Computable Structuralism: A Categorical Rewrite Calculus of Mythic Variants

TL;DR

This paper introduces a formal categorical framework for analyzing myths and narratives, enabling cross-tradition comparison and computational modeling of story variants, coherence, and order effects.

Contribution

It develops a novel mathematical model using rewrite calculus and natural transformations to formalize narrative structures and transformations across diverse storytelling traditions.

Findings

Applied to 80 narratives across genres, successfully modeled variants and coherence data.

74% of stories explicitly encode normative constraints supporting the model.

Provides a bridge between structural anthropology and computational cultural analysis.

Abstract

Structural approaches to myth and narrative are compelling in close reading but hard to compare across traditions, media, and scale. We propose a formal framework that renders L\'evi-Straussian transformation as mathematics while remaining readable as narrative analysis. Variants, superhero continuities, and franchise arcs are modeled as typed rewrite programs on a coupled two-register state $(X,Y)$, abstracting an everyday/social channel and a symbolic/legitimation channel. The canonical formula becomes coherence data: a natural transformation $\eta:U\Rightarrow V$ between update endofunctors, where $U$ updates each register in place and $V$ performs a swap+inversion. Context is internalized by operator choice, turning naturality into a corpus-facing type check: failures diagnose mis-specified oppositions or illegal transport; successes witness coherent structural models. Order effects are summarized by a five-value invariant (Key). We apply the method to 80 narratives (20 folktales, 20 religious myths, 20 superheroes, 20 franchises), each encoded as $(a,b,x,y)$ with a Key. 59/80 (74\%) explicitly name a normative constraint in $y$ (law, taboo, contract, prophecy), supporting the two-register abstraction. The result is a testable bridge between structural anthropology and cultural analytics: stories remain interpretable yet become transportable objects for computation, comparison, and falsifiable constraints on transformation.