diff --git a/README.md b/README.md
index d4b953f..46e6429 100644
--- a/README.md
+++ b/README.md
@@ -40,6 +40,7 @@ Simple usage:
 ```python
 import datafusion
 from datafusion import functions as f
+from datafusion import col
 import pyarrow
 
 # create a context
@@ -54,8 +55,8 @@ df = ctx.create_dataframe([[batch]])
 
 # create a new statement
 df = df.select(
-    f.col("a") + f.col("b"),
-    f.col("a") - f.col("b"),
+    col("a") + col("b"),
+    col("a") - col("b"),
 )
 
 # execute and collect the first (and only) batch
@@ -68,12 +69,18 @@ assert result.column(1) == pyarrow.array([-3, -3, -3])
 ### UDFs
 
 ```python
+from datafusion import udf
+
 def is_null(array: pyarrow.Array) -> pyarrow.Array:
     return array.is_null()
 
-udf = f.udf(is_null, [pyarrow.int64()], pyarrow.bool_())
+is_null_arr = udf(is_null, [pyarrow.int64()], pyarrow.bool_(), 'stable')
+
+df = df.select(is_null_arr(col("a")))
+
+result = df.collect()
 
-df = df.select(udf(f.col("a")))
+assert result.column(0) == pyarrow.array([False] * 3)
 ```
 
 ### UDAF
@@ -81,18 +88,16 @@ df = df.select(udf(f.col("a")))
 ```python
 import pyarrow
 import pyarrow.compute
+from datafusion import udaf, Accumulator
 
 
-class Accumulator:
+class MyAccumulator(Accumulator):
     """
     Interface of a user-defined accumulation.
     """
     def __init__(self):
         self._sum = pyarrow.scalar(0.0)
 
-    def to_scalars(self) -> [pyarrow.Scalar]:
-        return [self._sum]
-
     def update(self, values: pyarrow.Array) -> None:
         # not nice since pyarrow scalars can't be summed yet. This breaks on `None`
         self._sum = pyarrow.scalar(self._sum.as_py() + pyarrow.compute.sum(values).as_py())
@@ -101,18 +106,25 @@ class Accumulator:
         # not nice since pyarrow scalars can't be summed yet. This breaks on `None`
         self._sum = pyarrow.scalar(self._sum.as_py() + pyarrow.compute.sum(states).as_py())
 
+    def state(self) -> pyarrow.Array:
+        return pyarrow.array([self._sum.as_py()])
+
     def evaluate(self) -> pyarrow.Scalar:
         return self._sum
 
 
-df = ...
+df = ctx.create_dataframe([[batch]])
 
-udaf = f.udaf(Accumulator, pyarrow.float64(), pyarrow.float64(), [pyarrow.float64()])
+my_udaf = udaf(MyAccumulator, pyarrow.float64(), pyarrow.float64(), [pyarrow.float64()], 'stable')
 
 df = df.aggregate(
     [],
-    [udaf(f.col("a"))]
+    [my_udaf(col("a"))]
 )
+
+result = df.collect()[0]
+
+assert result.column(0) == pyarrow.array([6.0])
 ```
 
 ## How to install (from pip)