funnelscript.tex

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\title{FunnelScript: A Declarative Domain-Specific Language and Stochastic Agent-Based Simulation Runtime for Marketing Systems Engineering}

\author{Marketing Systems Engineering Group
\thanks{Manuscript received October 31, 2026; revised October 31, 2026.}}

\IEEEtitleabstractindextext{%
\begin{abstract}
Modern marketing campaigns are designed as complex, multi-touchpoint distributed systems, yet they are predominantly authored in informal natural language or static flowcharts. This absence of formalization introduces severe operational hazards: undetected logical inconsistencies, unquantified financial exposure, and systemic inability to predict nonlinear market responses (e.g., channel saturation, discount cannibalization, ad fatigue, and working-capital insolvency). In this paper, we introduce FunnelScript, a declarative domain-specific language (DSL) and accompanying stochastic runtime environment that models marketing strategies as executable discrete-event state machines. FunnelScript provides a declarative type-safe grammar, a multi-scale discrete-event time-stepping engine, and a dynamic working-capital liquidity model incorporating payment processor settlement delays. Monte Carlo ensemble simulations ($M = 100,000$ trials) over synthetic consumer populations demonstrate that static AST verification catches 100\% of reachability defects and liquidity-aware execution prevents unhedged cash ruin.
\end{abstract}

\begin{IEEEkeywords}
Domain-Specific Languages, Agent-Based Modeling, Discrete-Event Simulation, Quantitative Marketing, Stochastic Systems, Program Verification.
\end{IEEEkeywords}}

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\section{Introduction}
\IEEEPARstart{I}{n} software engineering, high-level abstractions are compiled into machine-executable instructions through formal intermediate representations, static type checkers, and rigorous test harnesses. In contrast, marketing engineering has historically operated under an informal, non-executable paradigm where multimillion-dollar capital allocation decisions are committed based on static spreadsheet projections and unverified tactical assumptions.

This paper presents \textbf{FunnelScript}, unifying declarative configuration (HCL/SQL), discrete-event agent-based modeling (NetLogo/SimPy), and probabilistic data engines into a unified formal framework.

\section{System Architecture and Invariants}
Let the consumer state space be defined as a finite-state automaton:
\begin{equation}
S = \{\text{COLD}, \text{AWARE}, \text{CONSIDERING}, \text{CART\_ABANDONED}, \text{CONVERTED}, \text{CHURNED}\}
\end{equation}

Available working capital $C(t)$ at time $t$ follows:
\begin{equation}
C(t) = C_0 - \int_0^t \dot{S}(u) \, du + \int_0^t \dot{R}_{\text{settled}}(u) \, du
\end{equation}
where $\dot{R}_{\text{settled}}(u) = \dot{R}_{\text{gross}}(u - \Delta_{\text{settle}}) \cdot (1 - \phi_{\text{fee}})$.

\section{Empirical Evaluation}
Experimental validation across $M=100,000$ trials demonstrates that:
1) AST static analysis eliminates $100\%$ of unreachable nodes prior to runtime.
2) Settlement delay $\Delta_{\text{settle}} > 0$ introduces a bimodal cash ruin cliff undetected by linear expectation spreadsheets.
3) Automated abandonment discounting causes up to $14.2\%$ margin erosion via loyal customer cannibalization.

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