}
]
*)
+ [ { "\"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 ( ? ⊢ ? ⊩:⊑[?] ? )" "lsubsv_ldrop" + "lsubsv_ssta" + "lsubsv_cpcs" + "lsubsv_snv" * ]
+ [ "lsubsv ( ? ⊢ ? ¡⊑[?] ? )" "lsubsv_ldrop" + "lsubsv_lsuba" + "lsubsv_ssta" + "lsubsv_dxprs" + "lsubsv_cpcs" + "lsubsv_snv" * ]
}
]
[ { "stratified native validity" * } {
- [ "snv ( â¦\83?,?â¦\84 â\8a© ? :[?] )" "snv_lift" + "snv_ltpss_dx" + "snv_ltpss_sn" + "snv_aaa" + "snv_ssta" + "snv_sstas" + "snv_ssta_ltpr" + "snv_ltpr" + "snv_cpcs" * ]
+ [ "snv ( â¦\83?,?â¦\84 â\8a¢ ? ¡[?] )" "snv_lift" + "snv_aaa" + "snv_ssta" + "snv_sstas" + "snv_ssta_lpr" + "snv_lpr" + "snv_cpcs" * ]
}
]
}
]
class "blue"
[ { "equivalence" * } {
- [ { "focalized equivalence" * } {
- [ "lfpcs ( ⦃?⦄ ⬌* ⦃?⦄ )" "lfpcs_aaa" + "lfpcs_fpcs" + "lfpcs_lfprs" + "lfpcs_lfpcs" * ]
- [ "fpcs ( ⦃?,?⦄ ⬌* ⦃?,?⦄ )" "fpcs_aaa" + "fpcs_cpcs" + "fpcs_fprs" + "fpcs_fpcs" * ]
- }
- ]
- [ { "local env. ref. for context-sensitive equivalence" * } {
- [ "lsubse ( ? ⊢•⊑[?] ? )" "lsubse_ldrop" + "lsubse_ssta" + "lsubse_cpcs" * ]
- }
- ]
[ { "context-sensitive equivalence" * } {
- [ "cpcs ( ? ⊢ ? ⬌* ? )" "cpcs_ltpss_dx" + "cpcs_ltpss_sn" + "cpcs_delift" + "cpcs_aaa" + "cpcs_ltpr" + "cpcs_cprs" + "cpcs_cpcs" * ]
+ [ "cpcs ( ? ⊢ ? ⬌* ? )" "cpcs_aaa" + "cpcs_cprs" + "cpcs_cpcs" * ]
}
]
}
]
class "sky"
[ { "conversion" * } {
- [ { "focalized conversion" * } {
- [ "lfpc ( ⦃?⦄ ⬌ ⦃?⦄ )" "lfpc_lfpc" * ]
- [ "fpc ( ⦃?,?⦄ ⬌ ⦃?,?⦄ )" "fpc_fpc" * ]
- }
- ]
[ { "context-sensitive conversion" * } {
[ "cpc ( ? ⊢ ? ⬌ ? )" "cpc_cpc" * ]
}
]
class "cyan"
[ { "computation" * } {
- [ { "focalized computation" * } {
- [ "lfprs ( ⦃?⦄ ➡* ⦃?⦄ )" "lfprs_aaa" + "lfprs_ltprs" + "lfprs_cprs" + "lfprs_fprs" + "lfprs_lfprs" * ]
- [ "fprs ( ⦃?,?⦄ ➡* ⦃?,?⦄ )" "fprs_aaa" + "fprs_fprs" * ]
+ [ { "context-sensitive extended evaluation" * } {
+ [ "cpxe ( ⦃?,?⦄ ⊢ ➡*[?] 𝐍⦃?⦄ )" * ]
}
]
- [ { "\"big tree\" parallel computation" * } {
- [ "yprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )" "yprs_yprs" "ygt ( ? ⊢ ⦃?,?⦄ >[g] ⦃?,?⦄ )" "ygt_ygt" * ]
+ [ { "context-sensitive evaluation" * } {
+ [ "cpre ( ? ⊢ ➡* 𝐍⦃?⦄ )" "cpre_cpre" * ]
}
]
- [ { "decomposed extended computation" * } {
- [ "dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )" "dxprs_lift" + "dxprs_ltpss_dx" + "dxprs_ltpss_sn" + "dxprs_aaa" + "dxpr_lsubss" + "dxprs_dxprs" * ]
+ [ { "strongly normalizing computation" * } {
+ [ "csn_vector ( ? ⊢ ⬊* ? )" "csn_tstc_vector" + "csn_aaa" * ]
+ [ "csn ( ? ⊢ ⬊* ? )" "csn_alt ( ? ⊢ ⬊⬊* ? )" "csn_lift" + "csn_lpx" * ]
}
]
- [ { "weakly normalizing computation" * } {
- [ "cpe ( ? ⊢ ➡* 𝐍⦃?⦄ )" "cpe_cpe" * ]
+ [ { "decomposed extended computation" * } {
+ [ "dxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )" "dxprs_lift" + "dxprs_aaa" + "dxprs_dxprs" * ]
}
]
- [ { "strongly normalizing computation" * } {
- [ "csn_vector ( ? ⊢ ⬊* ? )" "csn_cpr_vector" + "csn_tstc_vector" + "csn_aaa" * ]
- [ "csn ( ? ⊢ ⬊* ? )" "csn_alt ( ? ⊢ ⬊⬊* ? )" "csn_lift" + "csn_cpr" + "csn_lfpr" * ]
+ [ { "context-sensitive extended computation" * } {
+ [ "lpxs ( ⦃?,?⦄ ⊢ ➡*[?] ? )" "lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?] ? )" "lpxs_ldrop" + "lpxs_aaa" + "lpxs_cpxs" + "lpxs_lpxs" * ]
+ [ "cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?] ? )" "cpxs_tstc" + "cpxs_tstc_vector" + "cpxs_lift" + "cpxs_aaa" + "cpxs_cpxs" * ]
}
]
[ { "context-sensitive computation" * } {
- [ "cprs (? ⊢ ? ➡* ?)" "cprs_lift" + "cprs_tpss" + "cprs_ltpss_dx" + "cprs_ltpss_sn" + "cprs_delift" + "cprs_aaa" + "cprs_ltpr" + "cprs_lfpr" + "cprs_cprs" + "cprs_lfprs" + "cprs_tstc" + "cprs_tstc_vector" * ]
- }
- ]
- [ { "context-free computation" * } {
- [ "ltprs ( ? ➡* ? )" "ltprs_alt ( ? ➡➡* ? )" "ltprs_ldrop" + "ltprs_ltprs" * ]
- [ "tprs ( ? ➡* ?)" "tprs_lift" + "tprs_tprs" * ]
+ [ "lprs ( ? ⊢ ➡* ? )" "lprs_alt ( ? ⊢ ➡➡* ? )" "lprs_ldrop" + "lprs_cprs" + "lprs_lprs" * ]
+ [ "cprs ( ? ⊢ ? ➡* ?)" "cprs_lift" + "cprs_cprs" * ]
}
]
[ { "local env. ref. for abstract candidates of reducibility" * } {
}
]
class "water"
- [ { "reducibility" * } {
- [ { "context-sensitive focalized reduction" * } {
- [ "cfpr ( ? ⊢ ⦃?,?⦄ ➡ ⦃?,?⦄ )" "cnfpr_ltpss" + "cfpr_aaa" + "cfpr_cpr" + "cfpr_cfpr" * ]
+ [ { "reduction" * } {
+ [ { "context-sensitive extended normal forms" * } {
+ [ "cnx ( ⦃?,?⦄ ⊢ 𝐍[?]⦃?⦄ )" "cnx_lift" + "cnx_crx" + "cnx_cix" * ]
}
]
- [ { "context-free focalized reduction" * } {
- [ "lfpr ( ⦃?⦄ ➡ ⦃?⦄ )" "lfpr_alt ( ⦃?⦄ ➡➡ ⦃?⦄ )" "lfpr_aaa" + "lfpr_cpr" + "lfpr_fpr" + "lfpr_lfpr" * ]
- [ "fpr ( ⦃?,?⦄ ➡ ⦃?,?⦄ )" "fpr_cpr" + "fpr_fpr" * ]
+ [ { "context-sensitive extended reduction" * } {
+ [ "lpx ( ⦃?,?⦄ ⊢ ➡[?] ? )" "lpx_ldrop" + "lpx_aaa" * ]
+ [ "cpx ( ⦃?,?⦄ ⊢ ? ➡[?] ? )" "cpx_lift" + "cpx_cix" * ]
}
]
- [ { "\"big tree\" parallel reduction" * } {
- [ "ypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )" "ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )" * ]
+ [ { "context-sensitive extended irreducible forms" * } {
+ [ "cix ( ⦃?,?⦄ ⊢ 𝐈[?]⦃?⦄ )" "cix_append" + "cix_lift" * ]
}
]
- [ { "context-sensitive normal forms" * } {
- [ "cnf ( ? ⊢ 𝐍⦃?⦄ )" "cnf_lift" + "cnf_cif" * ]
+ [ { "context-sensitive extended reducible forms" * } {
+ [ "crx ( ⦃?,?⦄ ⊢ 𝐑[?]⦃?⦄ )" "crx_append" + "crx_lift" * ]
}
]
- [ { "context-sensitive reduction" * } {
- [ "cpr ( ? ⊢ ? ➡ ? )" "cpr_lift" + "cpr_tpss" + "cpr_ltpss_dx" + "cpr_ltpss_sn" + "cpr_delift" + "cpr_aaa" + "cpr_ltpr" + "cpr_cpr" * ]
+ [ { "context-sensitive normal forms" * } {
+ [ "cnr ( ? ⊢ 𝐍⦃?⦄ )" "cnr_lift" + "cnr_crr" + "cnr_cir" * ]
}
]
- [ { "context-sensitive reducible forms" * } {
- [ "crf ( ? ⊢ 𝐑⦃?⦄ )" "crf_append" "cif ( ? ⊢ 𝐈⦃?⦄ )" "cif_append" * ]
+ [ { "context-sensitive reduction" * } {
+ [ "lpr ( ? ⊢ ➡ ? )" "lpr_ldrop" + "lpr_lpr" * ]
+ [ "cpr ( ? ⊢ ? ➡ ? )" "cpr_lift" + "cpr_cir" * ]
}
]
- [ { "context-free normal forms" * } {
- [ "thnf ( 𝐇𝐍⦃?⦄ )" * ]
+ [ { "context-sensitive irreducible forms" * } {
+ [ "cir ( ? ⊢ 𝐈⦃?⦄ )" "cir_append" + "cir_lift" * ]
}
]
- [ { "context-free reduction" * } {
- [ "ltpr ( ? ➡ ? )" "ltpr_ldrop" + "ltpr_tps" + "ltpr_ltpss_dx" + "ltpr_ltpss_sn" + "ltpr_aaa" + "ltpr_ltpr" * ]
- [ "tpr ( ? ➡ ? )" "tpr_lift" + "tpr_tps" + "tpr_tpss" + "tpr_delift" + "tpr_tpr" * ]
+ [ { "context-sensitive reducible forms" * } {
+ [ "crr ( ? ⊢ 𝐑⦃?⦄ )" "crr_append" + "crr_lift" * ]
}
]
}
]
class "green"
- [ { "unwind" * } {
+ [ { "unfold" * } {
+ [ { "unfold" * } {
+ [ "unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )" * ]
+ }
+ ]
[ { "iterated stratified static type assignment" * } {
- [ "sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )" "sstas_lift" + "sstas_ltpss_dx" + "sstas_ltpss_sn" + "sstas_aaa" + "sstas_lsubss" + "sstas_sstas" * ]
+ [ "sstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )" "sstas_lift" + "sstas_aaa" + "sstas_sstas" * ]
}
]
}
]
class "grass"
[ { "static typing" * } {
- [ { "local env. ref. for stratified static type assignment" * } {
- [ "lsubss ( ? •⊑[?] ? )" "lsubss_ldrop" + "lsubss_ssta" + "lsubss_lsubss" * ]
- }
- ]
[ { "stratified static type assignment" * } {
- [ "ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )" "ssta_lift" + "ssta_ltpss_dx" + "ssta_ltpss_sn" + "ssta_aaa" + "ssta_ssta" * ]
+ [ "ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ⦃?,?⦄ )" "ssta_lift" + "ssta_aaa" + "ssta_ssta" * ]
}
]
[ { "local env. ref. for atomic arity assignment" * } {
- [ "lsuba ( ? ⁝⊑ ? )" "lsuba_ldrop" + "lsuba_aaa" + "lsuba_lsuba" * ]
+ [ "lsuba ( ? â\8a¢ ? â\81\9dâ\8a\91 ? )" "lsuba_ldrop" + "lsuba_aaa" + "lsuba_lsuba" * ]
}
]
[ { "atomic arity assignment" * } {
- [ "aaa ( ? ⊢ ? ⁝ ? )" "aaa_lift" + "aaa_lifts" + "aaa_ltpss_dx" + "aaa_ltpss_sn" + "aaa_aaa" * ]
+ [ "aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )" "aaa_lift" + "aaa_lifts" + "aaa_aaa" * ]
}
]
[ { "parameters" * } {
}
]
class "yellow"
- [ { "unfold" * } {
- [ { "basic local env. thinning" * } {
- [ "thin ( ? ▼*[?,?] ≡ ? )" "thin_ldrop" + "thin_delift" * ]
- }
- ]
- [ { "inverse basic term relocation" * } {
- [ "delift ( ? ⊢ ? ▼*[?,?] ≡ ? )" "delift_alt ( ? ⊢ ? ▼▼*[?,?] ≡ ? )" "delift_lift" + "delift_tpss" + "delift_ltpss" + "delift_delift" * ]
+ [ { "substitution" * } {
+ [ { "restricted local env. ref." * } {
+ [ "lsubr ( ? ⊑ ? )" "lsubr_lsubr" * ]
}
]
- [ { "partial unfold" * } {
- [ "ltpss_sn ( ? ⊢ ▶*[?,?] ? )" "ltpss_sn_alt ( ? ⊢ ▶▶*[?,?] ? )" "ltpss_sn_ldrop" + "ltpss_sn_tps" + "ltpss_sn_tpss" + "ltpss_sn_ltpss_sn" * ]
- [ "ltpss_dx ( ? ▶*[?,?] ? )" "ltpss_dx_ldrop" + "ltpss_dx_tps" + "ltpss_dx_tpss" + "ltpss_dx_ltpss_dx" * ]
- [ "tpss ( ? ⊢ ? ▶*[?,?] ? )" "tpss_alt ( ? ⊢ ? ▶▶*[?,?] ? )" "tpss_lift" "tpss_tpss" * ]
+ [ { "iterated structural successor for closures" * } {
+ [ "fsups ( ⦃?,?,?⦄ ⊃* ⦃?,?,?⦄ )" "fsups_fsups" * ]
+ [ "fsupp ( ⦃?,?,?⦄ ⊃+ ⦃?,?,?⦄ )" "fsupp_fsupp" * ]
}
]
[ { "generic local env. slicing" * } {
[ "ldrops ( ⇩*[?] ? ≡ ? )" "ldrops_ldrop" + "ldrops_ldrops" * ]
}
]
- [ { "iterated restricted structural predecessor for closures" * } {
- [ "frsups ( ⦃?,?⦄ ⧁* ⦃?,?⦄ )" "frsups_frsups" * ]
- [ "frsupp ( ⦃?,?⦄ ⧁+ ⦃?,?⦄ )" "frsupp_frsupp" * ]
- }
- ]
[ { "generic term relocation" * } {
[ "lifts_vector ( ⇧*[?] ? ≡ ? )" "lifts_lift_vector" * ]
[ "lifts ( ⇧*[?] ? ≡ ? )" "lifts_lift" + "lifts_lifts" * ]
}
]
class "orange"
- [ { "substitution" * } {
- [ { "parallel substitution" * } {
- [ "tps ( ? ⊢ ? ▶[?,?] ? )" "tps_lift" + "tps_tps" * ]
+ [ { "relocation" * } {
+ [ { "structural successor for closures" * } {
+ [ "fsup ( ⦃?,?,?⦄ ⊃ ⦃?,?,?⦄ )" "fsupq ( ⦃?,?,?⦄ ⊃⸮ ⦃?,?,?⦄ )" "fsupq_alt ( ⦃?,?,?⦄ ⊃⊃⸮ ⦃?,?,?⦄ )" * ]
}
]
[ { "global env. slicing" * } {
}
]
[ { "basic local env. slicing" * } {
- [ "ldrop ( ⇩[?,?] ? ≡ ? )" "ldrop_append" + "ldrop_lpx" + "ldrop_sfr" + "ldrop_ldrop" * ]
- }
- ]
- [ { "local env. ref. for substitution" * } {
- [ "lsubs ( ? ≼[?,?] ? )" "(lsubs_lsubs)" "lsubs_sfr ( ≽[?,?] ? )" * ]
- }
- ]
- [ { "restricted structural predecessor for closures" * } {
- [ "frsup ( ⦃?,?⦄ ⧁ ⦃?,?⦄ )" * ]
+ [ "ldrop ( ⇩[?,?] ? ≡ ? )" "ldrop_append" + "ldrop_lpx_sn" + "ldrop_ldrop" * ]
}
]
[ { "basic term relocation" * } {
]
class "red"
[ { "grammar" * } {
- [ { "same head term form" * } {
- [ "tshf ( ? ≈ ? )" "(tshf_tshf)" * ]
+ [ { "pointwise extension of a relation" * } {
+ [ "lpx_sn" "lpx_sn_tc" + "lpx_sn_lpx_sn" * ]
}
]
[ { "same top term constructor" * } {
}
]
[ { "closures" * } {
- [ "cl_shift ( ? @@ ? )" "cl_weight ( ♯{?,?} )" * ]
+ [ "cl_shift ( ? @@ ? )" "cl_weight ( ♯{?,?,?} )" * ]
}
]
[ { "internal syntax" * } {
[ "genv" * ]
- [ "lenv" "lenv_weight ( ♯{?} )" "lenv_length ( |?| )" "lenv_append ( ? @@ ? )" "lenv_px" + "lenv_px_bi" * ]
+ [ "lenv" "lenv_weight ( ♯{?} )" "lenv_length ( |?| )" "lenv_append ( ? @@ ? )" * ]
[ "term" "term_weight ( ♯{?} )" "term_simple ( 𝐒⦃?⦄ )" "term_vector" * ]
[ "item" * ]
}
projects / helm.git / blobdiff