A Monadic Calculus with Episodic Flows
Sotirios Henning
TL;DR
This work builds a monadic-style calculus based on episodic flows, introducing the episodic category $Ep$ and the matrix-like episodic flow category $Φ$ to model computation as nested actions. It develops encodings for numbers, arithmetic, formal logic, typing, and invariants within process lattices, and introduces an information-theoretic notion of episodic entropy to analyze data mutation and memory lifetimes. By treating flows as mathematical objects whose inspection yields results, the framework provides a principled method to reason about success/failure of computations and the reproduction of data structures. The approach promises a quantitative, mutation-aware foundation for reasoning about data encoding, memory behavior, and information-theoretic aspects of computation within a unified categorical setting.
Abstract
We define computational atoms named "actions" equipped primarily with three operations: reduction, collection, and inspection. We show how actions can be used for decision-making algorithms from simple axioms. We describe the encodings of typical data structures as actions, and provide a method of analysis for algorithms on the basis of data mutation.