python
diff --git a/‎mypy/build.py
+2-104 b/‎mypy/build.py
+2-104
diff --git a/‎mypy/checkexpr.py
+143-2 b/‎mypy/checkexpr.py
+143-2
diff --git a/‎mypy/constraints.py
+24-1 b/‎mypy/constraints.py
+24-1
@@ -31,14 +31,12 @@
     Callable,
     ClassVar,
     Dict,
-    Iterable,
     Iterator,
     Mapping,
     NamedTuple,
     NoReturn,
     Sequence,
     TextIO,
-    TypeVar,
 )
 from typing_extensions import Final, TypeAlias as _TypeAlias
 
@@ -47,6 +45,7 @@
 import mypy.semanal_main
 from mypy.checker import TypeChecker
 from mypy.errors import CompileError, ErrorInfo, Errors, report_internal_error
+from mypy.graph_utils import prepare_sccs, strongly_connected_components, topsort
 from mypy.indirection import TypeIndirectionVisitor
 from mypy.messages import MessageBuilder
 from mypy.nodes import Import, ImportAll, ImportBase, ImportFrom, MypyFile, SymbolTable, TypeInfo
@@ -3466,15 +3465,8 @@ def sorted_components(
     edges = {id: deps_filtered(graph, vertices, id, pri_max) for id in vertices}
     sccs = list(strongly_connected_components(vertices, edges))
     # Topsort.
-    sccsmap = {id: frozenset(scc) for scc in sccs for id in scc}
-    data: dict[AbstractSet[str], set[AbstractSet[str]]] = {}
-    for scc in sccs:
-        deps: set[AbstractSet[str]] = set()
-        for id in scc:
-            deps.update(sccsmap[x] for x in deps_filtered(graph, vertices, id, pri_max))
-        data[frozenset(scc)] = deps
     res = []
-    for ready in topsort(data):
+    for ready in topsort(prepare_sccs(sccs, edges)):
         # Sort the sets in ready by reversed smallest State.order.  Examples:
         #
         # - If ready is [{x}, {y}], x.order == 1, y.order == 2, we get
@@ -3499,100 +3491,6 @@ def deps_filtered(graph: Graph, vertices: AbstractSet[str], id: str, pri_max: in
     ]
 
 
-def strongly_connected_components(
-    vertices: AbstractSet[str], edges: dict[str, list[str]]
-) -> Iterator[set[str]]:
-    """Compute Strongly Connected Components of a directed graph.
-
-    Args:
-      vertices: the labels for the vertices
-      edges: for each vertex, gives the target vertices of its outgoing edges
-
-    Returns:
-      An iterator yielding strongly connected components, each
-      represented as a set of vertices.  Each input vertex will occur
-      exactly once; vertices not part of a SCC are returned as
-      singleton sets.
-
-    From https://code.activestate.com/recipes/578507/.
-    """
-    identified: set[str] = set()
-    stack: list[str] = []
-    index: dict[str, int] = {}
-    boundaries: list[int] = []
-
-    def dfs(v: str) -> Iterator[set[str]]:
-        index[v] = len(stack)
-        stack.append(v)
-        boundaries.append(index[v])
-
-        for w in edges[v]:
-            if w not in index:
-                yield from dfs(w)
-            elif w not in identified:
-                while index[w] < boundaries[-1]:
-                    boundaries.pop()
-
-        if boundaries[-1] == index[v]:
-            boundaries.pop()
-            scc = set(stack[index[v] :])
-            del stack[index[v] :]
-            identified.update(scc)
-            yield scc
-
-    for v in vertices:
-        if v not in index:
-            yield from dfs(v)
-
-
-T = TypeVar("T")
-
-
-def topsort(data: dict[T, set[T]]) -> Iterable[set[T]]:
-    """Topological sort.
-
-    Args:
-      data: A map from vertices to all vertices that it has an edge
-            connecting it to.  NOTE: This data structure
-            is modified in place -- for normalization purposes,
-            self-dependencies are removed and entries representing
-            orphans are added.
-
-    Returns:
-      An iterator yielding sets of vertices that have an equivalent
-      ordering.
-
-    Example:
-      Suppose the input has the following structure:
-
-        {A: {B, C}, B: {D}, C: {D}}
-
-      This is normalized to:
-
-        {A: {B, C}, B: {D}, C: {D}, D: {}}
-
-      The algorithm will yield the following values:
-
-        {D}
-        {B, C}
-        {A}
-
-    From https://code.activestate.com/recipes/577413/.
-    """
-    # TODO: Use a faster algorithm?
-    for k, v in data.items():
-        v.discard(k)  # Ignore self dependencies.
-    for item in set.union(*data.values()) - set(data.keys()):
-        data[item] = set()
-    while True:
-        ready = {item for item, dep in data.items() if not dep}
-        if not ready:
-            break
-        yield ready
-        data = {item: (dep - ready) for item, dep in data.items() if item not in ready}
-    assert not data, f"A cyclic dependency exists amongst {data!r}"
-
-
 def missing_stubs_file(cache_dir: str) -> str:
     return os.path.join(cache_dir, "missing_stubs")
 
 
@@ -12,7 +12,7 @@
 import mypy.errorcodes as codes
 from mypy import applytype, erasetype, join, message_registry, nodes, operators, types
 from mypy.argmap import ArgTypeExpander, map_actuals_to_formals, map_formals_to_actuals
-from mypy.checkmember import analyze_member_access, type_object_type
+from mypy.checkmember import analyze_member_access, freeze_all_type_vars, type_object_type
 from mypy.checkstrformat import StringFormatterChecker
 from mypy.erasetype import erase_type, remove_instance_last_known_values, replace_meta_vars
 from mypy.errors import ErrorWatcher, report_internal_error
@@ -98,8 +98,15 @@
 )
 from mypy.semanal_enum import ENUM_BASES
 from mypy.state import state
-from mypy.subtypes import is_equivalent, is_same_type, is_subtype, non_method_protocol_members
+from mypy.subtypes import (
+    find_member,
+    is_equivalent,
+    is_same_type,
+    is_subtype,
+    non_method_protocol_members,
+)
 from mypy.traverser import has_await_expression
+from mypy.type_visitor import TypeTranslator
 from mypy.typeanal import (
     check_for_explicit_any,
     has_any_from_unimported_type,
@@ -114,6 +121,7 @@
     false_only,
     fixup_partial_type,
     function_type,
+    get_type_vars,
     is_literal_type_like,
     make_simplified_union,
     simple_literal_type,
@@ -146,6 +154,7 @@
     TypedDictType,
     TypeOfAny,
     TypeType,
+    TypeVarLikeType,
     TypeVarTupleType,
     TypeVarType,
     UninhabitedType,
@@ -300,6 +309,7 @@ def __init__(
         # on whether current expression is a callee, to give better error messages
         # related to type context.
         self.is_callee = False
+        type_state.infer_polymorphic = self.chk.options.new_type_inference
 
     def reset(self) -> None:
         self.resolved_type = {}
@@ -1791,6 +1801,51 @@ def infer_function_type_arguments(
                     inferred_args[0] = self.named_type("builtins.str")
                 elif not first_arg or not is_subtype(self.named_type("builtins.str"), first_arg):
                     self.chk.fail(message_registry.KEYWORD_ARGUMENT_REQUIRES_STR_KEY_TYPE, context)
+
+            if self.chk.options.new_type_inference and any(
+                a is None
+                or isinstance(get_proper_type(a), UninhabitedType)
+                or set(get_type_vars(a)) & set(callee_type.variables)
+                for a in inferred_args
+            ):
+                # If the regular two-phase inference didn't work, try inferring type
+                # variables while allowing for polymorphic solutions, i.e. for solutions
+                # potentially involving free variables.
+                # TODO: support the similar inference for return type context.
+                poly_inferred_args = infer_function_type_arguments(
+                    callee_type,
+                    arg_types,
+                    arg_kinds,
+                    formal_to_actual,
+                    context=self.argument_infer_context(),
+                    strict=self.chk.in_checked_function(),
+                    allow_polymorphic=True,
+                )
+                for i, pa in enumerate(get_proper_types(poly_inferred_args)):
+                    if isinstance(pa, (NoneType, UninhabitedType)) or has_erased_component(pa):
+                        # Indicate that free variables should not be applied in the call below.
+                        poly_inferred_args[i] = None
+                poly_callee_type = self.apply_generic_arguments(
+                    callee_type, poly_inferred_args, context
+                )
+                yes_vars = poly_callee_type.variables
+                no_vars = {v for v in callee_type.variables if v not in poly_callee_type.variables}
+                if not set(get_type_vars(poly_callee_type)) & no_vars:
+                    # Try applying inferred polymorphic type if possible, e.g. Callable[[T], T] can
+                    # be interpreted as def [T] (T) -> T, but dict[T, T] cannot be expressed.
+                    applied = apply_poly(poly_callee_type, yes_vars)
+                    if applied is not None and poly_inferred_args != [UninhabitedType()] * len(
+                        poly_inferred_args
+                    ):
+                        freeze_all_type_vars(applied)
+                        return applied
+                # If it didn't work, erase free variables as <nothing>, to avoid confusing errors.
+                inferred_args = [
+                    expand_type(a, {v.id: UninhabitedType() for v in callee_type.variables})
+                    if a is not None
+                    else None
+                    for a in inferred_args
+                ]
         else:
             # In dynamically typed functions use implicit 'Any' types for
             # type variables.
@@ -5393,6 +5448,92 @@ def replace_callable_return_type(c: CallableType, new_ret_type: Type) -> Callabl
     return c.copy_modified(ret_type=new_ret_type)
 
 
+def apply_poly(tp: CallableType, poly_tvars: Sequence[TypeVarLikeType]) -> Optional[CallableType]:
+    """Make free type variables generic in the type if possible.
+
+    This will translate the type `tp` while trying to create valid bindings for
+    type variables `poly_tvars` while traversing the type. This follows the same rules
+    as we do during semantic analysis phase, examples:
+      * Callable[Callable[[T], T], T] -> def [T] (def (T) -> T) -> T
+      * Callable[[], Callable[[T], T]] -> def () -> def [T] (T -> T)
+      * List[T] -> None (not possible)
+    """
+    try:
+        return tp.copy_modified(
+            arg_types=[t.accept(PolyTranslator(poly_tvars)) for t in tp.arg_types],
+            ret_type=tp.ret_type.accept(PolyTranslator(poly_tvars)),
+            variables=[],
+        )
+    except PolyTranslationError:
+        return None
+
+
+class PolyTranslationError(Exception):
+    pass
+
+
+class PolyTranslator(TypeTranslator):
+    """Make free type variables generic in the type if possible.
+
+    See docstring for apply_poly() for details.
+    """
+
+    def __init__(self, poly_tvars: Sequence[TypeVarLikeType]) -> None:
+        self.poly_tvars = set(poly_tvars)
+        # This is a simplified version of TypeVarScope used during semantic analysis.
+        self.bound_tvars: set[TypeVarLikeType] = set()
+        self.seen_aliases: set[TypeInfo] = set()
+
+    def visit_callable_type(self, t: CallableType) -> Type:
+        found_vars = set()
+        for arg in t.arg_types:
+            found_vars |= set(get_type_vars(arg)) & self.poly_tvars
+
+        found_vars -= self.bound_tvars
+        self.bound_tvars |= found_vars
+        result = super().visit_callable_type(t)
+        self.bound_tvars -= found_vars
+
+        assert isinstance(result, ProperType) and isinstance(result, CallableType)
+        result.variables = list(result.variables) + list(found_vars)
+        return result
+
+    def visit_type_var(self, t: TypeVarType) -> Type:
+        if t in self.poly_tvars and t not in self.bound_tvars:
+            raise PolyTranslationError()
+        return super().visit_type_var(t)
+
+    def visit_param_spec(self, t: ParamSpecType) -> Type:
+        # TODO: Support polymorphic apply for ParamSpec.
+        raise PolyTranslationError()
+
+    def visit_type_var_tuple(self, t: TypeVarTupleType) -> Type:
+        # TODO: Support polymorphic apply for TypeVarTuple.
+        raise PolyTranslationError()
+
+    def visit_type_alias_type(self, t: TypeAliasType) -> Type:
+        if not t.args:
+            return t.copy_modified()
+        if not t.is_recursive:
+            return get_proper_type(t).accept(self)
+        # We can't handle polymorphic application for recursive generic aliases
+        # without risking an infinite recursion, just give up for now.
+        raise PolyTranslationError()
+
+    def visit_instance(self, t: Instance) -> Type:
+        # There is the same problem with callback protocols as with aliases
+        # (callback protocols are essentially more flexible aliases to callables).
+        # Note: consider supporting bindings in instances, e.g. LRUCache[[x: T], T].
+        if t.args and t.type.is_protocol and t.type.protocol_members == ["__call__"]:
+            if t.type in self.seen_aliases:
+                raise PolyTranslationError()
+            self.seen_aliases.add(t.type)
+            call = find_member("__call__", t, t, is_operator=True)
+            assert call is not None
+            return call.accept(self)
+        return super().visit_instance(t)
+
+
 class ArgInferSecondPassQuery(types.BoolTypeQuery):
     """Query whether an argument type should be inferred in the second pass.
 
 
@@ -886,7 +886,30 @@ def visit_callable_type(self, template: CallableType) -> list[Constraint]:
             param_spec = template.param_spec()
             if param_spec is None:
                 # FIX verify argument counts
-                # FIX what if one of the functions is generic
+                # TODO: Erase template variables if it is generic?
+                if (
+                    type_state.infer_polymorphic
+                    and cactual.variables
+                    and cactual.param_spec() is None
+                    # Technically, the correct inferred type for application of e.g.
+                    # Callable[..., T] -> Callable[..., T] (with literal ellipsis), to a generic
+                    # like U -> U, should be Callable[..., Any], but if U is a self-type, we can
+                    # allow it to leak, to be later bound to self. A bunch of existing code
+                    # depends on this old behaviour.
+                    and not any(tv.id.raw_id == 0 for tv in cactual.variables)
+                ):
+                    # If actual is generic, unify it with template. Note: this is
+                    # not an ideal solution (which would be adding the generic variables
+                    # to the constraint inference set), but it's a good first approximation,
+                    # and this will prevent leaking these variables in the solutions.
+                    # Note: this may infer constraints like T <: S or T <: List[S]
+                    # that contain variables in the target.
+                    unified = mypy.subtypes.unify_generic_callable(
+                        cactual, template, ignore_return=True
+                    )
+                    if unified is not None:
+                        cactual = unified
+                        res.extend(infer_constraints(cactual, template, neg_op(self.direction)))
 
                 # We can't infer constraints from arguments if the template is Callable[..., T]
                 # (with literal '...').