1597 lines
34 KiB
JSON
1597 lines
34 KiB
JSON
{
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"paper": {
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"title": "Milner's Lambda-Calculus with Partial Substitutions",
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"authors": [
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"Delia Kesner",
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"Shane Ó Conchúir"
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],
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"url": "https://arxiv.org/abs/2312.13270",
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"html": "https://arxiv.org/html/2312.13270v1"
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},
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|
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|
"label": "has_red_spec",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M1",
|
|
"section": "",
|
|
"file": "theory/Reduction.v",
|
|
"depends": [
|
|
"has_red_f",
|
|
"steps_complete",
|
|
"steps_sound"
|
|
]
|
|
},
|
|
{
|
|
"id": "red1_dec",
|
|
"label": "red1_dec",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M1",
|
|
"section": "",
|
|
"file": "theory/Reduction.v",
|
|
"depends": [
|
|
"has_red_spec"
|
|
]
|
|
},
|
|
{
|
|
"id": "nf_iff_steps_nil",
|
|
"label": "nf_iff_steps_nil",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M1",
|
|
"section": "",
|
|
"file": "theory/Reduction.v",
|
|
"depends": [
|
|
"steps_complete",
|
|
"steps_sound_red1"
|
|
]
|
|
},
|
|
{
|
|
"id": "normal_form_iff_nf",
|
|
"label": "normal_form_iff_nf",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M1",
|
|
"section": "",
|
|
"file": "theory/Reduction.v",
|
|
"depends": [
|
|
"nf_iff_steps_nil"
|
|
]
|
|
},
|
|
{
|
|
"id": "nf_dec",
|
|
"label": "nf_dec",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M1",
|
|
"section": "",
|
|
"file": "theory/Reduction.v",
|
|
"depends": [
|
|
"nf_iff_steps_nil"
|
|
]
|
|
},
|
|
{
|
|
"id": "open_rec_app",
|
|
"label": "open_rec_app",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "open_rec_lam",
|
|
"label": "open_rec_lam",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "open_rec_esub",
|
|
"label": "open_rec_esub",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "close_rec_app",
|
|
"label": "close_rec_app",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "close_rec_lam",
|
|
"label": "close_rec_lam",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "close_rec_esub",
|
|
"label": "close_rec_esub",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "subst_app",
|
|
"label": "subst_app",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "subst_lam",
|
|
"label": "subst_lam",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "subst_esub",
|
|
"label": "subst_esub",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "subst_notin",
|
|
"label": "subst_notin",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": [
|
|
"close_rec_notin",
|
|
"open_rec_occurs_false"
|
|
]
|
|
},
|
|
{
|
|
"id": "subst_lc_self",
|
|
"label": "subst_lc_self",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": [
|
|
"subst_fvar_self"
|
|
]
|
|
},
|
|
{
|
|
"id": "subst_other",
|
|
"label": "subst_other",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": [
|
|
"subst_fvar_other"
|
|
]
|
|
},
|
|
{
|
|
"id": "open_rec_lc_atom",
|
|
"label": "open_rec_lc_atom",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "open_rec_lc",
|
|
"label": "open_rec_lc",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Substitution.v",
|
|
"depends": [
|
|
"open_rec_lc_atom"
|
|
]
|
|
},
|
|
{
|
|
"id": "red_sub_root_to_red1",
|
|
"label": "red_sub_root_to_red1",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M3",
|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "red_sub_to_red1",
|
|
"label": "red_sub_to_red1",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M3",
|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
"depends": [
|
|
"red_sub_root_to_red1"
|
|
]
|
|
},
|
|
{
|
|
"id": "red_sub_context",
|
|
"label": "red_sub_context",
|
|
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|
|
"status": "proved",
|
|
"milestone": "M3",
|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "red_sub_gc",
|
|
"label": "red_sub_gc",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M3",
|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "red_sub_r",
|
|
"label": "red_sub_r",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M3",
|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "occurs_zfill",
|
|
"label": "occurs_zfill",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M3",
|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "zfill_occurs0",
|
|
"label": "zfill_occurs0",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M3",
|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
"depends": [
|
|
"occurs_zfill"
|
|
]
|
|
},
|
|
{
|
|
"id": "R_Gc_disjoint",
|
|
"label": "R_Gc_disjoint",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M3",
|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
"depends": [
|
|
"zfill_occurs0"
|
|
]
|
|
},
|
|
{
|
|
"id": "Star_red_sub_context",
|
|
"label": "Star_red_sub_context",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M3",
|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
"depends": [
|
|
"red_sub_context"
|
|
]
|
|
},
|
|
{
|
|
"id": "full_comp_aux_sub",
|
|
"label": "full_comp_aux_sub",
|
|
"kind": "infra",
|
|
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|
|
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|
|
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|
|
"file": "theory/Subsystem.v",
|
|
"depends": [
|
|
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|
|
"occurs_count_zfill_plug",
|
|
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|
|
"open_rec_zplug_lift",
|
|
"red_sub_gc",
|
|
"red_sub_r",
|
|
"zdecs_nonempty",
|
|
"zdecs_sound"
|
|
]
|
|
},
|
|
{
|
|
"id": "plus_red_sub_full_comp",
|
|
"label": "plus_red_sub_full_comp",
|
|
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|
|
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|
|
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|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
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|
|
"full_comp_aux_sub"
|
|
]
|
|
},
|
|
{
|
|
"id": "star_red_sub_full_comp",
|
|
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|
|
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|
|
"status": "proved",
|
|
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|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
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|
|
"Plus_to_Star",
|
|
"plus_red_sub_full_comp"
|
|
]
|
|
},
|
|
{
|
|
"id": "es_count_plug_mono",
|
|
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|
|
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|
|
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|
|
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|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
"depends": []
|
|
},
|
|
{
|
|
"id": "red_gc_measure",
|
|
"label": "red_gc_measure",
|
|
"kind": "infra",
|
|
"status": "proved",
|
|
"milestone": "M3",
|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
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|
|
"es_count_plug_mono"
|
|
]
|
|
},
|
|
{
|
|
"id": "red_gc_terminates",
|
|
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|
|
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|
|
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|
|
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|
|
"section": "",
|
|
"file": "theory/Subsystem.v",
|
|
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|
|
"red_gc_measure"
|
|
]
|
|
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|
|
{
|
|
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|
|
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|
|
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|
|
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|
|
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|
|
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|
|
"file": "theory/Subsystem.v",
|
|
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|
|
"red_sub_gc"
|
|
]
|
|
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|
|
{
|
|
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|
|
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|
|
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|
|
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|
|
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|
|
"section": "",
|
|
"file": "theory/Tests.v",
|
|
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|
|
"steps_sound"
|
|
]
|
|
},
|
|
{
|
|
"id": "corpus_complete",
|
|
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|
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|
|
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|
|
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|
|
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|
|
"file": "theory/Tests.v",
|
|
"depends": [
|
|
"steps_complete"
|
|
]
|
|
},
|
|
{
|
|
"id": "corpus_decides",
|
|
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|
|
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|
|
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|
|
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|
|
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|
|
"file": "theory/Tests.v",
|
|
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|
|
"has_red_spec"
|
|
]
|
|
},
|
|
{
|
|
"id": "corpus_fv_preserved",
|
|
"label": "corpus_fv_preserved",
|
|
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|
|
"status": "proved",
|
|
"milestone": "M2",
|
|
"section": "",
|
|
"file": "theory/Tests.v",
|
|
"depends": [
|
|
"lemma_2_1_fv_preserved",
|
|
"steps_sound_red1"
|
|
]
|
|
}
|
|
]
|
|
}
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