FAOPs: Normal Forms and an Algebra for AI Agent Workflows

원문 초록

Organizations increasingly encode operational procedures as multi-step agent skills, here called Agent Operating Procedures (AOPs), that must be traceable, auditable, reproducible, access-controlled, and bounded in time and cost, as regulated sectors require. Yet AOPs are typically kept as coarse-grained files, in which steps bundle actions, copied procedures drift apart, any step may reach any tool, and refactoring goes unchecked. We present Functional Agent Operating Procedures (FAOP), a formal theory that brings database-grade discipline to AI agent workflows. FAOP recasts each workflow as a typed function over scoped state and subjects an entire library to four progressive normal forms: Decomposed (FNF-1) splits a workflow into atomic steps, Typed (FNF-2) makes its data flow explicit and type-checked, Factored (FNF-3) gives each shared sub-workflow a single canonical definition so a change propagates instead of drifting, and Scoped (FNF-4) checks that each FAOP lists resources used by its own actions and the FAOPs it calls, while guardrails declared by it and by FAOPs that call it remain attached to their sources. A FAOP algebra of provably sound equalities turns refactoring and parallelization into compiler rewrites; orthogonal extensions add optimization (+O), bounded completion with time and cost limits (+B), and reachability checks (+R); and an architectural-level classifier (0-3) determines whether a workflow needs AI at all. Together, these make integrity, isolation, typing, stopping limits, cost, and optimization compile-time concerns across the whole library, not runtime hopes. We implement the theory in SkillBase, an AOP management system (what PostgreSQL is to data, SkillBase is to AOPs), and a separate executor that loads FAOPs from SkillBase and enforces these guarantees at run time. A worked financial workflow illustrates the approach end to end.