The λεξις Paper

Full title λεξις (Lexis): A Language Design for Human–AI Collaborative Computation
Authors Paolo Tanzi & Claude (AI assistant)
Published
DOI 10.5281/zenodo.19302004
Repository Zenodo (CERN Open Repository)
Read on Zenodo → Language overview →

Abstract

We present λεξις (Lexis), a language design for human–AI collaborative computation. λεξις collapses the traditional gap between system design notation and executable code by making the diagram the program. The language is grounded in ten geometric primitives organized across five ontological levels, enabling incremental formalization from informal sketch to formally verified specification without changing notation.

λεξις is designed with AI co-authorship as a first-class concern: primitives are geometric and language-agnostic, making them legible to large language models without prompt engineering. An escape hatch mechanism allows natural-language intent to be translated into λεξις graphs, which can then be progressively formalized. We describe the language design, a proof calculus for inline obligations, and a reference implementation as a Lit Web Component (Morphē).

Paper Structure

  1. 1
    Introduction

    The translation gap between design and implementation. Motivation for a unified notation.

  2. 2
    Background

    Visual programming history. Formal methods landscape. Human-AI collaboration models.

  3. 3
    Language Design

    The ten geometric primitives. Syntax and composition rules. Grammar specification.

  4. 4
    Ontological Framework

    The five levels (L1–L5). Progression from sketch to formal proof.

  5. 5
    Proof Calculus

    Inline proof obligations. Type system. Decidability results.

  6. 6
    Implementation

    Morphē canvas as reference implementation. Escape hatch architecture.

  7. 7
    Worked Examples

    Healthcare triage, e-commerce order pipeline, AI tool-call graph in λεξις.

  8. 8
    Related Work

    Comparison with UML, Petri nets, pi-calculus, and visual dataflow languages.

  9. 9
    Conclusion

    Summary, open problems, and roadmap for λεξις v2.

Cite This Work

If you reference λεξις in your research, please use the following BibTeX entry:

@misc{tanzi2026lexis,
  title        = {λεξις (Lexis): A Language Design for Human–AI Collaborative Computation},
  author       = {Tanzi, Paolo and {Claude (AI assistant)}},
  year         = {2026},
  month        = mar,
  doi          = {10.5281/zenodo.19302004},
  url          = {https://doi.org/10.5281/zenodo.19302004},
  publisher    = {Zenodo},
  note         = {Preprint}
}

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