diff --git a/standard/attributes.md b/standard/attributes.md
index 758623ca5..00d8a502a 100644
--- a/standard/attributes.md
+++ b/standard/attributes.md
@@ -513,7 +513,7 @@ A class that is decorated with the `AttributeUsage` attribute shall derive from
 
 #### 23.5.3.1 General
 
-The attribute `Conditional` enables the definition of ***conditional methods*** and ***conditional attribute classes***.
+The attribute `Conditional` enables the definition of ***conditional methods***, ***conditional local functions***, and ***conditional attribute classes***.
 
 #### 23.5.3.2 Conditional methods
 
@@ -664,6 +664,12 @@ The use of conditional methods in an inheritance chain can be confusing. Calls m
 >
 > *end example*
 
+#### §conditional-local-function Conditional local functions
+
+A local function may be made conditional in the same sense as a conditional method ([§23.5.3.2](attributes.md#23532-conditional-methods)).
+
+A conditional local function shall have the modifier `static`.
+
 #### 23.5.3.3 Conditional attribute classes
 
 An attribute class ([§23.2](attributes.md#232-attribute-classes)) decorated with one or more `Conditional` attributes is a conditional attribute class. A conditional attribute class is thus associated with the conditional compilation symbols declared in its `Conditional` attributes.
@@ -833,6 +839,8 @@ For invocations that occur within field or event initializers, the member name u
 
 For invocations that occur within declarations of instance constructors, static constructors, finalizers and operators the member name used is implementation-dependent.
 
+For an invocation that occurs within a local function, the name of the method that calls that local function is used. Consider the following: if method `M` calls local function `F1`, which in turn calls local function `F2`, and `F2` has a parameter marked with this attribute, the method name passed to `F2` is `M`, because a local function is *not* a function member!
+
 ### 23.5.7 Code analysis attributes
 
 #### 23.5.7.1 General
diff --git a/standard/statements.md b/standard/statements.md
index 925564544..ced02972e 100644
--- a/standard/statements.md
+++ b/standard/statements.md
@@ -487,9 +487,9 @@ A *local_function_declaration* declares a local function.
 
 ```ANTLR
 local_function_declaration
-    : local_function_modifier* return_type local_function_header
+    : attributes? local_function_modifier* return_type local_function_header
       local_function_body
-    | ref_local_function_modifier* ref_kind ref_return_type
+    | attributes? ref_local_function_modifier* ref_kind ref_return_type
       local_function_header ref_local_function_body
     ;
 
@@ -506,6 +506,7 @@ local_function_modifier
 
 ref_local_function_modifier
     : 'static'
+    | 'extern'
     | unsafe_modifier   // unsafe code support
     ;
 
@@ -513,11 +514,13 @@ local_function_body
     : block
     | '=>' null_conditional_invocation_expression ';'
     | '=>' expression ';'
+    | ';'
     ;
 
 ref_local_function_body
     : block
     | '=>' 'ref' variable_reference ';'
+    | ';'
     ;
 ```
 
@@ -562,7 +565,11 @@ Unless specified otherwise below, the semantics of all grammar elements is the s
 
 The *identifier* of a *local_function_declaration* shall be unique in its declared block scope, including any enclosing local variable declaration spaces. One consequence of this is that overloaded *local_function_declaration*s are not allowed.
 
-A *local_function_declaration* may include one `async` ([§15.14](classes.md#1514-async-functions)) modifier and one `unsafe` ([§24.1](unsafe-code.md#241-general)) modifier. If the declaration includes the `async` modifier then the return type shall be `void` or a `«TaskType»` type ([§15.14.1](classes.md#15141-general)). If the declaration includes the `static` modifier, the function is a ***static local function***; otherwise, it is a ***non-static local function***. It is a compile-time error for *type_parameter_list* or *parameter_list* to contain *attributes*. If the local function is declared in an unsafe context ([§24.2](unsafe-code.md#242-unsafe-contexts)), the local function may include unsafe code, even if the local function declaration doesn’t include the `unsafe` modifier.
+A *local_function_declaration* may include one `async` ([§15.14](classes.md#1514-async-functions)) modifier and one `unsafe` ([§24.1](unsafe-code.md#241-general)) modifier. If the declaration includes the `async` modifier then the return type shall be `void` or a `«TaskType»` type ([§15.14.1](classes.md#15141-general)). If the declaration includes the `static` modifier, the function is a ***static local function***; otherwise, it is a ***non-static local function***. If the local function is declared in an unsafe context ([§24.2](unsafe-code.md#242-unsafe-contexts)), the local function may include unsafe code, even if the local function declaration doesn’t include the `unsafe` modifier.
+
+An external local function shall have the modifier `static`, and its *local_function_body* or *ref_local_function_body* shall be a semicolon.
+
+A *local_function_body* or *ref_local_function_body* shall be a semicolon only for an external local function.
 
 A local function is declared at block scope. A non-static local function may capture variables from the enclosing scope while a static local function shall not (so it has no access to enclosing locals, parameters, non-static local functions, or `this`). It is a compile-time error if a captured variable is read by the body of a non-static local function but is not definitely assigned before each call to the function. A compiler shall determine which variables are definitely assigned on return ([§9.4.4.33](variables.md#94433-rules-for-variables-in-local-functions)).