[ { "dynamic typing" * } {
(*
[ { "local env. ref. for native type assignment" * } {
- [ "lsubn ( ? â\8a¢ ? :â\8a\91 ? )" "lsubn_ldrop" "lsubn_cpcs" "lsubn_nta" * ]
+ [ "lsubn ( ? â\8a¢ ? :â«\83 ? )" "lsubn_ldrop" "lsubn_cpcs" "lsubn_nta" * ]
}
]
[ { "native type assignment" * } {
}
]
*)
- [ { "\"big tree\" parallel computation" * } {
- [ "yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )" "yprs_yprs" "ygt ( ? ⊢ ⦃?,?⦄ >[g] ⦃?,?⦄ )" "ygt_ygt" * ]
- }
- ]
- [ { "\"big tree\" parallel reduction" * } {
- [ "ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )" "ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )" * ]
- }
- ]
[ { "local env. ref. for stratified native validity" * } {
- [ "lsubsv ( ? â\8a¢ ? ¡â\8a\91[?] ? )" "lsubsv_ldrop" + "lsubsv_lsuba" + "lsubsv_ssta" + "lsubsv_dxprs" + "lsubsv_cpcs" + "lsubsv_snv" * ]
+ [ "lsubsv ( ? â\8a¢ ? ¡â«\83[?,?] ? )" "lsubsv_ldrop" + "lsubsv_lsubd" + "lsubsv_lsuba" + "lsubsv_lsstas" + "lsubsv_cpds" + "lsubsv_cpcs" + "lsubsv_snv" * ]
}
]
[ { "stratified native validity" * } {
- [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?] )" "snv_lift" + "snv_lpss" + "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" * } {
- [ { "local env. ref. for stratified static type assignment" * } {
- [ "lsubss ( ? •⊑[?] ? )" "lsubss_ldrop" + "lsubss_ssta" + "lsubss_cpcs" * ]
+ [ { "decomposed extended equivalence" * } {
+ [ "cpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?] ? )" "cpes_cpds" * ]
}
]
[ { "context-sensitive equivalence" * } {
- [ "cpcs ( ? ⊢ ? ⬌* ? )" "cpcs_lpss" + "cpcs_aaa" + "cpcs_cprs" + "cpcs_cpcs" * ]
+ [ "cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )" "cpcs_aaa" + "cpcs_cprs" + "cpcs_cpcs" * ]
}
]
}
class "sky"
[ { "conversion" * } {
[ { "context-sensitive conversion" * } {
- [ "cpc ( ? ⊢ ? ⬌ ? )" "cpc_cpc" * ]
+ [ "cpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )" "cpc_cpc" * ]
}
]
}
]
class "cyan"
[ { "computation" * } {
- [ { "decomposed extended computation" * } {
- [ "dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )" "dxprs_lift" + "dxprs_lpss" + "dxprs_aaa" + "dxprs_dxprs" * ]
+ [ { "evaluation for context-sensitive extended reduction" * } {
+ [ "cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )" * ]
+ }
+ ]
+ [ { "evaluation for context-sensitive reduction" * } {
+ [ "cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )" "cpre_cpre" * ]
+ }
+ ]
+ [ { "strongly normalizing \"big tree\" computation" * } {
+ [ "fsb ( ⦃?,?⦄ ⊢ ⦥[?,?] ? )" "fsb_alt ( ⦃?,?⦄ ⊢ ⦥⦥[?,?] ? )" "fsb_aaa" + "fsb_csx" * ]
+ }
+ ]
+ [ { "strongly normalizing extended computation" * } {
+ [ "lcosx ( ? ⊢ ~⬊*[?,?,?] ? )" "lcosx_cpx" * ]
+ [ "lsx ( ? ⊢ ⬊*[?,?,?,?] ? )" "lsx_alt ( ? ⊢ ⬊⬊*[?,?,?,?] ? )" "lsx_ldrop" + "lsx_lpx" + "lsx_lpxs" + "llsx_csx" * ]
+ [ "csx_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )" "csx_tstc_vector" + "csx_aaa" * ]
+ [ "csx ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )" "csx_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )" "csx_lift" + "csx_lleq" + "csx_lpx" + "csx_lpxs" + "csx_fpbs" * ]
+ }
+ ]
+ [ { "\"big tree\" parallel computation" * } {
+ [ "fpbg ( ⦃?,?,?⦄ >⋕[?,?] ⦃?,?,?⦄ )" "fpbg_lift" + "fpbg_fleq" + "fpbg_fpbg" * ]
+ [ "fpbc ( ⦃?,?,?⦄ ≻⋕[?,?] ⦃?,?,?⦄ )" "fpbc_fleq" + "fpbc_fpbs" * ]
+ [ "fpbu ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpbu_lift" + "fpbu_lleq" "fpbu_fleq" * ]
+ [ "fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )" "fpbs_lift" + "fpbs_fleq" + "fpbs_aaa" + "fpbs_fpbs" + "fpbs_ext" * ]
}
]
- [ { "weakly normalizing computation" * } {
- [ "cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )" "cpe_cpe" * ]
+ [ { "decomposed extended computation" * } {
+ [ "cpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?] ? )" "cpds_lift" + "cpds_aaa" + "cpds_cpds" * ]
}
]
- [ { "strongly normalizing computation" * } {
- [ "csn_vector ( ? ⊢ ⬊* ? )" "csn_tstc_vector" + "csn_aaa" * ]
- [ "csn ( ? ⊢ ⬊* ? )" "csn_alt ( ? ⊢ ⬊⬊* ? )" "csn_lift" + "csn_lpr" * ]
+ [ { "context-sensitive extended computation" * } {
+ [ "lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )" "lpxs_ldrop" + "lpxs_lleq" + "lpxs_aaa" + "lpxs_cpxs" + "lpxs_lpxs" * ]
+ [ "cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )" "cpxs_tstc" + "cpxs_tstc_vector" + "cpxs_leq" + "cpxs_lift" + "cpxs_lleq" + "cpxs_aaa" + "cpxs_cpxs" * ]
}
]
[ { "context-sensitive computation" * } {
- [ "lprs ( ? ⊢ ➡* ? )" "lprs_alt ( ? ⊢ ➡➡* ? )" "lprs_ldrop" + "lprs_lpss" + "lprs_aaa" + "lprs_cprs" + "lprs_lprs" * ]
- [ "cprs ( ? ⊢ ? ➡* ?)" "cprs_tstc" + "cprs_tstc_vector" + "cprs_lift" + "cprs_lpss" + "cprs_aaa" + "cprs_cprs" * ]
+ [ "lprs ( ⦃?,?⦄ ⊢ ➡* ? )" "lprs_ldrop" + "lprs_cprs" + "lprs_lprs" * ]
+ [ "cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)" "cprs_lift" + "cprs_cprs" * ]
}
]
[ { "local env. ref. for abstract candidates of reducibility" * } {
- [ "lsubc ( ? â\8a\91[?] ? )" "lsubc_ldrop" + "lsubc_ldrops" + "lsubc_lsuba" * ]
+ [ "lsubc ( ? â\8a¢ ? â«\83[?] ? )" "lsubc_ldrop" + "lsubc_ldrops" + "lsubc_lsuba" * ]
}
]
[ { "support for abstract computation properties" * } {
- [ "acp" "acp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )" "acp_aaa" * ]
+ [ "acp" "acp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )" "acp_aaa" * ]
}
]
}
]
class "water"
[ { "reduction" * } {
+ [ { "\"big tree\" parallel reduction" * } {
+ [ "fpb ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpb_lift" + "fpb_aaa" * ]
+ }
+ ]
+ [ { "normal forms for context-sensitive extended reduction" * } {
+ [ "cnx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐍⦃?⦄ )" "cnx_lift" + "cnx_crx" + "cnx_cix" * ]
+ }
+ ]
[ { "context-sensitive extended reduction" * } {
- [ "lpx ( ⦃?,?⦄ ⊢ ➡[?] ? )" "lpx_ldrop" + "lpx_aaa" * ]
- [ "cpx ( ⦃?,?⦄ ⊢ ? ➡[?] ? )" "cpx_lift" * ]
+ [ "lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lpx_ldrop" + "lpx_frees" "lpx_lleq" + "lpx_aaa" * ]
+ [ "cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )" "cpx_leq" + "cpx_lift" + "cpx_llpx_sn" + "cpx_lleq" + "cpx_cix" * ]
+ }
+ ]
+ [ { "irreducible forms for context-sensitive extended reduction" * } {
+ [ "cix ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐈⦃?⦄ )" "cix_lift" * ]
}
]
- [ { "context-sensitive normal forms" * } {
- [ "cnf ( ? ⊢ 𝐍⦃?⦄ )" "cnf_liftt" + "cnf_crf" + "cnf_cif" * ]
+ [ { "reducible forms for context-sensitive extended reduction" * } {
+ [ "crx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐑⦃?⦄ )" "crx_lift" * ]
+ }
+ ]
+ [ { "normal forms for context-sensitive reduction" * } {
+ [ "cnr ( ⦃?,?⦄ ⊢ ➡ 𝐍⦃?⦄ )" "cnr_lift" + "cnr_crr" + "cnr_cir" * ]
}
]
[ { "context-sensitive reduction" * } {
- [ "lpr ( ? ⊢ ➡ ? )" "lpr_ldrop" + "lpr_lpss" + "lpr_lpr" * ]
- [ "cpr ( ? ⊢ ? ➡ ? )" "cpr_lift" + "cpr_cif" * ]
+ [ "lpr ( ⦃?,?⦄ ⊢ ➡ ? )" "lpr_ldrop" + "lpr_lpr" * ]
+ [ "cpr ( ⦃?,?⦄ ⊢ ? ➡ ? )" "cpr_lift" + "cpr_llpx_sn" + "cpr_cir" * ]
+ }
+ ]
+ [ { "irreducible forms for context-sensitive reduction" * } {
+ [ "cir ( ⦃?,?⦄ ⊢ ➡ 𝐈⦃?⦄ )" "cir_lift" * ]
}
]
- [ { "context-sensitive reducible forms" * } {
- [ "crf ( ? ⊢ 𝐑⦃?⦄ )" "crf_append" "cif ( ? ⊢ 𝐈⦃?⦄ )" "cif_append" * ]
+ [ { "reducible forms for context-sensitive reduction" * } {
+ [ "crr ( ⦃?,?⦄ ⊢ ➡ 𝐑⦃?⦄ )" "crr_lift" * ]
}
]
}
]
class "green"
[ { "unfold" * } {
- [ { "restricted parallel computation" * } {
- [ "lpqs ( ? ⊢ ➤* ? )" "lpqs_ldrop" + "lpqs_cpqs" + "lpqs_lpqs" * ]
- [ "cpqs ( ? ⊢ ? ➤* ? )" "cpqs_lift" * ]
- }
- ]
[ { "unfold" * } {
- [ "unfold ( ? ⊢ ? ⧫* ? )" * ]
+ [ "unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )" * ]
}
]
- [ { "iterated stratified static type assignment" * } {
- [ "sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )" "sstas_lift" + "sstas_lpss" + "sstas_aaa" + "sstas_sstas" * ]
+ [ { "iterated static type assignment" * } {
+ [ "lsstas ( ⦃?,?⦄ ⊢ ? •*[?,?,?] ? )" "lsstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?,?] ? )" "lsstas_lift" + "lsstas_aaa" + "lsstas_lsstas" * ]
}
]
}
]
class "grass"
[ { "static typing" * } {
+ [ { "local env. ref. for atomic arity assignment" * } {
+ [ "lsuba ( ? ⊢ ? ⁝⫃ ? )" "lsuba_ldrop" + "lsuba_aaa" + "lsuba_lsuba" * ]
+ }
+ ]
+ [ { "atomic arity assignment" * } {
+ [ "aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )" "aaa_lift" + "aaa_lifts" + "aaa_fqus" + "aaa_lleq" + "aaa_da" + "aaa_ssta" + "aaa_aaa" * ]
+ }
+ ]
[ { "stratified static type assignment" * } {
- [ "ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )" "ssta_lift" + "ssta_lpss" + "ssta_aaa" + "ssta_ssta" * ]
+ [ "ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )" "ssta_lift" + "ssta_lpx_sn" + "ssta_ssta" * ]
}
]
- [ { "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_lpss" + "aaa_aaa" * ]
+ [ { "degree assignment" * } {
+ [ "da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )" "da_lift" + "da_da" * ]
}
]
[ { "parameters" * } {
[ "sh" "sd" * ]
}
]
+ [ { "restricted local env. ref." * } {
+ [ "lsubr ( ? ⫃ ? )" "lsubr_lsubr" * ]
+ }
+ ]
}
]
class "yellow"
- [ { "substitution" * } {
- [ { "parallel substitution" * } {
- [ "lpss ( ? ⊢ ▶* ? )" "lpss_ldrop" + "lpss_cpss" + "lpss_lpss" * ]
- [ "cpss ( ? ⊢ ? ▶* ? )" "cpss_lift" * ]
+ [ { "multiple substitution" * } {
+ [ { "lazy equivalence" * } {
+ [ "fleq ( ⦃?,?,?⦄ ⋕[?] ⦃?,?,?⦄ )" "fleq_fleq" * ]
+ [ "lleq ( ? ⋕[?,?] ? )" "lleq_alt" + "lleq_alt_rec" + "lleq_leq" + "lleq_ldrop" + "lleq_fqus" + "lleq_llor" + "lleq_lleq" * ]
}
- ]
- [ { "local env. ref. for substitution" * } {
- [ "lsubr ( ? ⊑ ? )" "lsubr_lsubr" * ]
+ ]
+ [ { "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_ldrop" * ]
+ }
+ ]
+ [ { "context-sensitive exclusion from free variables" * } {
+ [ "frees ( ? ⊢ ? ϵ 𝐅*[?]⦃?⦄ )" "frees_leq" + "frees_lift" * ]
+ }
+ ]
+ [ { "contxt-sensitive extended multiple substitution" * } {
+ [ "cpys ( ⦃?,?⦄ ⊢ ? ▶*[?,?] ? )" "cpys_alt ( ⦃?,?⦄ ⊢ ? ▶▶*[?,?] ? )" "cpys_lift" + "cpys_cpys" * ]
}
]
[ { "iterated structural successor for closures" * } {
- [ "fsups ( ⦃?,?⦄ ⊃* ⦃?,?⦄ )" "fsups_fsups" * ]
- [ "fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )" "fsupp_fsupp" * ]
+ [ "fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )" "fqus_alt" + "fqus_fqus" * ]
+ [ "fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )" "fqup_fqup" * ]
}
]
- [ { "generic local env. slicing" * } {
- [ "ldrops ( ⇩*[?] ? ≡ ? )" "ldrops_ldrop" + "ldrops_ldrops" * ]
+ [ { "iterated local env. slicing" * } {
+ [ "ldrops ( ⇩*[?,?] ? ≡ ? )" "ldrops_ldrop" + "ldrops_ldrops" * ]
}
]
[ { "generic term relocation" * } {
}
]
class "orange"
- [ { "relocation" * } {
+ [ { "substitution" * } {
[ { "structural successor for closures" * } {
- [ "fsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )" "fsupq ( ⦃?,?⦄ ⊃⸮ ⦃?,?⦄ )" * ]
+ [ "fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )" "fquq_alt ( ⦃?,?,?⦄ ⊐⊐⸮ ⦃?,?,?⦄ )" * ]
+ [ "fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )" * ]
}
]
[ { "global env. slicing" * } {
- [ "gdrop ( ⇩[?] ? ≡ ? )" "gdrop_gdrop" * ]
+ [ "gget ( ⇩[?] ? ≡ ? )" "gget_gget" * ]
+ }
+ ]
+ [ { "contxt-sensitive extended ordinary substitution" * } {
+ [ "cpy ( ⦃?,?⦄ ⊢ ? ▶[?,?] ? )" "cpy_lift" + "cpy_nlift" + "cpy_cpy" * ]
+ }
+ ]
+ [ { "local env. ref. for extended substitution" * } {
+ [ "lsuby ( ? ⊑×[?,?] ? )" "lsuby_lsuby" * ]
+ }
+ ]
+ [ { "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_lpx_sn" + "ldrop_ldrop" * ]
+ [ "ldrop ( ⇩[?,?,?] ? ≡ ? )" "ldrop_append" + "ldrop_leq" + "ldrop_ldrop" * ]
}
]
[ { "basic term relocation" * } {
[ "lift_vector ( ⇧[?,?] ? ≡ ? )" "lift_lift_vector" * ]
- [ "lift ( ⇧[?,?] ? ≡ ? )" "lift_lift" * ]
+ [ "lift ( ⇧[?,?] ? ≡ ? )" "lift_neq" + "lift_lift" * ]
}
]
}
]
class "red"
[ { "grammar" * } {
- [ { "pointwise extension of a relation" * } {
- [ "lpx_sn" "lpx_sn_tc" + "lpx_sn_lpx_sn" * ]
+ [ { "equivalence for local environments" * } {
+ [ "leq ( ? ≃[?,?] ? )" "leq_leq" * ]
}
]
[ { "same top term constructor" * } {
}
]
[ { "closures" * } {
- [ "cl_shift ( ? @@ ? )" "cl_weight ( ♯{?,?} )" * ]
+ [ "cl_weight ( ♯{?,?,?} )" "cl_restricted_weight ( ♯{?,?} )" * ]
}
]
[ { "internal syntax" * } {
projects / helm.git / blobdiff