diff --git a/guppylang/checker/func_checker.py b/guppylang/checker/func_checker.py
index c79c9e97..cd04ca8f 100644
--- a/guppylang/checker/func_checker.py
+++ b/guppylang/checker/func_checker.py
@@ -16,7 +16,7 @@
 from guppylang.definition.common import DefId
 from guppylang.error import GuppyError
 from guppylang.nodes import CheckedNestedFunctionDef, NestedFunctionDef
-from guppylang.tys.parsing import type_from_ast
+from guppylang.tys.parsing import type_from_ast, type_with_flags_from_ast
 from guppylang.tys.ty import FuncInput, FunctionType, InputFlags, NoneType
 
 if TYPE_CHECKING:
@@ -146,27 +146,14 @@ def check_signature(func_def: ast.FunctionDef, globals: Globals) -> FunctionType
     inputs = []
     input_names = []
     for inp in func_def.args.args:
-        ty_ast = inp.annotation
-        if ty_ast is None:
+        if inp.annotation is None:
             raise GuppyError("Argument type must be annotated", inp)
-        flags = InputFlags.NoFlags
-        # Detect `@flag` argument annotations
-        # TODO: This doesn't work if the type annotation is a string forward ref. We
-        #  should rethink how we handle these...
-        if isinstance(ty_ast, ast.BinOp) and isinstance(ty_ast.op, ast.MatMult):
-            ty = type_from_ast(ty_ast.left, globals, param_var_mapping)
-            match ty_ast.right:
-                case ast.Name(id="inout"):
-                    if not ty.linear:
-                        raise GuppyError(
-                            f"Non-linear type `{ty}` cannot be annotated as `@inout`",
-                            ty_ast.right,
-                        )
-                    flags |= InputFlags.Inout
-                case _:
-                    raise GuppyError("Invalid annotation", ty_ast.right)
-        else:
-            ty = type_from_ast(ty_ast, globals, param_var_mapping)
+        ty, flags = type_with_flags_from_ast(inp.annotation, globals, param_var_mapping)
+        if InputFlags.Inout in flags and not ty.linear:
+            raise GuppyError(
+                f"Non-linear type `{ty}` cannot be annotated as `@inout`",
+                inp.annotation,
+            )
         inputs.append(FuncInput(ty, flags))
         input_names.append(inp.arg)
     ret_type = type_from_ast(func_def.returns, globals, param_var_mapping)
diff --git a/guppylang/definition/struct.py b/guppylang/definition/struct.py
index 79ffd375..61e43415 100644
--- a/guppylang/definition/struct.py
+++ b/guppylang/definition/struct.py
@@ -21,10 +21,9 @@
     DefaultCallChecker,
 )
 from guppylang.definition.parameter import ParamDef
-from guppylang.definition.ty import TypeDef
+from guppylang.definition.ty import FlaggedArgs, TypeDef, check_no_flags
 from guppylang.error import GuppyError, InternalGuppyError
 from guppylang.hugr_builder.hugr import OutPortV
-from guppylang.tys.arg import Argument
 from guppylang.tys.param import Parameter, check_all_args
 from guppylang.tys.parsing import type_from_ast
 from guppylang.tys.ty import FuncInput, FunctionType, InputFlags, StructType, Type
@@ -133,7 +132,7 @@ def parse(self, globals: Globals) -> "ParsedStructDef":
         return ParsedStructDef(self.id, self.name, cls_def, params, fields)
 
     def check_instantiate(
-        self, args: Sequence[Argument], globals: "Globals", loc: AstNode | None = None
+        self, args: FlaggedArgs, globals: "Globals", loc: AstNode | None = None
     ) -> Type:
         raise InternalGuppyError("Tried to instantiate raw struct definition")
 
@@ -163,9 +162,10 @@ def check(self, globals: Globals) -> "CheckedStructDef":
         )
 
     def check_instantiate(
-        self, args: Sequence[Argument], globals: "Globals", loc: AstNode | None = None
+        self, args: FlaggedArgs, globals: "Globals", loc: AstNode | None = None
     ) -> Type:
         """Checks if the struct can be instantiated with the given arguments."""
+        args = check_no_flags(args, loc)
         check_all_args(self.params, args, self.name, loc)
         # Obtain a checked version of this struct definition so we can construct a
         # `StructType` instance
@@ -187,9 +187,10 @@ class CheckedStructDef(TypeDef, CompiledDef):
     fields: Sequence[StructField]
 
     def check_instantiate(
-        self, args: Sequence[Argument], globals: "Globals", loc: AstNode | None = None
+        self, args: FlaggedArgs, globals: "Globals", loc: AstNode | None = None
     ) -> Type:
         """Checks if the struct can be instantiated with the given arguments."""
+        args = check_no_flags(args, loc)
         check_all_args(self.params, args, self.name, loc)
         return StructType(args, self)
 
@@ -290,7 +291,7 @@ class DummyStructDef(TypeDef):
 
         def check_instantiate(
             self,
-            args: Sequence[Argument],
+            args: FlaggedArgs,
             globals: "Globals",
             loc: AstNode | None = None,
         ) -> Type:
diff --git a/guppylang/definition/ty.py b/guppylang/definition/ty.py
index f430fe7d..c301707b 100644
--- a/guppylang/definition/ty.py
+++ b/guppylang/definition/ty.py
@@ -1,20 +1,24 @@
 from abc import abstractmethod
 from collections.abc import Callable, Sequence
 from dataclasses import dataclass, field
-from typing import TYPE_CHECKING
+from typing import TYPE_CHECKING, TypeAlias
 
 from hugr.serialization import tys
 
 from guppylang.ast_util import AstNode
 from guppylang.definition.common import CompiledDef, Definition
+from guppylang.error import GuppyError
 from guppylang.tys.arg import Argument
 from guppylang.tys.param import Parameter, check_all_args
-from guppylang.tys.ty import OpaqueType, Type
+from guppylang.tys.ty import InputFlags, OpaqueType, Type
 
 if TYPE_CHECKING:
     from guppylang.checker.core import Globals
 
 
+FlaggedArgs: TypeAlias = Sequence[tuple[Argument, InputFlags]]
+
+
 @dataclass(frozen=True)
 class TypeDef(Definition):
     """Abstract base class for type definitions."""
@@ -23,7 +27,7 @@ class TypeDef(Definition):
 
     @abstractmethod
     def check_instantiate(
-        self, args: Sequence[Argument], globals: "Globals", loc: AstNode | None = None
+        self, args: FlaggedArgs, globals: "Globals", loc: AstNode | None = None
     ) -> Type:
         """Checks if the type definition can be instantiated with the given arguments.
 
@@ -42,12 +46,23 @@ class OpaqueTypeDef(TypeDef, CompiledDef):
     bound: tys.TypeBound | None = None
 
     def check_instantiate(
-        self, args: Sequence[Argument], globals: "Globals", loc: AstNode | None = None
+        self, args: FlaggedArgs, globals: "Globals", loc: AstNode | None = None
     ) -> OpaqueType:
         """Checks if the type definition can be instantiated with the given arguments.
 
         Returns the resulting concrete type or raises a user error if the arguments are
         invalid.
         """
+        args = check_no_flags(args, loc)
         check_all_args(self.params, args, self.name, loc)
         return OpaqueType(args, self)
+
+
+def check_no_flags(args: FlaggedArgs, loc: AstNode | None) -> list[Argument]:
+    """Checks that no argument to `check_instantiate` has any `@flags`."""
+    for _, flags in args:
+        if flags != InputFlags.NoFlags:
+            raise GuppyError(
+                "`@` type annotations are not allowed in this position", loc
+            )
+    return [ty for ty, _ in args]
diff --git a/guppylang/tys/builtin.py b/guppylang/tys/builtin.py
index 6de919dc..8ee95a52 100644
--- a/guppylang/tys/builtin.py
+++ b/guppylang/tys/builtin.py
@@ -1,13 +1,12 @@
 from collections.abc import Sequence
 from dataclasses import dataclass, field
-from itertools import repeat
 from typing import TYPE_CHECKING, Literal
 
 from hugr.serialization import tys
 
 from guppylang.ast_util import AstNode
 from guppylang.definition.common import DefId
-from guppylang.definition.ty import OpaqueTypeDef, TypeDef
+from guppylang.definition.ty import FlaggedArgs, OpaqueTypeDef, TypeDef, check_no_flags
 from guppylang.error import GuppyError
 from guppylang.tys.arg import Argument, ConstArg, TypeArg
 from guppylang.tys.param import ConstParam, TypeParam
@@ -36,22 +35,28 @@ class _CallableTypeDef(TypeDef):
     name: Literal["Callable"] = field(default="Callable", init=False)
 
     def check_instantiate(
-        self, args: Sequence[Argument], globals: "Globals", loc: AstNode | None = None
+        self, args: FlaggedArgs, globals: "Globals", loc: AstNode | None = None
     ) -> FunctionType:
         # We get the inputs/output as a flattened list: `args = [*inputs, output]`.
         if not args:
             raise GuppyError(f"Missing parameter for type `{self.name}`", loc)
         args = [
             # TODO: Better error location
-            TypeParam(0, f"T{i}", can_be_linear=True).check_arg(arg, loc).ty
-            for i, arg in enumerate(args)
-        ]
-        *input_tys, output = args
-        inputs = [
-            FuncInput(ty, flags)
-            for ty, flags in zip(input_tys, repeat(InputFlags.NoFlags), strict=False)
+            (TypeParam(0, f"T{i}", can_be_linear=True).check_arg(arg, loc).ty, flags)
+            for i, (arg, flags) in enumerate(args)
         ]
-        return FunctionType(list(inputs), output)
+        *inputs, (output_ty, output_flags) = args
+        for ty, flags in inputs:
+            if InputFlags.Inout in flags and not ty.linear:
+                raise GuppyError(
+                    f"Non-linear type `{ty}` cannot be annotated as `@inout`",
+                    loc,  # TODO: Better error location
+                )
+        if output_flags != InputFlags.NoFlags:
+            raise GuppyError(
+                "`@` type annotations are not allowed in this position", loc
+            )
+        return FunctionType([FuncInput(ty, flags) for ty, flags in inputs], output_ty)
 
 
 @dataclass(frozen=True)
@@ -64,8 +69,9 @@ class _TupleTypeDef(TypeDef):
     name: Literal["tuple"] = field(default="tuple", init=False)
 
     def check_instantiate(
-        self, args: Sequence[Argument], globals: "Globals", loc: AstNode | None = None
+        self, args: FlaggedArgs, globals: "Globals", loc: AstNode | None = None
     ) -> TupleType:
+        args = check_no_flags(args, loc)
         # We accept any number of arguments. If users just write `tuple`, we give them
         # the empty tuple type. We just have to make sure that the args are of kind type
         args = [
@@ -86,7 +92,7 @@ class _NoneTypeDef(TypeDef):
     name: Literal["None"] = field(default="None", init=False)
 
     def check_instantiate(
-        self, args: Sequence[Argument], globals: "Globals", loc: AstNode | None = None
+        self, args: FlaggedArgs, globals: "Globals", loc: AstNode | None = None
     ) -> NoneType:
         if args:
             raise GuppyError("Type `None` is not parameterized", loc)
@@ -103,7 +109,7 @@ class _NumericTypeDef(TypeDef):
     ty: NumericType
 
     def check_instantiate(
-        self, args: Sequence[Argument], globals: "Globals", loc: AstNode | None = None
+        self, args: FlaggedArgs, globals: "Globals", loc: AstNode | None = None
     ) -> NumericType:
         if args:
             raise GuppyError(f"Type `{self.name}` is not parameterized", loc)
@@ -119,10 +125,10 @@ class _ListTypeDef(OpaqueTypeDef):
     """
 
     def check_instantiate(
-        self, args: Sequence[Argument], globals: "Globals", loc: AstNode | None = None
+        self, args: FlaggedArgs, globals: "Globals", loc: AstNode | None = None
     ) -> OpaqueType:
         if len(args) == 1:
-            [arg] = args
+            [arg] = check_no_flags(args, loc)
             if isinstance(arg, TypeArg) and arg.ty.linear:
                 raise GuppyError(
                     "Type `list` cannot store linear data, use `linst` instead", loc
diff --git a/guppylang/tys/parsing.py b/guppylang/tys/parsing.py
index c73222b3..137f95a1 100644
--- a/guppylang/tys/parsing.py
+++ b/guppylang/tys/parsing.py
@@ -13,14 +13,14 @@
 from guppylang.tys.arg import Argument, ConstArg, TypeArg
 from guppylang.tys.const import ConstValue
 from guppylang.tys.param import Parameter, TypeParam
-from guppylang.tys.ty import NoneType, NumericType, TupleType, Type
+from guppylang.tys.ty import InputFlags, NoneType, NumericType, TupleType, Type
 
 
 def arg_from_ast(
     node: AstNode,
     globals: Globals,
     param_var_mapping: dict[str, Parameter] | None = None,
-) -> Argument:
+) -> tuple[Argument, InputFlags]:
     """Turns an AST expression into an argument."""
     # A single identifier
     if isinstance(node, ast.Name):
@@ -30,7 +30,8 @@ def arg_from_ast(
         match globals[x]:
             # Either a defined type (e.g. `int`, `bool`, ...)
             case TypeDef() as defn:
-                return TypeArg(defn.check_instantiate([], globals, node))
+                ty_arg = TypeArg(defn.check_instantiate([], globals, node))
+                return ty_arg, InputFlags.NoFlags
             # Or a parameter (e.g. `T`, `n`, ...)
             case ParamDef() as defn:
                 if param_var_mapping is None:
@@ -39,7 +40,7 @@ def arg_from_ast(
                     )
                 if x not in param_var_mapping:
                     param_var_mapping[x] = defn.to_param(len(param_var_mapping))
-                return param_var_mapping[x].to_bound()
+                return param_var_mapping[x].to_bound(), InputFlags.NoFlags
             case defn:
                 raise GuppyError(
                     f"Expected a type, got {defn.description} `{defn.name}`", node
@@ -70,7 +71,7 @@ def arg_from_ast(
                     for arg_node in arg_nodes
                 ]
                 ty = defn.check_instantiate(args, globals, node)
-                return TypeArg(ty)
+                return TypeArg(ty), InputFlags.NoFlags
             # We don't allow parametrised variables like `T[int]`
             if isinstance(defn, ParamDef):
                 raise GuppyError(
@@ -79,16 +80,26 @@ def arg_from_ast(
                     node,
                 )
 
+    # An annotated argument, e.g. `int @inout`
+    if isinstance(node, ast.BinOp) and isinstance(node.op, ast.MatMult):
+        arg, flags = arg_from_ast(node.left, globals, param_var_mapping)
+        match node.right:
+            case ast.Name(id="inout"):
+                flags |= InputFlags.Inout
+            case _:
+                raise GuppyError("Invalid annotation", node.right)
+        return arg, flags
+
     # We allow tuple types to be written as `(int, bool)`
     if isinstance(node, ast.Tuple):
         ty = TupleType(
             [type_from_ast(el, globals, param_var_mapping) for el in node.elts]
         )
-        return TypeArg(ty)
+        return TypeArg(ty), InputFlags.NoFlags
 
     # `None` is represented as a `ast.Constant` node with value `None`
     if isinstance(node, ast.Constant) and node.value is None:
-        return TypeArg(NoneType())
+        return TypeArg(NoneType()), InputFlags.NoFlags
 
     # Integer literals are turned into nat args since these are the only ones we support
     # right now.
@@ -98,7 +109,7 @@ def arg_from_ast(
         # `ast.UnaryOp` negation of a `ast.Constant(5)`
         assert node.value >= 0
         nat_ty = NumericType(NumericType.Kind.Nat)
-        return ConstArg(ConstValue(nat_ty, node.value))
+        return ConstArg(ConstValue(nat_ty, node.value)), InputFlags.NoFlags
 
     # Finally, we also support delayed annotations in strings
     if isinstance(node, ast.Constant) and isinstance(node.value, str):
@@ -122,15 +133,27 @@ def arg_from_ast(
 _type_param = TypeParam(0, "T", True)
 
 
+def type_with_flags_from_ast(
+    node: AstNode,
+    globals: Globals,
+    param_var_mapping: dict[str, Parameter] | None = None,
+) -> tuple[Type, InputFlags]:
+    """Turns an AST expression into a Guppy type possibly annotated with @flags."""
+    # Parse an argument and check that it's valid for a `TypeParam`
+    arg, flags = arg_from_ast(node, globals, param_var_mapping)
+    return _type_param.check_arg(arg, node).ty, flags
+
+
 def type_from_ast(
     node: AstNode,
     globals: Globals,
     param_var_mapping: dict[str, Parameter] | None = None,
 ) -> Type:
     """Turns an AST expression into a Guppy type."""
-    # Parse an argument and check that it's valid for a `TypeParam`
-    arg = arg_from_ast(node, globals, param_var_mapping)
-    return _type_param.check_arg(arg, node).ty
+    ty, flags = type_with_flags_from_ast(node, globals, param_var_mapping)
+    if flags != InputFlags.NoFlags:
+        raise GuppyError("`@` type annotations are not allowed in this position", node)
+    return ty
 
 
 def type_row_from_ast(node: ast.expr, globals: "Globals") -> Sequence[Type]:
diff --git a/tests/error/inout_errors/nonlinear.err b/tests/error/inout_errors/nonlinear.err
index 0e6c0e26..b7de73c2 100644
--- a/tests/error/inout_errors/nonlinear.err
+++ b/tests/error/inout_errors/nonlinear.err
@@ -2,5 +2,5 @@ Guppy compilation failed. Error in file $FILE:11
 
 9:     @guppy.declare(module)
 10:    def foo(x: int @inout) -> qubit: ...
-                       ^^^^^
+                  ^^^^^^^^^^
 GuppyError: Non-linear type `int` cannot be annotated as `@inout`
diff --git a/tests/error/inout_errors/nonlinear_callable.err b/tests/error/inout_errors/nonlinear_callable.err
new file mode 100644
index 00000000..4df85b50
--- /dev/null
+++ b/tests/error/inout_errors/nonlinear_callable.err
@@ -0,0 +1,6 @@
+Guppy compilation failed. Error in file $FILE:12
+
+10:    @guppy.declare(module)
+11:    def foo(f: Callable[[int @inout], None]) -> None: ...
+                  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+GuppyError: Non-linear type `int` cannot be annotated as `@inout`
diff --git a/tests/error/inout_errors/nonlinear_callable.py b/tests/error/inout_errors/nonlinear_callable.py
new file mode 100644
index 00000000..ed21ce94
--- /dev/null
+++ b/tests/error/inout_errors/nonlinear_callable.py
@@ -0,0 +1,15 @@
+from typing import Callable
+
+from guppylang.decorator import guppy
+from guppylang.module import GuppyModule
+from guppylang.prelude.builtins import inout
+
+
+module = GuppyModule("test")
+
+
+@guppy.declare(module)
+def foo(f: Callable[[int @inout], None]) -> None: ...
+
+
+module.compile()
diff --git a/tests/error/misc_errors/nested_arg_flag.err b/tests/error/misc_errors/nested_arg_flag.err
new file mode 100644
index 00000000..4f06ad67
--- /dev/null
+++ b/tests/error/misc_errors/nested_arg_flag.err
@@ -0,0 +1,6 @@
+Guppy compilation failed. Error in file $FILE:12
+
+10:    @guppy.declare(module)
+11:    def foo(x: list[qubit @inout]) -> qubit: ...
+                  ^^^^^^^^^^^^^^^^^^
+GuppyError: `@` type annotations are not allowed in this position
diff --git a/tests/error/misc_errors/nested_arg_flag.py b/tests/error/misc_errors/nested_arg_flag.py
new file mode 100644
index 00000000..fb8961a9
--- /dev/null
+++ b/tests/error/misc_errors/nested_arg_flag.py
@@ -0,0 +1,15 @@
+from guppylang.decorator import guppy
+from guppylang.module import GuppyModule
+from guppylang.prelude.builtins import inout
+from guppylang.prelude.quantum import quantum, qubit
+
+
+module = GuppyModule("test")
+module.load(quantum)
+
+
+@guppy.declare(module)
+def foo(x: list[qubit @inout]) -> qubit: ...
+
+
+module.compile()
diff --git a/tests/error/misc_errors/return_flag.err b/tests/error/misc_errors/return_flag.err
new file mode 100644
index 00000000..096ad4a6
--- /dev/null
+++ b/tests/error/misc_errors/return_flag.err
@@ -0,0 +1,6 @@
+Guppy compilation failed. Error in file $FILE:12
+
+10:    @guppy.declare(module)
+11:    def foo() -> qubit @inout: ...
+                    ^^^^^^^^^^^^
+GuppyError: `@` type annotations are not allowed in this position
diff --git a/tests/error/misc_errors/return_flag.py b/tests/error/misc_errors/return_flag.py
new file mode 100644
index 00000000..6191abc5
--- /dev/null
+++ b/tests/error/misc_errors/return_flag.py
@@ -0,0 +1,15 @@
+from guppylang.decorator import guppy
+from guppylang.module import GuppyModule
+from guppylang.prelude.builtins import inout
+from guppylang.prelude.quantum import quantum, qubit
+
+
+module = GuppyModule("test")
+module.load(quantum)
+
+
+@guppy.declare(module)
+def foo() -> qubit @inout: ...
+
+
+module.compile()
diff --git a/tests/error/misc_errors/return_flag_callable.err b/tests/error/misc_errors/return_flag_callable.err
new file mode 100644
index 00000000..3c69888d
--- /dev/null
+++ b/tests/error/misc_errors/return_flag_callable.err
@@ -0,0 +1,6 @@
+Guppy compilation failed. Error in file $FILE:14
+
+12:    @guppy.declare(module)
+13:    def foo(f: Callable[[], qubit @inout]) -> None: ...
+                  ^^^^^^^^^^^^^^^^^^^^^^^^^^
+GuppyError: `@` type annotations are not allowed in this position
diff --git a/tests/error/misc_errors/return_flag_callable.py b/tests/error/misc_errors/return_flag_callable.py
new file mode 100644
index 00000000..88534cba
--- /dev/null
+++ b/tests/error/misc_errors/return_flag_callable.py
@@ -0,0 +1,17 @@
+from typing import Callable
+
+from guppylang.decorator import guppy
+from guppylang.module import GuppyModule
+from guppylang.prelude.builtins import inout
+from guppylang.prelude.quantum import quantum, qubit
+
+
+module = GuppyModule("test")
+module.load(quantum)
+
+
+@guppy.declare(module)
+def foo(f: Callable[[], qubit @inout]) -> None: ...
+
+
+module.compile()
diff --git a/tests/integration/test_inout.py b/tests/integration/test_inout.py
index dfe7a512..5b4c789f 100644
--- a/tests/integration/test_inout.py
+++ b/tests/integration/test_inout.py
@@ -14,3 +14,13 @@ def test_declare(validate):
     def test(q: qubit @inout) -> qubit: ...
 
     validate(module.compile())
+
+
+def test_string_annotation(validate):
+    module = GuppyModule("test")
+    module.load(quantum)
+
+    @guppy.declare(module)
+    def test(q: "qubit @inout") -> qubit: ...
+
+    validate(module.compile())