GPT-4 Functions as Monoidal Structures: Sequential ∘ and Parallel ⊗ (lightcapai.medium.com)

The piece presents a practical tutorial showing how to treat GPT-4 tools as typed morphisms with explicit contracts and compose them using a monoidal structure: sequential composition (g ∘ f) and parallel composition (f ⊗ g). Using the gpt-4-0613 function-calling API, developers register functions with JSON parameter schemas and let the model choose function calls ("function_call":"auto"). The model plans which tool to call, returns a function-call message; the developer executes the function, returns its result as a "function" role message, and the loop continues until the model emits a final content response. The tutorial walks through a concrete sequential example—get_population -> get_wikipedia_summary—to show how outputs feed into subsequent calls and produce a combined answer. Technically, the approach enforces type alignment (f: A→B, g: B→C) so composed pipelines map A→C safely, reducing format errors and hallucination. Sequential composition maps cleanly to monadic workflows (handling dependent, ordered effects like I/O or state), while parallel composition corresponds to applicative patterns (independent calls whose results are aggregated, enabling concurrency and efficiency). Implications for the AI/ML community include more modular, debuggable agent design, predictable effect handling (retries, failure modes), and clearer programmatic orchestration of multi-step reasoning using LLMs.