}
]
*)
- [ { "\"big tree\" parallel computation" * } {
- [ "yprs ( ? ⊢ ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "yprs_yprs" "ygt ( ⦃?,?,?⦄ >[?,?] ⦃?,?,?⦄ )" "ygt_ygt" * ]
- }
- ]
- [ { "\"big tree\" parallel reduction" * } {
- [ "ypr ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "ysc ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" * ]
- }
- ]
[ { "local env. ref. for stratified native validity" * } {
- [ "lsubsv ( ? ⊢ ? ¡⊑[?,?] ? )" "lsubsv_ldrop" + "lsubsv_lsuba" + "lsubsv_ssta" + "lsubsv_dxprs" + "lsubsv_cpcs" + "lsubsv_snv" * ]
+ [ "lsubsv ( ? ⊢ ? ¡⊑[?,?] ? )" "lsubsv_ldrop" + "lsubsv_lsubd" + "lsubsv_lsuba" + "lsubsv_lsstas" + "lsubsv_cpds" + "lsubsv_cpcs" + "lsubsv_snv" * ]
}
]
[ { "stratified native validity" * } {
- [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )" "snv_lift" + "snv_aaa" + "snv_ssta" + "snv_sstas" + "snv_ssta_lpr" + "snv_lpr" + "snv_cpcs" * ]
+ [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )" "snv_lift" + "snv_da_lpr" + "snv_aaa" + "snv_lsstas" + "snv_lsstas_lpr" + "snv_lpr" + "snv_cpcs" * ]
}
]
}
]
class "blue"
[ { "equivalence" * } {
+ [ { "decomposed extended equivalence" * } {
+ [ "cpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?] ? )" "cpes_cpds" * ]
+ }
+ ]
[ { "context-sensitive equivalence" * } {
[ "cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )" "cpcs_aaa" + "cpcs_cprs" + "cpcs_cpcs" * ]
}
[ "cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )" "cpre_cpre" * ]
}
]
- [ { "strongly normalizing computation" * } {
- [ "csn_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )" "csn_tstc_vector" + "csn_aaa" * ]
- [ "csn ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )" "csn_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )" "csn_lift" + "csn_lpx" * ]
+ [ { "strongly normalizing \"big tree\" computation" * } {
+ [ "fsb ( ⦃?,?⦄ ⊢ ⦥[?,?] ? )" "fsb_alt ( ⦃?,?⦄ ⊢ ⦥⦥[?,?] ? )" "fsb_fleq" + "fsb_csx" * ]
+ }
+ ]
+ [ { "strongly normalizing extended computation" * } {
+ [ "csx_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )" "csx_tstc_vector" + "csx_aaa" * ]
+ [ "csx ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )" "csx_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )" "csx_lift" + "csx_lpx" * ]
+ }
+ ]
+ [ { "parallel computation for \"big tree\" normal forms" * } {
+ [ "fpns ( ⦃?,?,?⦄ ⊢ ⋕➡*[?,?] ⦃?,?,?⦄ )" "fpns_fpns" * ]
+ }
+ ]
+ [ { "\"big tree\" parallel computation" * } {
+ [ "fpbr ( ⦃?,?,?⦄ ⊃≥[?,?] ⦃?,?,?⦄ )" "fpbr_fpbr" * ]
+ [ "fpbg ( ⦃?,?,?⦄ >[?,?] ⦃?,?,?⦄ )" "fpbg_lift" + "fpbg_fpbg" * ]
+ [ "fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )" "fpbs_lift" + "fpbs_fleq" + "fpbs_fpbs" * ]
}
]
[ { "decomposed extended computation" * } {
- [ "dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?,?] ? )" "dxprs_lift" + "dxprs_aaa" + "dxprs_dxprs" * ]
+ [ "cpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?] ? )" "cpds_lift" + "cpds_aaa" + "cpds_cpds" * ]
}
]
[ { "context-sensitive extended computation" * } {
]
class "water"
[ { "reduction" * } {
+ [ { "\"big tree\" parallel reduction" * } {
+ [ "fpbc ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpbc_lift" * ]
+ [ "fpb ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpb_lift" * ]
+ }
+ ]
[ { "context-sensitive extended normal forms" * } {
[ "cnx ( ⦃?,?⦄ ⊢ 𝐍[?,?]⦃?⦄ )" "cnx_lift" + "cnx_crx" + "cnx_cix" * ]
}
]
[ { "context-sensitive extended reduction" * } {
- [ "lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lpx_ldrop" + "lpx_aaa" * ]
- [ "cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )" "cpx_lift" + "cpx_cix" * ]
+ [ "lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lpx_ldrop" + "lpx_aaa" + "lpx_lpx" * ]
+ [ "cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )" "cpx_lift" + "cpx_cix" + "cpx_cpx" * ]
}
]
[ { "context-sensitive extended irreducible forms" * } {
[ "unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )" * ]
}
]
- [ { "iterated stratified static type assignment" * } {
- [ "sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )" "sstas_lift" + "sstas_aaa" + "sstas_sstas" * ]
+ [ { "iterated static type assignment" * } {
+ [ "lsstas ( ⦃?,?⦄ ⊢ ? •*[?,?,?] ? )" "lsstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?,?] ? )" "lsstas_lift" + "lsstas_aaa" + "lsstas_lsstas" * ]
}
]
}
]
class "grass"
[ { "static typing" * } {
- [ { "stratified static type assignment" * } {
- [ "ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ⦃?,?⦄ )" "ssta_lift" + "ssta_aaa" + "ssta_ssta" * ]
- }
- ]
[ { "local env. ref. for atomic arity assignment" * } {
[ "lsuba ( ? ⊢ ? ⁝⊑ ? )" "lsuba_ldrop" + "lsuba_aaa" + "lsuba_lsuba" * ]
}
]
[ { "atomic arity assignment" * } {
- [ "aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )" "aaa_lift" + "aaa_lifts" + "aaa_aaa" * ]
+ [ "aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )" "aaa_lift" + "aaa_lifts" + "aaa_da" + "aaa_ssta" + "aaa_aaa" * ]
+ }
+ ]
+ [ { "stratified static type assignment" * } {
+ [ "ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )" "ssta_lift" + "ssta_ssta" * ]
+ }
+ ]
+ [ { "local env. ref. for degree assignment" * } {
+ [ "lsubd ( ? ⊢ ? ▪⊑ ? )" "lsubd_da" + "lsubd_lsubd" * ]
+ }
+ ]
+ [ { "degree assignment" * } {
+ [ "da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )" "da_lift" + "da_da" * ]
}
]
[ { "parameters" * } {
}
]
[ { "iterated structural successor for closures" * } {
- [ "fsups ( ⦃?,?,?⦄ ⊃* ⦃?,?,?⦄ )" "fsups_fsups" * ]
- [ "fsupp ( ⦃?,?,?⦄ ⊃+ ⦃?,?,?⦄ )" "fsupp_fsupp" * ]
+ [ "fqus ( ⦃?,?,?⦄ ⊃* ⦃?,?,?⦄ )" "fqus_alt" + "fqus_fqus" * ]
+ [ "fqup ( ⦃?,?,?⦄ ⊃+ ⦃?,?,?⦄ )" "fqup_fqup" * ]
}
]
[ { "generic local env. slicing" * } {
class "orange"
[ { "relocation" * } {
[ { "structural successor for closures" * } {
- [ "fsup ( ⦃?,?,?⦄ ⊃ ⦃?,?,?⦄ )" "fsupq ( ⦃?,?,?⦄ ⊃⸮ ⦃?,?,?⦄ )" "fsupq_alt ( ⦃?,?,?⦄ ⊃⊃⸮ ⦃?,?,?⦄ )" * ]
+ [ "fquq ( ⦃?,?,?⦄ ⊃⸮ ⦃?,?,?⦄ )" "fquq_alt ( ⦃?,?,?⦄ ⊃⊃⸮ ⦃?,?,?⦄ )" "fquq_fquq" * ]
+ [ "fqu ( ⦃?,?,?⦄ ⊃ ⦃?,?,?⦄ )" "fqu_fqu" * ]
+ }
+ ]
+ [ { "lazy equivalence for local environments" * } {
+ [ "lleq ( ? ⋕[?] ? )" "lleq_fleq" * ]
}
]
[ { "global env. slicing" * } {