{
  "paper": {
    "title": "Milner's Lambda-Calculus with Partial Substitutions",
    "authors": ["Delia Kesner", "Shane Ó Conchúir"],
    "url": "https://arxiv.org/abs/2312.13270",
    "html": "https://arxiv.org/html/2312.13270v1"
  },
  "milestones": ["M0", "M1", "M2", "M3", "M4", "M5", "M6"],
  "current": "M0",
  "nodes": [
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      "section": "",
      "file": "theory/ExecReducer.v",
      "depends": []
    },
    {
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      "depends": ["exec_step"]
    },
    {
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    },
    {
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    },
    {
      "id": "lemma_2_1_fv_preserved",
      "label": "Lemma 2.1 fv preserved",
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      "section": "2",
      "file": "",
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    },
    {
      "id": "lemma_2_2_full_comp",
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      "section": "2",
      "file": "",
      "depends": ["m1_red1"]
    },
    {
      "id": "lemma_2_3_beta_sim",
      "label": "Lemma 2.3 β-simulation",
      "kind": "paper",
      "status": "planned",
      "milestone": "M2",
      "section": "2",
      "file": "",
      "depends": ["m1_red1", "lemma_2_2_full_comp"]
    },
    {
      "id": "m3_measure",
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      "section": "A",
      "file": "",
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    },
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    },
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      "file": "",
      "depends": ["m3_termination", "m1_red1"]
    },
    {
      "id": "lemma_3_2_sub_nf_unique",
      "label": "Lemma 3.2 sub NF unique",
      "kind": "paper",
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      "file": "",
      "depends": ["m3_local_confluence"]
    },
    {
      "id": "m4_par",
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    },
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      "id": "theorem_confluence_terms",
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    },
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      "id": "m5_mvar",
      "label": "XΔ metaterms",
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      "section": "3.3",
      "file": "",
      "depends": ["m1_syntax"]
    },
    {
      "id": "m5_rx",
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      "section": "3.3",
      "file": "",
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    },
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      "file": "",
      "depends": ["m5_mvar"]
    },
    {
      "id": "m5_coherence",
      "label": "RX + =C coherence",
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      "section": "3.3",
      "file": "",
      "depends": ["m5_rx", "m5_eq_C", "lemma_3_2_sub_nf_unique"]
    },
    {
      "id": "theorem_confluence_metaterms",
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      "file": "",
      "depends": ["m5_coherence", "m4_par_diamond"]
    },
    {
      "id": "m6_translation",
      "label": "translation to λβp",
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      "file": "",
      "depends": ["m1_red1"]
    },
    {
      "id": "m6_sn",
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      "section": "6",
      "file": "",
      "depends": ["m6_translation"]
    },
    {
      "id": "m6_intersection",
      "label": "intersection typing",
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      "section": "6",
      "file": "",
      "depends": ["m6_sn"]
    },
    {
      "id": "m6_typable_sn",
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      "milestone": "M6",
      "section": "6",
      "file": "",
      "depends": ["m6_intersection"]
    },
    {
      "id": "m6_sn_typable",
      "label": "SN → typable",
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      "section": "6",
      "file": "",
      "depends": ["m6_typable_sn"]
    },
    {
      "id": "corollary_6_21_psn",
      "label": "Cor 6.21 PSN",
      "kind": "paper",
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      "section": "6",
      "file": "",
      "depends": ["m6_sn_typable", "theorem_confluence_terms"]
    }
  ]
}