Add memory to sql chain (#8597)

continuation of PR #8550

@hwchase17 please see and merge. And also close the PR #8550.

---------

Co-authored-by: Harrison Chase <hw.chase.17@gmail.com>
Co-authored-by: Erick Friis <erick@langchain.dev>

libs/experimental/langchain_experimental/sql/base.py

@@ -122,6 +122,9 @@ class SQLDatabaseChain(Chain):
             "table_info": table_info,
             "stop": ["\nSQLResult:"],
         }
+        if self.memory is not None:
+            for k in self.memory.memory_variables:
+                llm_inputs[k] = inputs[k]
         intermediate_steps: List = []
         try:
             intermediate_steps.append(llm_inputs)  # input: sql generation