{
  "annotation_id": "1325e7a5-46a7-40b8-8139-034920fdb8b9",
  "date_created": "2026-03-02T18:02:13.511000Z",
  "date_modified": "2026-03-02T18:02:13.511000Z",
  "file_hash": "c78ee77b006d2d04f63a10d3f05975c9a817cde616331dd399719daba0b1bc08",
  "private": false,
  "record": {
    "abstract": "With a view towards models of quantum computation and/or the interpretation\nof linear logic, we define a functional language where all functions are linear\noperators by construction. A small step operational semantic (and hence an\ninterpreter/simulator) is provided for this language in the form of a term\nrewrite system. The linear-algebraic lambda-calculus hereby constructed is\nlinear in a different (yet related) sense to that, say, of the linear\nlambda-calculus. These various notions of linearity are discussed in the\ncontext of quantum programming languages. KEYWORDS: quantum lambda-calculus,\nlinear lambda-calculus, $\\lambda$-calculus, quantum logics.",
    "arxiv_id": "quant-ph/0501150",
    "authors": [
      "Pablo Arrighi",
      "Gilles Dowek"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Quantum Programming Languages 2004, satellite of LICS, Turku\n  Centre for Computer Science General Publication, Vol. 33, (2004)",
    "title": "Linear-algebraic lambda-calculus",
    "url": "https://arxiv.org/abs/quant-ph/0501150"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "41109ef7-3058-4f50-96a9-1aeb6e4ff4cc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}