 use ruff_python_ast::{self as ast, AnyNodeRef, ExprContext};
@@ -919,7 +919,7 @@ impl<'db> TypeInferenceBuilder<'db> {
         self.infer_type_parameters(type_params);
 
         if let Some(arguments) = class.arguments.as_deref() {
-            self.infer_arguments(arguments);
+            self.infer_arguments(arguments, false);
         }
     }
 
@@ -2523,7 +2523,17 @@ impl<'db> TypeInferenceBuilder<'db> {
         self.infer_expression(expression)
     }
 
-    fn infer_arguments(&mut self, arguments: &ast::Arguments) -> CallArguments<'db> {
+    fn infer_arguments(
+        &mut self,
+        arguments: &ast::Arguments,
+        infer_as_type_expressions: bool,
+    ) -> CallArguments<'db> {
+        let infer_argument_type = if infer_as_type_expressions {
+            Self::infer_type_expression
+        } else {
+            Self::infer_expression
+        };
+
         arguments
             .arguments_source_order()
             .map(|arg_or_keyword| {
@@ -2534,19 +2544,19 @@ impl<'db> TypeInferenceBuilder<'db> {
                             range: _,
                             ctx: _,
                         }) => {
-                            let ty = self.infer_expression(value);
+                            let ty = infer_argument_type(self, value);
                             self.store_expression_type(arg, ty);
                             Argument::Variadic(ty)
                         }
                         // TODO diagnostic if after a keyword argument
-                        _ => Argument::Positional(self.infer_expression(arg)),
+                        _ => Argument::Positional(infer_argument_type(self, arg)),
                     },
                     ast::ArgOrKeyword::Keyword(ast::Keyword {
                         arg,
                         value,
                         range: _,
                     }) => {
-                        let ty = self.infer_expression(value);
+                        let ty = infer_argument_type(self, value);
                         if let Some(arg) = arg {
                             Argument::Keyword {
                                 name: arg.id.clone(),
@@ -3070,8 +3080,14 @@ impl<'db> TypeInferenceBuilder<'db> {
             arguments,
         } = call_expression;
 
-        let call_arguments = self.infer_arguments(arguments);
         let function_type = self.infer_expression(func);
+
+        let infer_arguments_as_type_expressions = function_type
+            .into_function_literal()
+            .and_then(|f| f.known(self.db()))
+            .is_some_and(KnownFunction::takes_type_expression_arguments);
+
+        let call_arguments = self.infer_arguments(arguments, infer_arguments_as_type_expressions);
         function_type
             .call(self.db(), &call_arguments)
             .unwrap_with_diagnostic(&self.context, call_expression.into())
@@ -4448,7 +4464,7 @@ impl<'db> TypeInferenceBuilder<'db> {
 
                         return dunder_getitem_method
                             .call(self.db(), &CallArguments::positional([value_ty, slice_ty]))
-                            .return_ty_result(&self.context, value_node.into())
+                            .return_ty_result( &self.context, value_node.into())
                             .unwrap_or_else(|err| {
                                 self.context.report_lint(
                                     &CALL_NON_CALLABLE,
@@ -5156,6 +5172,55 @@ impl<'db> TypeInferenceBuilder<'db> {
                 todo_type!("Callable types")
             }
 
+            // Type API special forms
+            KnownInstanceType::Not => match arguments_slice {
+                ast::Expr::Tuple(_) => {
+                    self.context.report_lint(
+                        &INVALID_TYPE_FORM,
+                        subscript.into(),
+                        format_args!(
+                            "Special form `{}` expected exactly one type parameter",
+                            known_instance.repr(self.db())
+                        ),
+                    );
+                    Type::Unknown
+                }
+                _ => {
+                    let argument_type = self.infer_type_expression(arguments_slice);
+                    argument_type.negate(self.db())
+                }
+            },
+            KnownInstanceType::Intersection => {
+                let elements = match arguments_slice {
+                    ast::Expr::Tuple(tuple) => Either::Left(tuple.iter()),
+                    element => Either::Right(std::iter::once(element)),
+                };
+
+                elements
+                    .fold(IntersectionBuilder::new(self.db()), |builder, element| {
+                        builder.add_positive(self.infer_type_expression(element))
+                    })
+                    .build()
+            }
+            KnownInstanceType::TypeOf => match arguments_slice {
+                ast::Expr::Tuple(_) => {
+                    self.context.report_lint(
+                        &INVALID_TYPE_FORM,
+                        subscript.into(),
+                        format_args!(
+                            "Special form `{}` expected exactly one type parameter",
+                            known_instance.repr(self.db())
+                        ),
+                    );
+                    Type::Unknown
+                }
+                _ => {
+                    // NB: This calls `infer_expression` instead of `infer_type_expression`.
+                    let argument_type = self.infer_expression(arguments_slice);
+                    argument_type
+                }
+            },
+
             // TODO: Generics
             KnownInstanceType::ChainMap => {
                 self.infer_type_expression(arguments_slice);
@@ -5241,7 +5306,9 @@ impl<'db> TypeInferenceBuilder<'db> {
                 );
                 Type::Unknown
             }
-            KnownInstanceType::TypingSelf | KnownInstanceType::TypeAlias => {
+            KnownInstanceType::TypingSelf
+            | KnownInstanceType::TypeAlias
+            | KnownInstanceType::Unknown => {
                 self.context.report_lint(
                     &INVALID_TYPE_FORM,
                     subscript.into(),
diff --git a/crates/red_knot_vendored/knot_extensions/README.md b/crates/red_knot_vendored/knot_extensions/README.md
new file mode 100644
index 0000000000000..d26f2802b53d3
--- /dev/null
+++ b/crates/red_knot_vendored/knot_extensions/README.md
@@ -0,0 +1,3 @@
+The `knot_extensions.pyi` file in this directory will be symlinked into
+the `vendor/typeshed/stdlib` directory every time we sync our `typeshed`
+stubs (see `.github/workflows/sync_typeshed.yaml`).
diff --git a/crates/red_knot_vendored/knot_extensions/knot_extensions.pyi b/crates/red_knot_vendored/knot_extensions/knot_extensions.pyi
new file mode 100644
index 0000000000000..581b2a3d29717
--- /dev/null
+++ b/crates/red_knot_vendored/knot_extensions/knot_extensions.pyi
@@ -0,0 +1,24 @@
+from typing import _SpecialForm, Any, LiteralString
+
+# Special operations
+def static_assert(condition: object, msg: LiteralString | None = None) -> None: ...
+
+# Types
+Unknown = object()
+
+# Special forms
+Not: _SpecialForm
+Intersection: _SpecialForm
+TypeOf: _SpecialForm
+
+# Predicates on types
+#
+# Ideally, these would be annotated using `TypeForm`, but that has not been
+# standardized yet (https://peps.python.org/pep-0747).
+def is_equivalent_to(type_a: Any, type_b: Any) -> bool: ...
+def is_subtype_of(type_derived: Any, typ_ebase: Any) -> bool: ...
+def is_assignable_to(type_target: Any, type_source: Any) -> bool: ...
+def is_disjoint_from(type_a: Any, type_b: Any) -> bool: ...
+def is_fully_static(type: Any) -> bool: ...
+def is_singleton(type: Any) -> bool: ...
+def is_single_valued(type: Any) -> bool: ...
diff --git a/crates/red_knot_vendored/vendor/typeshed/stdlib/VERSIONS b/crates/red_knot_vendored/vendor/typeshed/stdlib/VERSIONS
index 3c6898dc1a777..6cb47d4bfeb13 100644
--- a/crates/red_knot_vendored/vendor/typeshed/stdlib/VERSIONS
+++ b/crates/red_knot_vendored/vendor/typeshed/stdlib/VERSIONS
@@ -341,3 +341,5 @@ zipfile._path: 3.12-
 zipimport: 3.0-
 zlib: 3.0-
 zoneinfo: 3.9-
+# Patch applied for red_knot:
+knot_extensions: 3.0-
diff --git a/crates/red_knot_vendored/vendor/typeshed/stdlib/knot_extensions.pyi b/crates/red_knot_vendored/vendor/typeshed/stdlib/knot_extensions.pyi
new file mode 120000
index 0000000000000..8e6b527c81002
--- /dev/null
+++ b/crates/red_knot_vendored/vendor/typeshed/stdlib/knot_extensions.pyi
@@ -0,0 +1 @@
+../../../knot_extensions/knot_extensions.pyi
\ No newline at end of file