README.md

@@ -18,6 +18,25 @@ kernel.
 
 Only types supported in the kernel can be referenced.
 
+Examples:
+```python
+FOO = 0
+
+@kernel
+def correct() -> int:
+    global FOO
+    return FOO + 1
+
+@kernel
+def fail_without_global() -> int:
+    return FOO + 2
+
+@kernel
+def fail_write() -> None:
+    FOO += 1
+
+```
+
 ## Class and Functions
 * Instance variables must be annotated: (Issue #1)
     ```python
@@ -31,7 +50,7 @@ Only types supported in the kernel can be referenced.
 * Three types of instance variables: (Issue #5)
   * Host only variables: Do not add type annotation for it in the class.
   * Kernel Invariants: Immutable in the kernel and in the host while the kernel
-    is executing. Type: `KernelInvariant(T)`. The types must be immutable.
+    is executing. Type: `KernelInvariant[T]`. The types must be immutable.
     (use tuple instead of list in the host, but the type annotation should still
     be list?)
   * Normal Variables: The host can only assign to them in the `__init__`
@@ -47,6 +66,8 @@ Only types supported in the kernel can be referenced.
 * Function pointers are supported,  and lambda expression is not supported
   currently. (maybe support lambda after implementing type inference?)
 
+  Its type is denoted by the typing library, e.g. `Call[[int32, int32], int32]`.
+
 ## Built-in Types
 * Primitive types include:
     * `bool`