[DOC] Improve Pattern Language Docs (#5676)

* [DOC] Improve Pattern Language Docs

* address comments

* address comments

docs/langref/relay_pattern.rst

@@ -28,17 +28,35 @@ Such a language is not just useful for building a rewriter but also providing ex
 
 In the backend world, we could use the same machinery to build a higher level API using bring your own code generation. This API takes set of patterns describing your hardware capabilities and an external compiler, providing a relatively smooth heterogeneous experience out of the box.
 
-Examples
-========
+Pattern Examples
+================
 
-There are quite a few properties that are worth matching of operators below we examine how to match tree properties, and expand on some use cases that are not fully explored in the prototype. The first example is a simple case where we want to match one operator with a single input OR another operator with a single input, see the below diagram for a graphical representation and corresponding code::
+There are quite a few properties of operators that are worth matching. Below we examine how to match tree properties, and expand on some use cases that are not fully explored in the prototype. This section
+demonstrates how to write patterns. It is recommended to check `tests/python/relay/test_dataflow_pattern.py`_
+for more use cases.
+
+.. _tests/python/relay/test_dataflow_pattern.py: https://github.com/apache/incubator-tvm/blob/master/tests/python/relay/test_dataflow_pattern.py
+
+Matching One of Two Ops
+***********************
+
+The first example is a simple case where we want to match one operator with a single input OR
+another operator with a single input:
+
+.. code-block:: python
 
     def test_match_op_or():
         is_add_or_sub = is_op('add') | is_op('subtract')
         assert is_add_or_sub.match(relay.op.op.get("add"))
         assert is_add_or_sub.match(relay.op.op.get("subtract"))
 
-The next example is a dense operation with any operator that is marked element-wise::
+
+Matching an Op with Attributes
+******************************
+
+The next example is a dense operation with any operator that is marked element-wise:
+
+.. code-block:: python
 
     def test_no_match_attr():
         op = is_op('nn.dense').has_attr({"TOpPattern": K_ELEMWISE})
@@ -47,6 +65,87 @@ The next example is a dense operation with any operator that is marked element-w
         y = relay.var('y')
         assert not op_pat.match(relay.op.nn.dense(x, y))
 
+Here is another example to match an op with a specific attribute:
+
+.. code-block:: python
+
+    def test_match_data_layout():
+        is_conv2d = is_op('nn.conv2d')(wildcard(), wildcard()).has_attr({"data_layout": "NHWC"})
+        x = relay.var('x')
+        y = relay.var('y')
+        assert not is_conv2d.match(relay.op.nn.conv2d(x, y))
+
+Matching an Optional Op
+***********************
+
+The next example is matching a pattern with one optional operator. In this pattern,
+we can match the graph of conv2d+bias_add+relu or the graph of conv2d+bias_add.
+
+.. code-block:: python
+
+    def test_match_optional():
+        conv_node = is_op('nn.conv2d')(wildcard(), wildcard())
+        bias_node = is_op('nn.bias_add')(conv_node, wildcard())
+        pat = bias_node.optional(lambda x: is_op('nn.relu')(x))
+
+        x = relay.var('x')
+        y = relay.var('y')
+        z = relay.var('z')
+        conv2d = relay.op.nn.conv2d(x, y)
+        bias = relay.op.nn.bias_add(conv2d, z)
+        assert pat.match(bias)
+        relu = relay.op.nn.relu(bias)
+        assert pat.match(relu)
+
+Matching Non-Call Nodes
+***********************
+
+Sometimes we may also want to match a pattern that includes Tuple or TupleGetItem nodes.
+Since there are not call nodes, we need to use specific pattern nodes to match them:
+
+.. code-block:: python
+
+    def test_match_tuple():
+        x = relay.var('x')
+        y = relay.var('y')
+        z = relay.var('z')
+        tuple_pattern = TuplePattern((wildcard(), wildcard(), wildcard()))
+        assert tuple_pattern.match(relay.expr.Tuple((x,y,z)))
+
+The next example is matching a pattern of batch_norm -> get(0) -> relu:
+
+.. code-block:: python
+
+    def test_match_tuple_get_item():
+        bn_node = is_op('nn.batch_norm')(wildcard(), wildcard(), wildcard(), wildcard(), wildcard())
+        tuple_get_item_node = TupleGetItemPattern(bn_node, 0)
+        pat = is_op('nn.relu')(tuple_get_item_node)
+
+        x = relay.var('x', shape=(1, 8))
+        gamma = relay.var("gamma", shape=(8,))
+        beta = relay.var("beta", shape=(8,))
+        moving_mean = relay.var("moving_mean", shape=(8,))
+        moving_var = relay.var("moving_var", shape=(8,))
+        bn_node = relay.nn.batch_norm(x, gamma, beta, moving_mean, moving_var)
+        tuple_get_item_node = bn_node[0]
+        out = relay.nn.relu(tuple_get_item_node)
+        pat.match(out)
+
+The next example is matching function nodes with a specific attribute:
+
+.. code-block:: python
+
+    def test_match_function():
+        pattern = wildcard().has_attr({"Composite": "add"})
+
+        x = relay.var('x')
+        y = relay.var('y')
+        f = relay.Function([x, y], x + y).with_attr("Composite", "add")
+        assert pattern.match(f)
+
+Matching Diamonds and Post-Dominator Graphs
+*******************************************
+
 The next example is matching a diamond with two inputs at the top of the diamond::
 
     def test_match_diamond():
@@ -67,7 +166,7 @@ The next example is matching a diamond with two inputs at the top of the diamond
         # Check
         assert diamond.match(out)
 
-The final example  is matching diamonds with a post-dominator relationship. We embed dominator analysis as type of matching in the pattern language in order to allow for pattern matching with unknown topology. This is important because we want to be able to use the language to describe fuse patterns, like elementwise operations followed by a conv2d::
+The final example is matching diamonds with a post-dominator relationship. We embed dominator analysis as type of matching in the pattern language in order to allow for pattern matching with unknown topology. This is important because we want to be able to use the language to describe fuse patterns, like elementwise operations followed by a conv2d::
 
     def test_match_dom_diamond():
         # Pattern
@@ -86,8 +185,8 @@ The final example  is matching diamonds with a post-dominator relationship. We e
         # Check
         assert diamond.match(out)
 
-Design
-======
+Pattern Language Design
+=======================
 
 The pattern language proposed is designed to be a mirror of Relay's IR with additional support for common scenarios. The goal of the pattern language is to provide a regular-expression like capability for matching data-flow graphs and doing rewriting.
 
@@ -139,3 +238,124 @@ Domination
 **********
 
 Match child pattern, find a match for the parent pattern, insuring that the child ultimately dominates the parrent (i.e., no nodes outside the pattern use outputs of the parent), and that ever node betwen the child and the pattern matches the path pattern.
+
+Applications
+============
+
+The pattern language provides not only the pattern matching but also pattern processing.
+Here we introduce two pattern processing approaches and provide some examples.
+
+Pattern Rewriting
+*****************
+
+If you would like to replace the matched pattern with another subgraph, you can leverage
+the ``rewrite`` transformation. Here is an example of rewriting a series of arithmetic operators
+with a single batch_norm op:
+
+.. code-block:: python
+
+    class BatchnormCallback(DFPatternCallback):
+        # A callback class to rewrite the matched pattern to a batch_norm op.
+        def __init__(self):
+            self.x = wildcard()
+            self.var = wildcard()
+            self.mean = wildcard()
+            self.beta = wildcard()
+            self.gamma = wildcard()
+            self.eps = wildcard()
+            
+            self.pattern = self.gamma * (self.x - self.mean)/is_op("sqrt")(self.var + self.eps) + self.beta
+
+        def callback(self, pre, post, node_map):
+            x = node_map[self.x][0]
+            var = node_map[self.var][0]
+            mean = node_map[self.mean][0]
+            beta = node_map[self.beta][0]
+            gamma = node_map[self.gamma][0]
+            eps = node_map[self.eps][0]
+            return relay.op.nn.batch_norm(x, gamma, beta, mean, var, epsilon = eps.data.asnumpy().item())[0]
+
+        # A graph of arithmetic operators that are functional equivalent to batch_norm.
+        x = relay.var('x')
+        var = relay.var('var')
+        mean = relay.var('mean')
+        beta = relay.var('beta')
+        gamma = relay.var('gamma')
+        BN = gamma * (x - mean)/relay.op.sqrt(var + relay.const(1e-5)) + beta
+
+        from tvm.relay.dataflow_pattern import rewrite
+        out = rewrite(BatchnormCallback(), BN)
+        assert tvm.ir.structural_equal(out, relay.op.nn.batch_norm(x, gamma, beta, mean, var, epsilon = 1e-5)[0])
+
+The function ``def callback(self, pre, post, node_map)`` will be invoked when the rewriter matches
+``self.pattern``. ``node_map`` is a dictionary mapping from pattern nodes to matched nodes in the graph.
+
+Pattern Partitioning
+********************
+
+If you would like to perform a more complex processing for matched subgraphs and you are not
+satisfied with ``rewrite``, you may consider partitioning the matched subgraphs to a separate
+Relay function and perform other processes to the function. Here we use ``pattern.partition``
+to create a new Relay function for each matched subgraph. The functionality is similar to
+the op fusion pass in TVM:
+
+.. code-block:: python
+
+    # A pattern matching conv2d+relu.
+    pattern = is_op("nn.relu")(is_op("nn.conv2d")(wildcard(), wildcard()))
+
+    # A graph.
+    x = relay.var('input')
+    w = relay.var('weight')
+    conv2d = relay.op.nn.conv2d(x, w)
+    relu = relay.op.nn.relu(conv2d)
+    print('relu')
+    # free_var %x: Tensor[(1, 3, 224, 224), float32]
+    # free_var %w: Tensor[(3, 3, 3, 3), float32]
+    # %0 = nn.conv2d(%x, %w, padding=[0, 0, 0, 0]) /* ty=Tensor[(1, 3, 222, 222), float32] */;
+    # free_var %b: Tensor[(3), float32]
+    # nn.bias_add(%0, %b) /* ty=Tensor[(1, 3, 222, 222), float32] */
+
+    # After partition.
+    print(pattern.partition(relu))
+    # free_var %x: Tensor[(1, 3, 224, 224), float32]
+    # free_var %w: Tensor[(3, 3, 3, 3), float32]
+    # free_var %b: Tensor[(3), float32]
+    # %1 = fn (%FunctionVar_0_0, %FunctionVar_0_1,
+    #          %FunctionVar_0_2, PartitionedFromPattern="nn.conv2d_nn.bias_add_") {
+    #   %0 = nn.conv2d(%FunctionVar_0_0, %FunctionVar_0_1, padding=[0, 0, 0, 0]);
+    #   nn.bias_add(%0, %FunctionVar_0_2)
+    # };
+    # %1(%x, %w, %b)
+
+Note that you can also specify the attributes for the created functions:
+
+.. code-block:: python
+
+    print(pattern.partition(relu, {'Composite': 'one_layer'}))
+    # free_var %x: Tensor[(1, 3, 224, 224), float32]
+    # free_var %w: Tensor[(3, 3, 3, 3), float32]
+    # free_var %b: Tensor[(3), float32]
+    # %1 = fn (%FunctionVar_0_0, %FunctionVar_0_1,
+    #          %FunctionVar_0_2, Composite="one_layer",
+    #                            PartitionedFromPattern="nn.conv2d_nn.bias_add_") {
+    #   %0 = nn.conv2d(%FunctionVar_0_0, %FunctionVar_0_1, padding=[0, 0, 0, 0]);
+    #   nn.bias_add(%0, %FunctionVar_0_2)
+    # };
+    # %1(%x, %w, %b)
+
+If you need a customized checking function that cannot be specified using pattern language,
+you can specify ``check`` function when partitioning. The following example demonstrates a
+case that checks input data layout of a subgraph:
+
+.. code-block:: python
+
+    def check(pre):
+        conv = pre.args[0]
+        return (conv.attrs.data_layout == "NCHW") and bool(conv.checked_type.shape[0] == 1)
+
+    pattern.partition(relu, check=check)
+
+In this example, we check if the first argument of the matched subgraph (i.e., ``pre.args[0]``)
+has data layout "NCHW" and if its batch size is 1. This feature is useful if the conditions
+of matching a pattern cannot be verified by analyzing the pattern itself.