]
*)
[ { "local env. ref. for stratified native validity" * } {
- [ "lsubsv ( ? ⊢ ? ¡⫃[?,?] ? )" "lsubsv_ldrop" + "lsubsv_lsubd" + "lsubsv_lsuba" + "lsubsv_lsstas" + "lsubsv_cpds" + "lsubsv_cpcs" + "lsubsv_snv" * ]
+ [ "lsubsv ( ? ⊢ ? ¡⫃[?,?] ? )" "lsubsv_lsuba" + "lsubsv_lsubd" + "lsubsv_lstas" + "lsubsv_cpds" + "lsubsv_cpcs" + "lsubsv_snv" * ]
}
]
[ { "stratified native validity" * } {
- [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )" "snv_lift" + "snv_da_lpr" + "snv_aaa" + "snv_lsstas" + "snv_lsstas_lpr" + "snv_lpr" + "snv_cpcs" * ]
+ [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )" "snv_lift" + "snv_aaa" + "snv_da_lpr" + "snv_lstas" + "snv_lstas_lpr" + "snv_lpr" + "snv_cpcs" + "snv_preserve" * ]
}
]
}
}
]
[ { "\"big tree\" parallel computation" * } {
- [ "fpbg ( â¦\83?,?,?â¦\84 >â\8b\95[?,?] ⦃?,?,?⦄ )" "fpbg_lift" + "fpbg_fleq" + "fpbg_fpbg" * ]
- [ "fpbc ( â¦\83?,?,?â¦\84 â\89»â\8b\95[?,?] ⦃?,?,?⦄ )" "fpbc_fleq" + "fpbc_fpbs" * ]
+ [ "fpbg ( â¦\83?,?,?â¦\84 >â\89¡[?,?] ⦃?,?,?⦄ )" "fpbg_lift" + "fpbg_fleq" + "fpbg_fpbg" * ]
+ [ "fpbc ( â¦\83?,?,?â¦\84 â\89»â\89¡[?,?] ⦃?,?,?⦄ )" "fpbc_fleq" + "fpbc_fpbs" * ]
[ "fpbu ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpbu_lift" + "fpbu_lleq" "fpbu_fleq" * ]
[ "fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )" "fpbs_lift" + "fpbs_fleq" + "fpbs_aaa" + "fpbs_fpbs" + "fpbs_ext" * ]
}
}
]
[ { "context-sensitive extended reduction" * } {
- [ "lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lpx_ldrop" + "lpx_lleq" + "lpx_aaa" * ]
+ [ "lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lpx_ldrop" + "lpx_frees" "lpx_lleq" + "lpx_aaa" * ]
[ "cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )" "cpx_leq" + "cpx_lift" + "cpx_llpx_sn" + "cpx_lleq" + "cpx_cix" * ]
}
]
}
]
[ { "iterated static type assignment" * } {
- [ "lsstas ( ⦃?,?⦄ ⊢ ? •*[?,?,?] ? )" "lsstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?,?] ? )" "lsstas_lift" + "lsstas_aaa" + "lsstas_lsstas" * ]
+ [ "lstas ( ⦃?,?⦄ ⊢ ? •*[?,?] ? )" "lstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?] ? )" "lstas_lift" + "lstas_aaa" + "lstas_da" + "lstas_lstas" * ]
}
]
}
]
class "grass"
[ { "static typing" * } {
- [ { "local env. ref. for atomic arity assignment" * } {
- [ "lsuba ( ? ⊢ ? ⁝⫃ ? )" "lsuba_ldrop" + "lsuba_aaa" + "lsuba_lsuba" * ]
+ [ { "local env. ref. for degree assignment" * } {
+ [ "lsubd ( ? ⊢ ? ▪⫃ ? )" "lsubd_da" + "lsubd_lsubd" * ]
}
]
- [ { "atomic arity assignment" * } {
- [ "aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )" "aaa_lift" + "aaa_lifts" + "aaa_fqus" + "aaa_lleq" + "aaa_da" + "aaa_ssta" + "aaa_aaa" * ]
+ [ { "degree assignment" * } {
+ [ "da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )" "da_lift" + "da_aaa" + "da_sta" + "da_da" * ]
}
]
- [ { "stratified static type assignment" * } {
- [ "ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )" "ssta_lift" + "ssta_lpx_sn" + "ssta_ssta" * ]
+ [ { "static type assignment" * } {
+ [ "sta ( ⦃?,?⦄ ⊢ ? •[?] ? )" "sta_lift" + "sta_lpx_sn" + "sta_aaa" + "sta_sta" * ]
}
]
- [ { "local env. ref. for degree assignment" * } {
- [ "lsubd ( ? ⊢ ? ▪⫃ ? )" "lsubd_da" + "lsubd_lsubd" * ]
+ [ { "parameters" * } {
+ [ "sh" "sd" * ]
}
]
- [ { "degree assignment" * } {
- [ "da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )" "da_lift" + "da_da" * ]
+ [ { "local env. ref. for atomic arity assignment" * } {
+ [ "lsuba ( ? ⊢ ? ⁝⫃ ? )" "lsuba_aaa" + "lsuba_lsuba" * ]
}
]
- [ { "parameters" * } {
- [ "sh" "sd" * ]
+ [ { "atomic arity assignment" * } {
+ [ "aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )" "aaa_lift" + "aaa_lifts" + "aaa_fqus" + "aaa_lleq" + "aaa_aaa" * ]
}
]
[ { "restricted local env. ref." * } {
}
]
class "yellow"
- [ { "substitution" * } {
+ [ { "multiple substitution" * } {
[ { "lazy equivalence" * } {
- [ "fleq ( ⦃?,?,?⦄ ⋕[?] ⦃?,?,?⦄ )" "fleq_fleq" * ]
- [ "lleq ( ? ⋕[?,?] ? )" "lleq_alt" + "lleq_leq" + "lleq_ldrop" + "lleq_fqus" + "lleq_lleq" * ]
+ [ "fleq ( ⦃?,?,?⦄ ≡[?] ⦃?,?,?⦄ )" "fleq_fleq" * ]
+ [ "lleq ( ? ≡[?,?] ? )" "lleq_alt" + "lleq_alt_rec" + "lleq_leq" + "lleq_ldrop" + "lleq_fqus" + "lleq_llor" + "lleq_lleq" * ]
+ }
+ ]
+ [ { "lazy pointwise extension of a relation" * } {
+ [ "llpx_sn" "llpx_sn_alt" + "llpx_sn_alt_rec" + "llpx_sn_tc" + "llpx_sn_leq" + "llpx_sn_ldrop" + "llpx_sn_lpx_sn" + "llpx_sn_frees" + "llpx_sn_llor" * ]
+ }
+ ]
+ [ { "pointwise union for local environments" * } {
+ [ "llor ( ? ⩖[?,?] ? ≡ ? )" "llor_alt" + "llor_ldrop" * ]
+ }
+ ]
+ [ { "context-sensitive exclusion from free variables" * } {
+ [ "frees ( ? ⊢ ? ϵ 𝐅*[?]⦃?⦄ )" "frees_append" + "frees_leq" + "frees_lift" * ]
}
]
[ { "contxt-sensitive extended multiple substitution" * } {
[ "cpys ( ⦃?,?⦄ ⊢ ? ▶*[?,?] ? )" "cpys_alt ( ⦃?,?⦄ ⊢ ? ▶▶*[?,?] ? )" "cpys_lift" + "cpys_cpys" * ]
}
]
- [ { "iterated structural successor for closures" * } {
+ [ { "iterated structural successor for closures" * } {
[ "fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )" "fqus_alt" + "fqus_fqus" * ]
[ "fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )" "fqup_fqup" * ]
}
}
]
class "orange"
- [ { "relocation" * } {
+ [ { "substitution" * } {
[ { "structural successor for closures" * } {
[ "fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )" "fquq_alt ( ⦃?,?,?⦄ ⊐⊐⸮ ⦃?,?,?⦄ )" * ]
[ "fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )" * ]
}
]
[ { "global env. slicing" * } {
- [ "gdrop ( ⇩[?] ? ≡ ? )" "gdrop_gdrop" * ]
- }
- ]
- [ { "pointwise union for local environments" * } {
- [ "llor ( ? ⩖[?] ? ≡ ? )" * ]
- }
- ]
- [ { "pointwise extension of a relation" * } {
- [ "llpx_sn" "llpx_sn_alt" + "llpx_sn_tc" + "llpx_sn_leq" + "llpx_sn_ldrop" + "llpx_sn_lpx_sn" * ]
- [ "lpx_sn" "lpx_sn_alt" + "lpx_sn_tc" + "lpx_sn_ldrop" + "lpx_sn_lpx_sn" * ]
+ [ "gget ( ⇩[?] ? ≡ ? )" "gget_gget" * ]
}
]
[ { "contxt-sensitive extended ordinary substitution" * } {
- [ "cpy ( ⦃?,?⦄ ⊢ ? ▶[?,?] ? )" "cpy_lift" + "cpy_cpy" * ]
+ [ "cpy ( ⦃?,?⦄ ⊢ ? ▶[?,?] ? )" "cpy_lift" + "cpy_nlift" + "cpy_cpy" * ]
}
]
[ { "local env. ref. for extended substitution" * } {
[ "lsuby ( ? ⊑×[?,?] ? )" "lsuby_lsuby" * ]
}
]
- [ { "basic local env. slicing" * } {
- [ "ldrop ( ⇩[?,?,?] ? ≡ ? )" "ldrop_leq" + "ldrop_ldrop" * ]
+ [ { "pointwise extension of a relation" * } {
+ [ "lpx_sn" "lpx_sn_alt" + "lpx_sn_tc" + "lpx_sn_ldrop" + "lpx_sn_lpx_sn" * ]
+ }
+ ]
+ [ { "basic local env. slicing" * } {
+ [ "ldrop ( ⇩[?,?,?] ? ≡ ? )" "ldrop_append" + "ldrop_leq" + "ldrop_ldrop" * ]
}
]
[ { "basic term relocation" * } {