Add Programming section

doc/design/api.md

-# Design Doc: PaddlePaddle API
+# PaddlePaddle API
 
 ## Ingredients
 
@@ -27,8 +27,8 @@ indicates a *reference*, and `-` marks a "class method".
 
 ### Model
 
-We used to think that parameters are part of the toplogy (or layers).
-But that is not true, because multiple layers could share the same
+We used to think that parameters are part of the topology (or layers).
+But that is not true because multiple layers could share the same
 parameter matrix.  An example is a network that compares two text
 segments in a semantic space:
 
@@ -56,8 +56,7 @@ parameter sharing, please refer to [TODO: API].
 Supposed that we have a trained ranking model, we should be able to
 use it in our search engine.  The search engine's Web server is a
 concurrent program so to serve many HTTP requests simultaneously.  It
-doens't make sense for each of these threads to have its own copy of
-model, because that would duplicate topologies and parameters.
+doesn't make sense for each of these threads to have its own copy of the model because that would duplicate topologies and parameters.
 However, each thread should be able to record layer outputs, i.e.,
 activations, computed from an input, derived from the request.  With
 *Evaluator* that saves activations, we can write the over-simplified
@@ -86,5 +85,193 @@ Hence the `GradientMachine`.
 
 None of Model, Evaluator, nor GradientMachine implements the training
 loop, hence Optimizer.  We can define a concurrent optimizer that runs
-multiple simultaneious threads to train a model -- just let each
+multiple simultaneous threads to train a model -- just let each
 thread has its own GradientMachine object.
+
+Most models should be able to be trained using the
+`paddle.optimizer.SGD` by calling its `train` method.  Many
+customizations to the SGD algorithm happens with the update equation,
+e.g., momentum and the Adam SGD algorithm.  We make `train` calls
+`update` to do an update, so that we can derive a `paddle.optimizer.Adam`
+from `paddle.optimizer.SGD` by overrides only the `update` method.
+
+
+## Programming
+
+A fictive example of PaddlePaddle program looks like the following:
+
+```python
+import paddle
+
+def read(args):
+    f = open_file(args["filename"])
+    mb = read_a_minibatch(f)
+    end_pass = eof(f)
+    if end_pass:
+       f = open_file(args["filename"]) # rewind for reading again
+    yield mb, end_pass
+
+input = paddle.layer.data(...)
+intermediate = paddle.layers.fc(input)
+output = paddle.layer.softmax(intermediate)
+
+model = paddle.model.create(output)
+
+paddle.train(model, data_provider=read)
+```
+
+This shows some important part of a program:
+
+1. Define how to read (and augment) data by defining a function, in
+   this example, `read`, that `yields` a minibatch and a boolean flag
+   `eof_of_pass`.
+
+1. Define the topology, `input`, `intermediate`, and `output` in this
+   example.
+
+1. Create parameters from the topology thus forms the model by calling
+   `paddel.model.create`.
+
+1. Train the model by calling `paddle.train`.
+
+
+### Reader
+
+Not all programming frameworks allow users to define I/O functions.
+An example is Google MapReduce, which can only read from text,
+SSTable, and RecordIO files.  Hadoop MapReduce allows users to define
+readers and writers by deriving from base classes `Reader` and
+`Writer`.  The former is less flexible but also less error-prone.  We
+decide to provide the flexibility to users to define their readers.
+
+
+#### A Synthetic Data Reader
+
+Sometimes we want to test a topology and/or a training algorithm using
+synthetic data.  We can do this by defining the reader a synthesizer:
+
+```python
+def read(args):
+    x = sample_from_uniform(0.0, 1.0)
+    y = sample_from_gauss(2 * x, sigma)
+    yield {x, y}, False # no end-of-file so no end-of-pass
+```
+
+#### A Reader for Online Learning
+
+Readers can also read an infinite data stream, e.g., a log stream from
+a search engine and collected by Kafka:
+
+```python
+def read(args):
+    log_stream = kafka.open_channel(args["kafka channel name"])
+    yeild log_stream.read(), False # no end-of-pass in online learning
+```
+
+### Topology
+
+By default, layers don't have names.  But if we want to refer to a
+layer later some time, for example, when we do serving using the model
+and wants activations/outputs of a layer, we should give it a name.
+
+```python
+input = paddle.layer.data(...)
+intermediate = paddle.layer.fc(input, name="inter", ...)
+output = paddle.layer.softmax(intermediate, name="output", ...)
+
+m = paddle.model.create(output)
+e = paddle.evaluator.create(model)
+e.forward(read_an_input()) # compute activations of all layers.
+print e.activations(layer="inter")  # retrieve the activations of layer "inter"
+print e.activations(layer="output") # retrieve the activations of layer "output"
+```
+
+#### Sharing Parameters
+
+In [above section](#model) we shows a network whose two layers share
+the same parameter matrix.  To specify such cases, we give "parameter
+names" to layers.  If some layers have the same paraemter names,
+`paddle.model.create` creates a single parameter matrix for these
+layers:
+
+```python
+text1 = paddle.layer.data(...)
+sematic1 = paddle.layer.fc(text1, ..., parameter_name="sematic_projection")
+text2 = paddle.layer.data(...)
+sematic2 = paddle.layer.fc(text2, ..., parameter_name="sematic_projection")
+out = paddle.layer.cosine(semantic1, semantic2)
+```
+
+We can also share parameter matrices between layers in different
+models.  To do this, we need an additional parameter that refers to a
+model:
+
+```python
+model1_input = paddle.layer.data(...)
+model1_output = paddle.layer.softmax(model1_input, ...,
+                                     parameter_name="a_parameter_matrix")
+model1 = paddle.model.create(model1_output)
+
+# Another model
+model2_semantic = paddle.layer.fc(text2, ...,
+                                  parameter_name="a_parameter_matrix",
+                                  parameter_model=model1)
+```
+
+### Training
+
+The recommended way to training a model is to call `paddle.train`,
+which simply calls `paddle.optimizer.Default`, a global variable of
+type `paddle.optimizer.SGD`.  Equivalently, we can do
+
+```python
+opt = paddle.optimizer.SGD(...)
+opt.train(model, reader=read, ...)
+```
+
+#### Distributed Training
+
+If users want to do distributed training on a cluster, s/he should
+call `paddle.dist_train` and provides access tokens to the cluster as
+a parameter.
+
+For example, if the user has a TLS certificate that allows him to
+access a Kubernetes cluster, s/he should be able to call
+
+```python
+paddle.dist_train(model,
+                  reader=read,
+                  optimizer=paddle.optimizer.SGDOptimizer(...),
+                  k8s_user="yi",
+                  k8s_token="kube_cluster_tls.pem",
+                  k8s_job="hello",
+                  num_parameter_servers=15)
+```
+
+The pseudo code if `paddle.dist_train` is as follows:
+
+```python
+def dist_train():
+    if os.getenv("KUBERNETES_SERVICE_HOST") == None:
+        image_name = k8s_user + '/' + k8s_job
+        docker_build(image_name)
+        docker_push()
+        kube_ctrl_start_job(image_name, k8s_user, k8s_token)
+    else:
+        rank = kube_list_containers_in_job_and_return_current_containers_rank()
+        if rank == 0:
+            master()
+        elif rank < 15:
+            parameter_server()
+        else:
+            optimizer.train(model, reader=read)
+```
+
+Please be aware that if a process is running on the Kubernetes
+cluster, it will have some environment variables pre-defined.
+
+If `dist_train` doesn't see these environment variables, it knowns
+that it's running on users' personal computer, and it should work as a
+*launcher*.  Otherwise, it knows that it's running on the cluster and
+need to figure out its role as either the master, or a trainer, or a
+parameter server.