core[patch]: fix nested sections for mustache templating (#23747)

The prompt template variable detection only worked for singly-nested
sections because we just kept track of whether we were in a section and
then set that to false as soon as we encountered an end block. i.e. the
following:

```
{{#outerSection}}
    {{variableThatShouldntShowUp}}
    {{#nestedSection}}
        {{nestedVal}}
    {{/nestedSection}}
    {{anotherVariableThatShouldntShowUp}}
{{/outerSection}}
```

Would yield `['outerSection', 'anotherVariableThatShouldntShowUp']` as
input_variables (whereas it should just yield `['outerSection']`). This
fixes that by keeping track of the current depth and using a stack.

libs/core/langchain_core/prompts/string.py

@@ -97,19 +97,18 @@ def mustache_template_vars(
 ) -> Set[str]:
     """Get the variables from a mustache template."""
     vars: Set[str] = set()
-    in_section = False
+    section_depth = 0
     for type, key in mustache.tokenize(template):
         if type == "end":
-            in_section = False
-        elif in_section:
-            continue
+            section_depth -= 1
         elif (
             type in ("variable", "section", "inverted section", "no escape")
             and key != "."
+            and section_depth == 0
         ):
             vars.add(key.split(".")[0])
         if type in ("section", "inverted section"):
-                in_section = True
+            section_depth += 1
     return vars
 
 
@@ -122,12 +121,15 @@ def mustache_schema(
     """Get the variables from a mustache template."""
     fields = {}
     prefix: Tuple[str, ...] = ()
+    section_stack: List[Tuple[str, ...]] = []
     for type, key in mustache.tokenize(template):
         if key == ".":
             continue
         if type == "end":
-            prefix = prefix[: -key.count(".")]
+            if section_stack:
+                prefix = section_stack.pop()
         elif type in ("section", "inverted section"):
+            section_stack.append(prefix)
             prefix = prefix + tuple(key.split("."))
             fields[prefix] = False
         elif type in ("variable", "no escape"):

libs/core/tests/unit_tests/prompts/test_prompt.py

@@ -141,6 +141,115 @@ def test_mustache_prompt_from_template() -> None:
         },
     }
 
+    # more complex nested section/context variables
+    template = """This{{#foo}}
+        {{bar}}
+        {{#baz}}
+            {{qux}}
+        {{/baz}}
+        {{quux}}
+    {{/foo}}is a test."""
+    prompt = PromptTemplate.from_template(template, template_format="mustache")
+    assert prompt.format(
+        foo={"bar": "yo", "baz": [{"qux": "wassup"}], "quux": "hello"}
+    ) == (
+        """This
+        yo
+            wassup
+        hello
+    is a test."""
+    )
+    assert prompt.input_variables == ["foo"]
+    assert prompt.input_schema.schema() == {
+        "title": "PromptInput",
+        "type": "object",
+        "properties": {"foo": {"$ref": "#/definitions/foo"}},
+        "definitions": {
+            "foo": {
+                "title": "foo",
+                "type": "object",
+                "properties": {
+                    "bar": {"title": "Bar", "type": "string"},
+                    "baz": {"$ref": "#/definitions/baz"},
+                    "quux": {"title": "Quux", "type": "string"},
+                },
+            },
+            "baz": {
+                "title": "baz",
+                "type": "object",
+                "properties": {"qux": {"title": "Qux", "type": "string"}},
+            },
+        },
+    }
+
+    # triply nested section/context variables
+    template = """This{{#foo}}
+        {{bar}}
+        {{#baz.qux}}
+            {{#barfoo}}
+                {{foobar}}
+            {{/barfoo}}
+            {{foobar}}
+        {{/baz.qux}}
+        {{quux}}
+    {{/foo}}is a test."""
+    prompt = PromptTemplate.from_template(template, template_format="mustache")
+    assert prompt.format(
+        foo={
+            "bar": "yo",
+            "baz": {
+                "qux": [
+                    {"foobar": "wassup"},
+                    {"foobar": "yoyo", "barfoo": {"foobar": "hello there"}},
+                ]
+            },
+            "quux": "hello",
+        }
+    ) == (
+        """This
+        yo
+            wassup
+                hello there
+            yoyo
+        hello
+    is a test."""
+    )
+    assert prompt.input_variables == ["foo"]
+    assert prompt.input_schema.schema() == {
+        "title": "PromptInput",
+        "type": "object",
+        "properties": {"foo": {"$ref": "#/definitions/foo"}},
+        "definitions": {
+            "foo": {
+                "title": "foo",
+                "type": "object",
+                "properties": {
+                    "bar": {"title": "Bar", "type": "string"},
+                    "baz": {"$ref": "#/definitions/baz"},
+                    "quux": {"title": "Quux", "type": "string"},
+                },
+            },
+            "baz": {
+                "title": "baz",
+                "type": "object",
+                "properties": {"qux": {"$ref": "#/definitions/qux"}},
+            },
+            "qux": {
+                "title": "qux",
+                "type": "object",
+                "properties": {
+                    "foobar": {"title": "Foobar", "type": "string"},
+                    "barfoo": {"$ref": "#/definitions/barfoo"},
+                },
+            },
+            "barfoo": {
+                "title": "barfoo",
+                "type": "object",
+                "properties": {"foobar": {"title": "Foobar", "type": "string"}},
+            },
+        },
+    }
+
     # section/context variables with repeats
     template = """This{{#foo}}
         {{bar}}