Add caching to BaseChatModel (issue #1644) (#5089)

#  Add caching to BaseChatModel
Fixes #1644

(Sidenote: While testing, I noticed we have multiple implementations of
Fake LLMs, used for testing. I consolidated them.)

## Who can review?
Community members can review the PR once tests pass. Tag
maintainers/contributors who might be interested:
Models
- @hwchase17
- @agola11

Twitter: [@UmerHAdil](https://twitter.com/@UmerHAdil) | Discord:
RicChilligerDude#7589

---------

Co-authored-by: Harrison Chase <hw.chase.17@gmail.com>

docs/docs_skeleton/docs/modules/model_io/models/chat/how_to/chat_model_caching.mdx

@@ -0,0 +1,9 @@
+# Caching
+LangChain provides an optional caching layer for Chat Models. This is useful for two reasons:
+
+It can save you money by reducing the number of API calls you make to the LLM provider, if you're often requesting the same completion multiple times.
+It can speed up your application by reducing the number of API calls you make to the LLM provider.
+
+import CachingChat from "@snippets/modules/model_io/models/chat/how_to/chat_model_caching.mdx"
+
+<CachingChat/>

docs/snippets/modules/model_io/models/chat/how_to/chat_model_caching.mdx

@@ -0,0 +1,97 @@
+```python
+import langchain
+from langchain.chat_models import ChatOpenAI
+
+llm = ChatOpenAI()
+```
+
+## In Memory Cache
+
+
+```python
+from langchain.cache import InMemoryCache
+langchain.llm_cache = InMemoryCache()
+
+# The first time, it is not yet in cache, so it should take longer
+llm.predict("Tell me a joke")
+```
+
+<CodeOutputBlock lang="python">
+
+```
+    CPU times: user 35.9 ms, sys: 28.6 ms, total: 64.6 ms
+    Wall time: 4.83 s
+    
+
+    "\n\nWhy couldn't the bicycle stand up by itself? It was...two tired!"
+```
+
+</CodeOutputBlock>
+
+
+```python
+# The second time it is, so it goes faster
+llm.predict("Tell me a joke")
+```
+
+<CodeOutputBlock lang="python">
+
+```
+    CPU times: user 238 µs, sys: 143 µs, total: 381 µs
+    Wall time: 1.76 ms
+
+
+    '\n\nWhy did the chicken cross the road?\n\nTo get to the other side.'
+```
+
+</CodeOutputBlock>
+
+## SQLite Cache
+
+
+```bash
+rm .langchain.db
+```
+
+
+```python
+# We can do the same thing with a SQLite cache
+from langchain.cache import SQLiteCache
+langchain.llm_cache = SQLiteCache(database_path=".langchain.db")
+```
+
+
+```python
+# The first time, it is not yet in cache, so it should take longer
+llm.predict("Tell me a joke")
+```
+
+<CodeOutputBlock lang="python">
+
+```
+    CPU times: user 17 ms, sys: 9.76 ms, total: 26.7 ms
+    Wall time: 825 ms
+
+
+    '\n\nWhy did the chicken cross the road?\n\nTo get to the other side.'
+```
+
+</CodeOutputBlock>
+
+
+```python
+# The second time it is, so it goes faster
+llm.predict("Tell me a joke")
+```
+
+<CodeOutputBlock lang="python">
+
+```
+    CPU times: user 2.46 ms, sys: 1.23 ms, total: 3.7 ms
+    Wall time: 2.67 ms
+
+
+    '\n\nWhy did the chicken cross the road?\n\nTo get to the other side.'
+```
+
+</CodeOutputBlock>

docs/snippets/modules/model_io/models/llms/how_to/llm_caching.mdx

@@ -14,7 +14,7 @@ from langchain.cache import InMemoryCache
 langchain.llm_cache = InMemoryCache()
 
 # The first time, it is not yet in cache, so it should take longer
-llm("Tell me a joke")
+llm.predict("Tell me a joke")
 ```
 
 <CodeOutputBlock lang="python">
@@ -32,7 +32,7 @@ llm("Tell me a joke")
 
 ```python
 # The second time it is, so it goes faster
-llm("Tell me a joke")
+llm.predict("Tell me a joke")
 ```
 
 <CodeOutputBlock lang="python">
@@ -64,7 +64,7 @@ langchain.llm_cache = SQLiteCache(database_path=".langchain.db")
 
 ```python
 # The first time, it is not yet in cache, so it should take longer
-llm("Tell me a joke")
+llm.predict("Tell me a joke")
 ```
 
 <CodeOutputBlock lang="python">
@@ -82,7 +82,7 @@ llm("Tell me a joke")
 
 ```python
 # The second time it is, so it goes faster
-llm("Tell me a joke")
+llm.predict("Tell me a joke")
 ```
 
 <CodeOutputBlock lang="python">