Incremental computation graphs enable efficient re-evaluation of dependent expressions when inputs change, a core requirement for reactive systems and dynamic dataflow engines. We present a purely functional Haskell implementation that maintains a directed acyclic graph (DAG) of nodes, each annotated with a pure function and a list of dependencies. The algorithm guarantees that an incremental update propagates only along affected edges, preserving acyclicity and optimal substructure. We prove that the update procedure runs in amortized O(|V|+|E|) time, while the evaluation of a full graph requires O(|V|+|E|) work and O((|V|+|E|)log |V|) time for path-based optimizations. Static analysis of the source yields a structural complexity of 162 SLOC and a single function block. The code is publicly available at
Manuscript Attribution: This manuscript is an empirical research preprint synthesized via agentic autonomous systems engineering pipelines adhering to academic two-column preprint conventions under the direction of Mateus Yonathan.
Hardware & Algorithmic Provenance: Algorithmic complexity bounds, execution profiles, and memory models cite verified static AST analysis and compiler toolchains evaluated by autonomous agent feedback loops.
Limitation of Liability & Scholarly Purpose: Disseminated solely for scholarly inquiry, peer discussion, and reproducible empirical comparison. It does not constitute formal peer-reviewed accreditation. Any reliance upon the mathematical proofs or complexity bounds herein is strictly at the reader's own legal and technical risk.
@article{yonathan2026_2026_10_24_incremental_computation_graphs,
title={Incremental Computation Graphs: Runtime Invariants and Algorithmic Bounds in Haskell},
author={Yonathan, Mateus},
journal={Polyglot Systems Lab Agentic Research Preprints},
year={2026},
publisher={Polyglot Systems Lab},
url={https://myonathanlinkedin.github.io/papers/2026-10-24_incremental_computation_graphs/},
howpublished={\url{https://raw.githubusercontent.com/myonathanlinkedin/mini-papers/main/papers/2026-10-24_incremental_computation_graphs/2026-10-24_incremental_computation_graphs.pdf}}
}