Embody - R&D

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This contains a medley of documents for embody R&D.

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Structural Embodiment: A Theoretical and Practical Analysis of Recursive Object Templating

1. Introduction: The Paradigm of Structural Embodiment

In the domain of software architecture and data engineering, the instantiation of complex object graphs has historically been bifurcated into two distinct paradigms: static class instantiation, governed by the strict rules of compiled languages or runtime interpreters, and textual templating, dominated by string manipulation engines. However, a third paradigm is emerging, driven by the needs of configuration management, dynamic UI generation, and infrastructure-as-code. This paradigm can be formalized as the operation obj = embody(template, parameters). Unlike traditional instantiation, which creates a new instance from a class definition, or textual rendering, which produces a flat string from a template, structural embodiment operates on the topology of data itself. It is the recursive hydration of a skeletal object graph—a template—with context-specific parameters to produce a fully realized, semantically valid data structure.

The term "embodiment" is chosen deliberately to distinguish this process from mere "formatting." Embodiment implies giving concrete form to an abstract schema. It is a process of reification, where a latent structure (the template) is imbued with state (the parameters) to become an active participant in the system's logic. This report provides an exhaustive analysis of this concept, exploring its theoretical roots in computer science and cognitive linguistics, surveying the existing landscape of Python tools that implement variations of this pattern, and detailing the algorithmic mechanics required to build a robust embodiment engine. The analysis further extends to the architectural patterns for "recompiling" these embodied objects into uniform mapping interfaces and concludes with a directive for implementing these systems using modern AI-driven development workflows.

1.1. Theoretical Deconstruction of the Embodiment Operator

To fully appreciate the complexity of embody(template, parameters), one must analyze the nature of the operands. The template is not merely a passive data structure; it is a homomorphic representations of the desired output. In mathematical terms, the relationship between the template and the final object is often a tree homomorphism, where the structure of the template tree maps to the structure of the output tree, but the nodes themselves undergo transformation. The template acts as a higher-order function, a "recipe" or "blueprint," that dictates the topological constraints of the result.

The parameters, conversely, act as the "fluid" that fills the container defined by the template. This interaction is frequently described using the metaphor of "hydration". In modern web development and database interactions, hydration refers to the process of filling a "dry" object—often a serialized representation or a bare-bones instance—with data fetched from a storage layer or API. In structural embodiment, hydration is recursive. A parameter is not always a scalar value; it may be a complex object that requires its own sub-template for proper instantiation. Thus, the embodiment operator is fundamentally recursive: the embodiment of a parent node is contingent upon the successful embodiment of its child nodes, potentially requiring the resolution of dependencies that ripple through the object graph.

1.2. Cognitive Metaphors in Software Scaffolding

Software engineering is a discipline deeply rooted in metaphor. We speak of "building" software, "bugs" in the code, and "architecting" systems. These metaphors are not merely linguistic flourishes but cognitive tools that shape how we reason about abstract concepts. The concept of embodiment relies heavily on the metaphor of scaffolding. Just as physical scaffolding provides a temporary structure that allows a permanent building to be erected, a data template provides the temporary structural context required to organize raw parameters into a coherent object.

Furthermore, the distinction between abstract and concrete concepts is central to this domain. Abstract concepts represent generalized notions or reusable patterns, while concrete concepts are specific instances. The template represents the abstract—the "Platonic ideal" of the object—while the embodied result is the concrete instance. This transition from abstract to concrete is often mediated by "embodied metaphors," where we understand the digital object in terms of physical containment or manipulation. For example, a dictionary is conceptualized as a container (a box or a drawer) that holds values. The embodiment process is the act of placing specific items into these containers. Understanding these metaphors is crucial for designing intuitive APIs for embodiment libraries; if the API contradicts the user's mental model of "filling a container," it will be cognitively dissonant and difficult to use.

1.3. Structural vs. Textual Interpolation

A critical distinction must be drawn between structural interpolation and textual interpolation. Standard templating engines like Jinja2 or the Python string.Template class operate on linear sequences of characters. They scan for delimiters (e.g., ${var}), perform string substitution, and output a stream of text. This is an "isomorphic" operation in the sense that the output is of the same type as the input (text to text), but it is structurally blind. The engine does not know if it is generating HTML, JSON, or Python code; it only knows characters.

Structural embodiment, by contrast, is type-aware and topology-aware. When a substitution marker is encountered within a data structure—for example, a value in a dictionary {'key': '${var}'}—the replacement is not limited to string insertion. If the parameter associated with var is a list ``, structural embodiment replaces the scalar placeholder with the list object itself, altering the graph from a leaf node to a branch node. This capability allows for structural mutation, where the topology of the graph changes based on the data. This is akin to "structural interpolation" in formal verification, where complex data structures like arrays and sets are abstracted and refined. The embodiment engine must therefore respect the contracts of the container types (Lists, Mappings) and ensure that the injection of dynamic data preserves the semantic integrity of the object graph.

2. The Landscape of Existing Tooling and Patterns

Before designing a novel solution for obj = embody(template, parameters), it is rigorous to survey the existing ecosystem. The Python landscape is populated with libraries that solve partial aspects of this problem, ranging from configuration management to object validation. Analyzing these tools reveals the different strategies employed to tackle the challenge of structural hydration.

2.1. Configuration Composition Engines

The most direct implementations of structural embodiment are found in modern configuration management libraries. These tools are designed to take static configuration files (YAML, JSON) and "hydrate" them with environment variables, command-line arguments, and computed values, effectively turning a static description into a dynamic object graph.

2.1.1. OmegaConf: The Resolver Paradigm

OmegaConf stands as a premier example of a library designed for hierarchical configuration merging and variable interpolation. It introduces the concept of Resolvers, which are functions registered to the configuration engine that can be invoked during the value retrieval process. For instance, the syntax ${oc.env:VAR} triggers a resolver that looks up an environment variable.

This maps directly to the embodiment pattern. The DictConfig object acts as the template. The resolvers and the environment act as the parameters. OmegaConf supports "lazy evaluation," meaning the interpolation happens only when the value is accessed. This allows for the definition of cyclic dependencies or complex relationships that are resolved at runtime. OmegaConf also supports "custom resolvers," allowing users to register arbitrary functions (e.g., ${my_func:arg}) that act as dynamic embodiment logic. This transforms the configuration file from a static data store into a reactive data structure.

2.1.2. Hydra: Instantiation as Configuration

Built upon OmegaConf, Hydra takes embodiment to its logical conclusion by introducing Object Instantiation. Hydra allows a configuration dictionary to define a special key, _target_, which specifies a Python class or function. When the hydra.utils.instantiate() function is called on this dictionary, Hydra imports the specified target and passes the remaining dictionary keys as arguments to the constructor.

This is a literal implementation of obj = embody(template). The template is the configuration defining the _target_, and the embodiment process transforms this description into a live Python object instance (e.g., a Neural Network layer, a Database connection). This pattern decouples the system's architecture from its configuration, allowing the behavior of the system to be radically altered by changing the template, without modifying the code.

2.1.3. Dynaconf: Environment-Aware Hydration

Dynaconf focuses heavily on the management of environment variables and multi-layered configuration (default, development, production). It employs a "validator" pattern, ensuring that the hydrated object meets specific constraints (e.g., type checking, existence checks) before it is used. Dynaconf uses specific tokens like @Format and @Jinja to trigger interpolation. The @Jinja token is particularly interesting as it bridges the gap between textual and structural templating, allowing the full power of the Jinja2 template language to be used within specific values of the configuration structure.

2.2. Data Transformation and Traversal Libraries

While configuration libraries focus on creating objects, data transformation libraries focus on reshaping them. These tools provide the "mechanics" for the embodiment process, specifically the traversal and modification of nested structures.

2.2.1. Glom: Declarative Restructuring

Glom offers a declarative approach to data transformation. Instead of writing imperative loops to traverse a structure, the user defines a "spec" (template) that describes the desired output. Glom’s assign function allows for deep modification of structures using dot-notation paths, which is essential for the "Indexed" embodiment strategy. Glom treats the path as a first-class citizen, handling the complexity of navigating through mixed lists and dictionaries, and provides meaningful error messages when paths are invalid.

2.2.2. Dpath: Filesystem Semantics for Data

dpath-python brings the semantics of filesystem operations—specifically globbing—to dictionaries. It allows users to access and modify data using paths like /a/*/b, where * is a wildcard matching any key. This capability is powerful for embodiment templates that need to apply changes to broad categories of data (e.g., "update the 'status' field in all sub-modules") without knowing the exact structure of the tree.

2.3. Textual Engines and Logic

It is worth noting that traditional textual engines like Jinja2 and Cheetah are often used in this domain, primarily to generate JSON or YAML strings which are then parsed. While this approach offers the full Turing-completeness of the template language (loops, macros), it suffers from the "stringly typed" problem. Types are lost during the rendering phase; a float 1.0 might inadvertently become a string "1.0". Debugging syntax errors in the generated JSON is also notoriously difficult, as the error location in the generated string does not easily map back to the source template.

2.4. Data Configuration Languages (Jsonnet)

Jsonnet represents a fusion of data and code. It is a functional configuration language that extends JSON. It supports variables, functions, and "mixins" (object inheritance). Jsonnet templates are evaluated to produce JSON. The "mixin" capability is a sophisticated form of embodiment: a base template can be defined, and then "embodied" by overlaying a parameter object that overrides specific fields or appends to lists. This relies on "late binding," where references to self are resolved only when the final object is materialized.

Table 1: Comparative Analysis of Embodiment Tools

Feature	Jinja2	OmegaConf/Hydra	Jsonnet	Glom	Custom Embody
Primary Domain	Text Generation	Configuration	Data Language	Transformation	Object Templating
Input Type	Text String	YAML / Dict	Jsonnet Code	Python Object	Python Dict/Obj
Output Type	Text String	Python Object	JSON	Python Object	Python Object
Logic Support	High (Loops, Macros)	Moderate (Resolvers)	High (OO, Funcs)	Declarative	Variable
Type Safety	Low (String based)	High (Runtime Typed)	High	High	High (Goal)
Recursion	Manual	Implicit (Lazy)	Implicit	Explicit Spec	Implementation Dependent
Instantiation	No	Yes (_target_)	No (JSON only)	No	Yes (Goal)

3. The Mechanics of Embodiment: Strategies for Implementation

To implement obj = embody(template, parameters), one must choose an algorithmic strategy for traversing the template and injecting the parameters. The research identifies two primary methodologies: Dynamic Traversal (The Visitor) and Indexed Compilation (The Path flattener). Furthermore, the handling of recursive data structures presents specific challenges regarding performance and memory.

3.1. Strategy A: Dynamic Traversal (The Recursive Visitor)

The most intuitive implementation of structural embodiment is the Recursive Visitor pattern. This approach walks the object graph at runtime, visiting each node, determining its type, and making substitution decisions on the fly.

3.1.1. Algorithmic Structure

The algorithm functions as a recursive descent parser adapted for object graphs.

1. Visit Node: The function visit(node, context) is called.
2. Type Check:
   • If node is a Mapping (Dict): Create a new container. Iterate over key, value pairs. Recursively call visit(value, context). Note that keys themselves may require substitution (see Section 3.3).
   • If node is a Sequence (List): Create a new list. Iterate over items. Recursively call visit(item, context).
   • If node is a Scalar (String/Int): Check for substitution syntax (e.g., ${var}). If present, resolve the value from context. If the resolved value is complex, it is returned directly, effectively grafting a new subgraph in place of the leaf node.
3. Return: The constructed object is returned to the caller.

3.1.2. The Visitor Pattern

In Object-Oriented Programming, this is formalized as the Visitor Pattern. A TemplateVisitor class defines methods like visit_dict, visit_list, and visit_str. This separation of concerns allows the traversal logic (how to walk the tree) to be decoupled from the action logic (what to do at each node). This is particularly useful if the template contains custom types; the visitor can simply implement a visit_MyCustomType method to handle them.

3.1.3. Advantages and Limitations

The primary advantage of this approach is Context Awareness. As the visitor descends the tree, it can maintain a stack of scopes, allowing for variable shadowing (where a variable defined in a sub-template overrides a global one). It also supports Lazy Evaluation, where branches are only processed if reached (useful for conditionals).

However, the major limitation is Performance. Python function calls involve significant overhead due to stack frame allocation. Deeply nested structures can trigger a RecursionError if the depth exceeds the interpreter's limit (typically 1000). Furthermore, simple recursion cannot easily handle Reference Cycles (where A points to B, and B points back to A). Without explicit cycle detection (tracking id(node) in a visited set), the embodiment process will enter an infinite loop and crash.

3.2. Strategy B: Indexed Compilation (Path Flattening)

This strategy attempts to linearize the recursive structure, transforming the tree into a flat map of paths and values. This converts the recursive problem into an iterative one, which is generally more performant in Python.

3.2.1. Flattening Mechanics

The first step is to "flatten" the template. A nested dictionary {'a': {'b': 1}} is converted into a flat dictionary where keys are paths:

• 'a.b.0': 1
• 'a.b.1': 2

Libraries like flatten-dict or custom recursive generators are used for this purpose. The separator (usually .) must be chosen carefully to avoid ambiguity with keys that contain the separator. Tuple paths ('a', 'b', 0) are a robust alternative that avoids string parsing ambiguity.

3.2.2. Substitution and Recompilation (Unflattening)

Once flattened, the embodiment engine iterates over the flat dictionary. This is an O(N) linear scan. It identifies keys whose values require substitution (e.g., val == '${x}') and replaces them using the parameter context.

The final step is "unflattening" or "recompiling" the object. This is the inverse operation: taking {'a.b.0': 1} and reconstructing {'a': {'b': 1}}. This is algorithmically complex. The engine must infer container types. If a path contains an integer (.0.), it implies a List; otherwise, it implies a Dictionary. Handling "sparse arrays" (e.g., having a.0 and a.2 but no a.1) requires explicit logic to fill gaps with None or raise errors.

3.2.3. JSON Pointer and Patch Integration

To standardize the path handling, one can leverage JSON Pointer (RFC 6901). Instead of custom dot notation, paths are expressed as /a/b/0. This allows the use of standard libraries like jsonpointer to resolve paths. Furthermore, the embodiment process can be conceptually modeled as generating a JSON Patch (RFC 6902) document. The template is the "original" document. The parameters generate a list of patch operations (e.g., {"op": "replace", "path": "/a/b", "value": "new_val"}). Applying this patch yields the embodied object. This delegates the structural mutation logic to a standardized, battle-tested specification.

3.3. Special Considerations for Mappings

The user specifically requested a focus on Mappings (dictionaries). A unique challenge in Python dictionaries is that keys can also be dynamic. In a structure {'${key_name}': 'value'}, the key itself must be substituted.

• Hash Stability: You cannot modify a dictionary's keys while iterating over it. Doing so invalidates the internal hash table and raises a RuntimeError.
• Reconstruction: The embodiment engine must essentially rebuild the dictionary. It iterates over the template items, resolves the key (if dynamic), resolves the value (recursively), and inserts the pair into a new dictionary.
• Key Collision: If two dynamic keys resolve to the same string, the engine must have a defined behavior (usually last-write-wins or raising an error).

4. Performance Benchmarks: Recursion vs. Flat Access

A critical engineering decision in the implementation of embody is the choice between maintaining nested structures or flattening them for access. Benchmarks and theoretical analysis provide guidance here.

4.1. Lookup Complexity

In a flat dictionary, looking up a value by path (e.g., data['a_b_c']) is an O(1) operation, involving a single hash computation. In a nested dictionary, the lookup data['a']['b']['c'] involves three separate hash computations and three pointer dereferences. Theoretically, the flat approach is faster for deep access.

However, empirical benchmarks in Python suggest that the overhead of constructing the flat key (string concatenation a + '_' + b + '_' + c) often negates the benefit of the single lookup. Python's dictionary implementation is highly optimized C code. Chained lookups are extremely fast. The "flattening" strategy is therefore most beneficial when the structure is static and read-heavy (read-many), justifying the one-time cost of flattening. For "embodiment," which is a write-heavy operation (constructing a new object), the overhead of flattening and unflattening might exceed the cost of simple recursive traversal.

4.2. The Cost of Recursion vs. Iteration

Python does not support Tail Call Optimization (TCO). Every recursive call adds a frame to the stack. For extremely deep structures (e.g., parsing a massive JSON dump), the recursive visitor can crash. Iterative approaches using an explicit stack (a list of nodes to visit) move the memory pressure from the call stack (limited) to the heap (abundant RAM). While recursive code is often more readable and "elegant", a robust production-grade library should likely employ an iterative stack-based walker or provide a configurable backend.

5. Recompiling to Uniform Interfaces

The output of the embodiment process—the "hydrated" object—must be usable by the rest of the application. The user's desire to "go from any nested structure to a uniform Mapping interface" speaks to the need for Interface Adaptation.

5.1. The Uniform Mapping Interface

Python’s collections.abc.Mapping abstract base class defines the contract for read-only mappings. By ensuring the embodied object implements this interface, consumers can treat it as a standard dictionary, regardless of whether it is backed by a YAML file, a database, or a computation.

5.2. Wrapper Patterns (The Box)

A popular pattern for interacting with nested dictionaries is the Box pattern (exemplified by python-box). This wrapper converts dictionary keys into object attributes, allowing obj.key access instead of obj['key']. This "recompilation" involves wrapping the raw dictionary in a proxy class that intercepts attribute access (__getattr__) and delegates it to dictionary lookup (__getitem__). This provides a very fluid developer experience for configuration objects.

5.3. Schema Validation (Marshmallow/Pydantic)

"Recompiling" can also imply Validation. A raw dictionary is structurally loose. Libraries like Pydantic and Marshmallow allow for the definition of rigid schemas. The embodiment process creates the raw dictionary, and then Pydantic "parses" this dictionary into a strictly typed Model. This phase catches errors such as missing fields or incorrect types (e.g., providing a string where an int was expected). This is the ultimate form of "embodiment"—transforming raw data into a guaranteed, type-safe application object.

6. Architectural Blueprint for an Embodiment Engine

Based on the comprehensive analysis, we can now outline the architecture for the Embodiment library. This section provides the technical specifications an AI agent would need to implement this system.

6.1. Core Class Structure

The system should be composed of four primary interacting components:

1. The Context (Parameter Store):
   • Responsibility: Holds the data used for hydration. It must support hierarchical scoping (global params vs. local params).
   • Feature: Resolvers. The Context should not just hold static values; it should support callables. If a parameter is a function func, the embodiment process should call func() to retrieve the value. This allows for dynamic values like timestamps or random numbers.
2. The Weaver (Substitution Engine):
   • Responsibility: The execution engine. It implements the traversal strategy.
   • Design: It should be pluggable, allowing the user to switch between a RecursiveVisitorEngine (for dynamic structures with logic) and a CompiledPathEngine (for static, repetitive instantiation where performance is key).
3. The Template (Scaffold):
   • Responsibility: Wraps the raw template data. It provides methods to parse the structure and identify dependencies (variables).
   • Feature: Cycle Detection. The Template must track visited nodes during traversal to prevent infinite recursion if the graph contains cycles.
4. The Proxy (Interface Layer):
   • Responsibility: The "Uniform Interface." It wraps the final result.
   • Design: Implement collections.UserDict or Mapping. Provide freeze() functionality to make the embodied object immutable after creation, preventing accidental modification of the configuration.

6.2. Implementation Instructions for AI Agents

To utilize an AI Coding Agent (like GitHub Copilot or Replit Agent) to build this system, one must provide a precise "System Prompt" that establishes the persona and constraints.

System Prompt Pattern:

• Role: Expert Python Systems Architect.
• Task: Implement a library Embodiment.
• Constraints:
  1. Type Preservation: Do not cast values to strings. If a parameter is an int, the embodied value must be an int.
  2. Recursion Safety: Use an iterative stack or implement explicit recursion depth checks.
  3. Interface: The result must support both dict access (['k']) and attribute access (.k).
  4. Standard: Use JSON Pointer (RFC 6901) syntax for path addressing internally.

Chain of Thought Prompting:
Use "Chain of Thought" (CoT) prompting to ensure the agent handles the recursive logic correctly.

• Prompt: "Explain step-by-step how the engine handles a template where a key is a variable ${key}. How do you ensure the hash table remains valid during iteration? Write the code only after explaining the algorithm."
• Expected Logic: The agent should identify that the dictionary cannot be modified in place. It must create a new dictionary, iterate the source, resolve keys, resolve values, and populate the new dictionary.

7. Future Outlook and Conclusion

The concept of obj = embody(template, parameters) is moving from a pattern implemented ad-hoc in various scripts to a formalized component of system architecture. As systems become more distributed and configuration becomes more complex (Kubernetes manifests, ML model hyperparameters), the need for robust, type-safe, and structurally aware templating increases.

We are seeing a convergence of Configuration (OmegaConf), Data (Jsonnet), and Code (Hydra). The future of embodiment likely lies in Language-Agnostic Data Protocols—standardizing not just the format (JSON/YAML) but the logic of instantiation (like WASM for configuration).

For the developer, mastering structural embodiment means moving beyond string concatenation. It means treating data topology as a first-class citizen, allowing for the creation of systems that are flexible, verifiable, and deeply expressive. By leveraging the architectures and tools detailed in this report, one avoids "reinventing the wheel" and builds upon a foundation of rigorous computer science and cognitive design.

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Tables and Structured Data

Table 2: Performance Characteristics of Traversal Strategies

Strategy	Setup Cost	Execution Cost	Memory Overhead	Best Use Case
Recursive Visitor	Zero	High (Function calls)	High (Stack frames)	Dynamic, one-off templates
Iterative Stack	Low	Moderate	Moderate (Heap)	Deeply nested structures
Indexed Compilation	High (Flattening)	Low (Linear scan)	Low	Static templates embodied frequently
Lazy Proxy	Zero	High (Per access)	Low	Large configs accessed sparsely

Table 3: Theoretical Mapping of Embodiment Concepts

Concept	Software Metaphor	Mathematical Basis	Implementation Pattern
Template	Blueprint / Scaffold	Tree Homomorphism	Schema / DictConfig
Parameter	Water / Fluid	Variable / Constant	Context / Environment
Embody	Hydration / Construction	Function Application	Factory / Builder
Result	Instance / Concrete Object	Image of Homomorphism	Object / Mapping

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References

Metaphors & Theory

• Scaffolding in Software:(https://openresearch.ocadu.ca/id/eprint/3865/3/Lockton_Metaphors_paper_2021.pdf),(https://whatsthepont.blog/2021/07/25/scaffolding-temporary-lightweight-and-a-utilitarian-metaphor/,(https://whatsthepont.blog/2021/07/25/scaffolding-temporary-lightweight-and-a-utilitarian-metaphor/))
• Embodied Cognition & Metaphors: Manches et al. "Identifying Embodied Metaphors",(https://educery.dev/papers/software-metaphors/)
• Abstract vs Concrete Concepts:(https://medium.com/@sameera.madushan98/abstract-concepts-and-concrete-concepts-a-journey-from-philosophy-to-software-engineering-67a5653d9768)
• Homomorphic Substitutions:(https://www.eecs.harvard.edu/\~shieber/Projects/Transducers/Papers/comon-tata.pdf), Constructing a tree from homeomorphic subtrees

Templating & Configuration Libraries

• Jinja2:(https://jinja.palletsprojects.com/en/stable/templates/)
• OmegaConf:(https://omegaconf.readthedocs.io/),(https://omegaconf.readthedocs.io/en/latest/usage.html,(https://omegaconf.readthedocs.io/en/latest/usage.html))
• Hydra: Hydra Instantiate Objects, Hydra Overview
• Jsonnet: Jsonnet Comparison, Jsonnet Home
• Cheetah:(https://cheetahtemplate.org/)

Data Transformation Tools

• Glom:(https://glom.readthedocs.io/en/latest/),(https://glom.readthedocs.io/en/latest/tutorial.html,(https://glom.readthedocs.io/en/latest/tutorial.html))
• Dpath:(https://pypi.org/project/dpath/)
• JSON Pointer/Patch:(https://jsonpatch.com/),(https://pypi.org/project/jsonpointer/,(https://pypi.org/project/jsonpointer/))

Algorithms & Performance

• Recursion vs Iteration:(https://medium.com/@ireneselenam/big-o-big-efficiency-recursion-vs-iteration-unveiled-f0707501be5b),(https://www.reddit.com/r/programming/comments/19d797p/performance_analysis_of_pythons_dict_and/,(https://www.reddit.com/r/programming/comments/19d797p/performance_analysis_of_pythons_dict_and/))
• Flattening Dictionaries:(https://www.freecodecamp.org/news/how-to-flatten-a-dictionary-in-python-in-4-different-ways/)

AI & Prompting

• Prompt Engineering: OpenAI Prompt Engineering Guide,(https://www.ibm.com/think/topics/chain-of-thoughts)