15 [ { "terms with special features" * } {
16 [ "ex_sta_ldec" + "ex_cpr_omega" + "ex_fpbg_refl" + "ex_snv_eta" * ]
30 [ { "higher order dynamic typing" * } {
31 [ { "higher order native type assignment" * } {
32 [ "ntas ( ⦃?,?⦄ ⊢ ? :* ? )" "nta_lift" * ]
39 [ { "dynamic typing" * } {
41 [ { "local env. ref. for native type assignment" * } {
42 [ "lsubn ( ? ⊢ ? :⫃ ? )" "lsubn_drop" "lsubn_cpcs" "lsubn_nta" * ]
45 [ { "native type assignment" * } {
46 [ "nta ( ⦃?,?⦄ ⊢ ? : ? )" "nta_alt ( ⦃?,?⦄ ⊢ ? :: ? )" "nta_lift" "nta_ltpss" "nta_thin" "nta_aaa" "nta_sta" "nta_ltpr" "nta_nta" * ]
50 [ { "local env. ref. for stratified native validity" * } {
51 [ "lsubsv ( ? ⊢ ? ⫃¡[?,?] ? )" "lsubsv_lsuba" + "lsubsv_lsubd" + "lsubsv_lstas" + "lsubsv_scpds" + "lsubsv_cpcs" + "lsubsv_snv" * ]
54 [ { "stratified native validity" * } {
55 [ "shnv ( ⦃?,?⦄ ⊢ ? ¡[?,?,?] )" * ]
56 [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )" "snv_lift" + "snv_aaa" + "snv_da_lpr" + "snv_lstas" + "snv_lstas_lpr" + "snv_lpr" + "snv_fsb" + "snv_scpes" + "snv_preserve" * ]
62 [ { "equivalence" * } {
63 [ { "decomposed rt-equivalence" * } {
64 [ "scpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?,?,?] ? )" "scpes_aaa" + "scpes_cpcs" + "scpes_scpes" * ]
67 [ { "context-sensitive equivalence" * } {
68 [ "cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )" "cpcs_aaa" + "cpcs_cprs" + "cpcs_cpcs" * ]
74 [ { "conversion" * } {
75 [ { "context-sensitive conversion" * } {
76 [ "cpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )" "cpc_cpc" * ]
83 [ { "rt-computation" * } {
85 [ { "evaluation for context-sensitive rt-reduction" * } {
86 [ "cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )" * ]
89 [ { "evaluation for context-sensitive reduction" * } {
90 [ "cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )" "cpre_cpre" * ]
93 [ { "strongly normalizing qrst-computation" * } {
94 [ "fsb ( ⦥[?,?] ⦃?,?,?⦄ )" "fsb_alt ( ⦥⦥[?,?] ⦃?,?,?⦄ )" "fsb_aaa" + "fsb_csx" * ]
97 [ { "strongly normalizing rt-computation" * } {
98 [ "lcosx ( ? ⊢ ~⬊*[?,?,?] ? )" "lcosx_cpx" * ]
99 [ "lsx ( ? ⊢ ⬊*[?,?,?,?] ? )" "lsx_alt ( ? ⊢ ⬊⬊*[?,?,?,?] ? )" "lsx_drop" + "lsx_lpx" + "lsx_lpxs" + "llsx_csx" * ]
100 [ "csx_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )" "csx_tsts_vector" + "csx_aaa" * ]
101 [ "csx ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )" "csx_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )" "csx_lift" + "csx_lleq" + "csx_lpx" + "csx_lpxs" + "csx_fpbs" * ]
104 [ { "parallel qrst-computation" * } {
105 [ "fpbg ( ⦃?,?,?⦄ >≡[?,?] ⦃?,?,?⦄ )" "fpbg_lift" + "fpbg_fleq" + "fpbg_fpbs" + "fpbg_fpbg" * ]
106 [ "fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )" "fpbs_lift" + "fpbs_aaa" + "fpbs_fpb" + "fpbs_fpbs" * ]
109 [ { "decomposed rt-computation" * } {
110 [ "scpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?,?] ? )" "scpds_lift" + "scpds_aaa" + "scpds_scpds" * ]
113 [ { "context-sensitive computation" * } {
114 [ "lprs ( ⦃?,?⦄ ⊢ ➡* ? )" "lprs_drop" + "lprs_cprs" + "lprs_lprs" * ]
115 [ "cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)" "cprs_lift" + "cprs_cprs" * ]
119 [ { "uncounted context-sensitive rt-transition" * } {
121 [ "lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )" "lpxs_drop" + "lpxs_lleq" + "lpxs_aaa" + "lpxs_cpxs" + "lpxs_lpxs" * ]
122 [ "cpxs_tsts" + "cpxs_tsts_vector" + "cpxs_lreq" + "cpxs_lift" + "cpxs_lleq" + "cpxs_aaa" + "cpxs_cpxs" * ]
124 [ "cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" * ]
127 [ { "generic reducibility" * } {
128 [ "lsubc ( ? ⊢ ? ⫃[?] ? )" "lsubc_drop" + "lsubc_drops" + "lsubc_lsubr" + "lsubc_lsuba" * ]
129 [ "gcp" "gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )" "gcp_aaa" * ]
135 [ { "rt-transition" * } {
136 [ { "parallel qrst-rtransition" * } {
137 (* [ "fpbq ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpbq_alt ( ⦃?,?,?⦄ ≽≽[?,?] ⦃?,?,?⦄ )" + "fpbq_aaa" * ] *)
138 [ "fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" (* "fpb_lleq" + "fpb_fleq" *) * ]
142 [ { "context-sensitive rt-reduction" * } {
148 [ { "t-bound context-sensitive rt-transition" * } {
149 [ "lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lfpr_length" + "lfpr_drops" + "lfpr_fqup" + "lfpr_frees" + "lfpr_aaa" + "lfpr_lfpx" + "lfpr_lfpr" * ]
150 [ "cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )" "cpr_drops" * ]
151 [ "cpm ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )" "cpm_simple" + "cpm_drops" + "cpm_lsubr" + "cpm_lfxs" + "cpm_cpx" * ]
154 [ { "uncounted context-sensitive rt-transition" * } {
155 [ "cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )" "cnx_simple" + "cnx_drops" * ]
156 [ "lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )" "lfpx_length" + "lfpx_drops" + "lfpx_fqup" + "lfpx_frees" + "lfpx_aaa" * ]
157 [ "cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )" "cpx_simple" + "cpx_drops" + "cpx_fqus" + "cpx_lsubr" + "cpx_lfxs" + "cpx_lfdeq" * ]
160 [ { "counted context-sensitive rt-transition" * } {
161 [ "cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )" "cpg_simple" + "cpg_drops" + "cpg_lsubr" * ]
167 [ { "static typing" * } {
168 [ { "atomic arity assignment" * } {
169 [ "lsuba ( ? ⊢ ? ⫃⁝ ? )" "lsuba_drops" + "lsuba_lsubr" + "lsuba_aaa" + "lsuba_lsuba" * ]
170 [ "aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )" "aaa_drops" + "aaa_fqus" + "aaa_lfdeq" + "aaa_aaa" * ]
173 [ { "degree-based equivalence on referred entries" * } {
174 [ "ffdeq ( ⦃?,?,?⦄ ≡[?,?] ⦃?,?,?⦄ )" "ffdeq_fqup" + "ffdeq_ffdeq" * ]
175 [ "lfdeq ( ? ≡[?,?,?] ? )" "lfdeq_length" + "lfdeq_fqup" + "lfdeq_lfdeq" * ]
178 [ { "generic extension on referred entries" * } {
179 [ "lfxs ( ? ⦻*[?,?] ? )" "lfxs_length" + "lfxs_drops" + "lfxs_fqup" + "lfxs_lfxs" * ]
182 [ { "context-sensitive free variables" * } {
183 [ "lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )" "lsubf_frees" * ]
184 [ "frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )" "frees_weight" + "frees_drops" + "frees_fqup" + "frees_frees" * ]
187 [ { "restricted ref. for local env." * } {
188 [ "lsubr ( ? ⫃ ? )" "lsubr_length" + "lsubr_drops" + "lsubr_lsubr" * ]
194 [ { "s-computation" * } {
195 [ { "iterated structural successor for closures" * } {
196 [ "fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )" "fqus_weight" + "fqus_drops" + "fqus_fqup" + "fqus_fqus" * ]
197 [ "fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )" "fqup_weight" + "fqup_drops" + "fqup_fqup" * ]
203 [ { "s-transition" * } {
204 [ { "structural successor for closures" * } {
205 [ "fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )" "fquq_length" + "fquq_weight" * ]
206 [ "fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )" "fqu_length" + "fqu_weight" * ]
212 [ { "relocation" * } {
213 [ { "generic slicing for local environments" * } {
214 [ "drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )" * ]
215 [ "drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )" "drops_lstar" + "drops_weight" + "drops_length" + "drops_ceq" + "drops_lexs" + "drops_lreq" + "drops_drops" * ]
218 [ { "generic relocation for terms" * } {
219 [ "lifts_vector ( ⬆*[?] ? ≡ ? )" "lifts_lifts_vector" * ]
220 [ "lifts ( ⬆*[?] ? ≡ ? )" "lifts_simple" + "lifts_weight" + "lifts_tdeq" + "lifts_lifts" * ]
223 [ { "ranged equivalence for local environments" * } {
224 [ "lreq ( ? ≡[?] ? )" "lreq_length" + "lreq_lreq" * ]
227 [ { "generic entrywise extension" * } {
228 [ "lexs ( ? ⦻*[?,?,?] ? )" "lexs_length" + "lexs_lexs" * ]
235 [ { "append for local environments" * } {
236 [ "append ( ? @@ ? )" "append_length" * ]
239 [ { "degree-based equivalence for terms" * } {
240 [ "deq ( ? ≡[?,?] ? ) " "deq_deq" * ]
243 [ { "same top term structure" * } {
244 [ "tsts ( ? ≂ ? )" "tsts_tsts" + "tsts_vector" * ]
248 [ "cl_weight ( ♯{?,?,?} )" * ]
249 [ "cl_restricted_weight ( ♯{?,?} )" * ]
252 [ { "global environments" * } {
256 [ { "local environments" * } {
257 [ "lenv_length ( |?| )" * ]
258 [ "lenv_weight ( ♯{?} )" * ]
263 [ "term_vector ( Ⓐ?.? )" * ]
264 [ "term_simple ( 𝐒⦃?⦄ )" * ]
265 [ "term_weight ( ♯{?} )" * ]
275 [ { "atomic arities" * } {
285 class "capitalize italic" { 0 }
289 [ { "normal forms for context-sensitive rt-reduction" * } {
290 [ "cnx_crx" + "cnx_cix" * ]
293 [ { "irreducible forms for context-sensitive rt-reduction" * } {
294 [ "cix ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐈⦃?⦄ )" "cix_lift" * ]
297 [ { "reducible forms for context-sensitive rt-reduction" * } {
298 [ "crx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐑⦃?⦄ )" "crx_lift" * ]
301 [ { "normal forms for context-sensitive reduction" * } {
302 [ "cnr ( ⦃?,?⦄ ⊢ ➡ 𝐍⦃?⦄ )" "cnr_lift" + "cnr_crr" + "cnr_cir" * ]
305 [ { "irreducible forms for context-sensitive reduction" * } {
306 [ "cir ( ⦃?,?⦄ ⊢ ➡ 𝐈⦃?⦄ )" "cir_lift" * ]
309 [ { "reducible forms for context-sensitive reduction" * } {
310 [ "crr ( ⦃?,?⦄ ⊢ ➡ 𝐑⦃?⦄ )" "crr_lift" * ]
314 [ "unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )" * ]
317 [ { "iterated static type assignment" * } {
318 [ "lstas ( ⦃?,?⦄ ⊢ ? •*[?,?] ? )" "lstas_lift" + "lstas_llpx_sn.ma" + "lstas_aaa" + "lstas_da" + "lstas_lstas" * ]
321 [ { "local env. ref. for degree assignment" * } {
322 [ "lsubd ( ? ⊢ ? ⫃▪[?,?] ? )" "lsubd_da" + "lsubd_lsubd" * ]
325 [ { "degree assignment" * } {
326 [ "da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )" "da_lift" + "da_aaa" + "da_da" * ]
329 [ { "context-sensitive multiple rt-substitution" * } {
330 [ "cpys ( ⦃?,?⦄ ⊢ ? ▶*[?,?] ? )" "cpys_alt ( ⦃?,?⦄ ⊢ ? ▶▶*[?,?] ? )" "cpys_lift" + "cpys_cpys" * ]
333 [ { "pointwise union for local environments" * } {
334 [ "llor ( ? ⋓[?,?] ? ≡ ? )" "llor_alt" + "llor_drop" * ]
337 [ { "lazy pointwise extension of a relation" * } {
338 [ "llpx_sn" "llpx_sn_alt" + "llpx_sn_alt_rec" + "llpx_sn_tc" + "llpx_sn_lreq" + "llpx_sn_drop" + "llpx_sn_lpx_sn" + "llpx_sn_frees" + "llpx_sn_llor" * ]
341 [ { "global env. slicing" * } {
342 [ "gget ( ⬇[?] ? ≡ ? )" "gget_gget" * ]
345 [ { "context-sensitive ordinary rt-substitution" * } {
346 [ "cpy ( ⦃?,?⦄ ⊢ ? ▶[?,?] ? )" "cpy_lift" + "cpy_nlift" + "cpy_cpy" * ]
349 [ { "local env. ref. for rt-substitution" * } {
350 [ "lsuby ( ? ⊆[?,?] ? )" "lsuby_lsuby" * ]
353 [ { "pointwise extension of a relation" * } {
354 [ "lpx_sn" "lpx_sn_alt" + "lpx_sn_tc" + "lpx_sn_drop" + "lpx_sn_lpx_sn" * ]
357 [ "cpx_lreq" + "cpr_cir" + "fpb_lift" + "fpbq_lift" ]
358 [ "lleq ( ? ≡[?,?] ? )" "lleq_alt" + "lleq_alt_rec" + "lleq_lreq" + "lleq_drop" + "lleq_fqus" + "lleq_llor" + "lleq_lleq" * ]