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initial commit: confluence and normalisation

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milner committed 2026-09-22 09:20:00 +02:00
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{
"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": [
{
"id": "exec_step",
"label": "exec_step",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/ExecReducer.v",
"depends": []
},
{
"id": "exec_examples",
"label": "exec_examples",
"kind": "infra",
"status": "proved",
"milestone": "M0",
"section": "",
"file": "theory/ExecReducer.v",
"depends": ["exec_step"]
},
{
"id": "m1_syntax",
"label": "M1 syntax/binding",
"kind": "infra",
"status": "planned",
"milestone": "M1",
"section": "2",
"file": "",
"depends": ["exec_examples"]
},
{
"id": "m1_open_close",
"label": "open/close laws",
"kind": "infra",
"status": "planned",
"milestone": "M1",
"section": "2",
"file": "",
"depends": ["m1_syntax"]
},
{
"id": "m1_red1",
"label": "red1 (B, Gc, R)",
"kind": "infra",
"status": "planned",
"milestone": "M1",
"section": "2",
"file": "",
"depends": ["m1_syntax", "m1_open_close"]
},
{
"id": "lemma_2_1_fv_preserved",
"label": "Lemma 2.1 fv preserved",
"kind": "paper",
"status": "planned",
"milestone": "M2",
"section": "2",
"file": "",
"depends": ["m1_red1"]
},
{
"id": "lemma_2_2_full_comp",
"label": "Lemma 2.2 full composition",
"kind": "paper",
"status": "planned",
"milestone": "M2",
"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",
"label": "sub measure",
"kind": "infra",
"status": "planned",
"milestone": "M3",
"section": "A",
"file": "",
"depends": ["m1_red1"]
},
{
"id": "m3_termination",
"label": "{R,Gc} termination",
"kind": "paper",
"status": "planned",
"milestone": "M3",
"section": "3.1",
"file": "",
"depends": ["m3_measure"]
},
{
"id": "m3_local_confluence",
"label": "{R,Gc} local confluence",
"kind": "paper",
"status": "planned",
"milestone": "M3",
"section": "3.1",
"file": "",
"depends": ["m3_termination", "m1_red1"]
},
{
"id": "lemma_3_2_sub_nf_unique",
"label": "Lemma 3.2 sub NF unique",
"kind": "paper",
"status": "planned",
"milestone": "M3",
"section": "3.1",
"file": "",
"depends": ["m3_local_confluence"]
},
{
"id": "m4_par",
"label": "parallel reduction par",
"kind": "infra",
"status": "planned",
"milestone": "M4",
"section": "3.2",
"file": "",
"depends": ["m1_red1", "lemma_3_2_sub_nf_unique"]
},
{
"id": "m4_par_diamond",
"label": "par diamond",
"kind": "paper",
"status": "planned",
"milestone": "M4",
"section": "3.2",
"file": "",
"depends": ["m4_par"]
},
{
"id": "theorem_confluence_terms",
"label": "Confluence on terms",
"kind": "paper",
"status": "planned",
"milestone": "M4",
"section": "3.2",
"file": "",
"depends": ["m4_par_diamond", "lemma_2_3_beta_sim"]
},
{
"id": "m5_mvar",
"label": "XΔ metaterms",
"kind": "infra",
"status": "planned",
"milestone": "M5",
"section": "3.3",
"file": "",
"depends": ["m1_syntax"]
},
{
"id": "m5_rx",
"label": "RX rule",
"kind": "paper",
"status": "planned",
"milestone": "M5",
"section": "3.3",
"file": "",
"depends": ["m5_mvar", "m1_red1"]
},
{
"id": "m5_eq_C",
"label": "=C setoid",
"kind": "paper",
"status": "planned",
"milestone": "M5",
"section": "3.3",
"file": "",
"depends": ["m5_mvar"]
},
{
"id": "m5_coherence",
"label": "RX + =C coherence",
"kind": "paper",
"status": "planned",
"milestone": "M5",
"section": "3.3",
"file": "",
"depends": ["m5_rx", "m5_eq_C", "lemma_3_2_sub_nf_unique"]
},
{
"id": "theorem_confluence_metaterms",
"label": "Confluence on metaterms",
"kind": "paper",
"status": "planned",
"milestone": "M5",
"section": "3.3",
"file": "",
"depends": ["m5_coherence", "m4_par_diamond"]
},
{
"id": "m6_translation",
"label": "translation to λβp",
"kind": "paper",
"status": "planned",
"milestone": "M6",
"section": "4",
"file": "",
"depends": ["m1_red1"]
},
{
"id": "m6_sn",
"label": "SN for simply typed",
"kind": "paper",
"status": "planned",
"milestone": "M6",
"section": "6",
"file": "",
"depends": ["m6_translation"]
},
{
"id": "m6_intersection",
"label": "intersection typing",
"kind": "paper",
"status": "planned",
"milestone": "M6",
"section": "6",
"file": "",
"depends": ["m6_sn"]
},
{
"id": "m6_typable_sn",
"label": "typable → SN",
"kind": "paper",
"status": "planned",
"milestone": "M6",
"section": "6",
"file": "",
"depends": ["m6_intersection"]
},
{
"id": "m6_sn_typable",
"label": "SN → typable",
"kind": "paper",
"status": "planned",
"milestone": "M6",
"section": "6",
"file": "",
"depends": ["m6_typable_sn"]
},
{
"id": "corollary_6_21_psn",
"label": "Cor 6.21 PSN",
"kind": "paper",
"status": "planned",
"milestone": "M6",
"section": "6",
"file": "",
"depends": ["m6_sn_typable", "theorem_confluence_terms"]
}
]
}