22 [ { "higher order dynamic typing" * } {
23 [ { "higher order native type assignment" * } {
24 [ "ntas ( ⦃?,?⦄ ⊢ ? :* ? )" "nta_lift" * ]
31 [ { "dynamic typing" * } {
33 [ { "local env. ref. for native type assignment" * } {
34 [ "lsubn ( ? ⊢ ? :⫃ ? )" "lsubn_ldrop" "lsubn_cpcs" "lsubn_nta" * ]
37 [ { "native type assignment" * } {
38 [ "nta ( ⦃?,?⦄ ⊢ ? : ? )" "nta_alt ( ⦃?,?⦄ ⊢ ? :: ? )" "nta_lift" "nta_ltpss" "nta_thin" "nta_aaa" "nta_sta" "nta_ltpr" "nta_nta" * ]
42 [ { "local env. ref. for stratified native validity" * } {
43 [ "lsubsv ( ? ⊢ ? ¡⫃[?,?] ? )" "lsubsv_ldrop" + "lsubsv_lsubd" + "lsubsv_lsuba" + "lsubsv_lsstas" + "lsubsv_cpds" + "lsubsv_cpcs" + "lsubsv_snv" * ]
46 [ { "stratified native validity" * } {
47 [ "snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )" "snv_lift" + "snv_da_lpr" + "snv_aaa" + "snv_lsstas" + "snv_lsstas_lpr" + "snv_lpr" + "snv_cpcs" * ]
53 [ { "equivalence" * } {
54 [ { "decomposed extended equivalence" * } {
55 [ "cpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?] ? )" "cpes_cpds" * ]
58 [ { "context-sensitive equivalence" * } {
59 [ "cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )" "cpcs_aaa" + "cpcs_cprs" + "cpcs_cpcs" * ]
65 [ { "conversion" * } {
66 [ { "context-sensitive conversion" * } {
67 [ "cpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )" "cpc_cpc" * ]
73 [ { "computation" * } {
74 [ { "evaluation for context-sensitive extended reduction" * } {
75 [ "cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )" * ]
78 [ { "evaluation for context-sensitive reduction" * } {
79 [ "cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )" "cpre_cpre" * ]
82 [ { "strongly normalizing \"big tree\" computation" * } {
83 [ "fsb ( ⦃?,?⦄ ⊢ ⦥[?,?] ? )" "fsb_alt ( ⦃?,?⦄ ⊢ ⦥⦥[?,?] ? )" "fsb_aaa" + "fsb_csx" * ]
86 [ { "strongly normalizing extended computation" * } {
87 [ "lcosx ( ? ⊢ ~⬊*[?,?,?] ? )" "lcosx_cpx" * ]
88 [ "lsx ( ? ⊢ ⬊*[?,?,?,?] ? )" "lsx_alt ( ? ⊢ ⬊⬊*[?,?,?,?] ? )" "lsx_ldrop" + "lsx_lpx" + "lsx_lpxs" + "llsx_csx" * ]
89 [ "csx_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )" "csx_tstc_vector" + "csx_aaa" * ]
90 [ "csx ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )" "csx_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )" "csx_lift" + "csx_lleq" + "csx_lpx" + "csx_lpxs" + "csx_fpbs" * ]
93 [ { "\"big tree\" parallel computation" * } {
94 [ "fpbg ( ⦃?,?,?⦄ >⋕[?,?] ⦃?,?,?⦄ )" "fpbg_lift" + "fpbg_fleq" + "fpbg_fpbg" * ]
95 [ "fpbc ( ⦃?,?,?⦄ ≻⋕[?,?] ⦃?,?,?⦄ )" "fpbc_fleq" + "fpbc_fpbs" * ]
96 [ "fpbu ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpbu_lift" + "fpbu_lleq" "fpbu_fleq" * ]
97 [ "fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )" "fpbs_lift" + "fpbs_fleq" + "fpbs_aaa" + "fpbs_fpbs" + "fpbs_ext" * ]
100 [ { "decomposed extended computation" * } {
101 [ "cpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?] ? )" "cpds_lift" + "cpds_aaa" + "cpds_cpds" * ]
104 [ { "context-sensitive extended computation" * } {
105 [ "lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )" "lpxs_ldrop" + "lpxs_lleq" + "lpxs_aaa" + "lpxs_cpxs" + "lpxs_lpxs" * ]
106 [ "cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )" "cpxs_tstc" + "cpxs_tstc_vector" + "cpxs_leq" + "cpxs_lift" + "cpxs_lleq" + "cpxs_aaa" + "cpxs_cpxs" * ]
109 [ { "context-sensitive computation" * } {
110 [ "lprs ( ⦃?,?⦄ ⊢ ➡* ? )" "lprs_ldrop" + "lprs_cprs" + "lprs_lprs" * ]
111 [ "cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)" "cprs_lift" + "cprs_cprs" * ]
114 [ { "local env. ref. for abstract candidates of reducibility" * } {
115 [ "lsubc ( ? ⊢ ? ⫃[?] ? )" "lsubc_ldrop" + "lsubc_ldrops" + "lsubc_lsuba" * ]
118 [ { "support for abstract computation properties" * } {
119 [ "acp" "acp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )" "acp_aaa" * ]
125 [ { "reduction" * } {
126 [ { "\"big tree\" parallel reduction" * } {
127 [ "fpb ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpb_lift" + "fpb_aaa" * ]
130 [ { "normal forms for context-sensitive extended reduction" * } {
131 [ "cnx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐍⦃?⦄ )" "cnx_lift" + "cnx_crx" + "cnx_cix" * ]
134 [ { "context-sensitive extended reduction" * } {
135 [ "lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lpx_ldrop" + "lpx_lleq" + "lpx_aaa" * ]
136 [ "cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )" "cpx_leq" + "cpx_lift" + "cpx_llpx_sn" + "cpx_lleq" + "cpx_cix" * ]
139 [ { "irreducible forms for context-sensitive extended reduction" * } {
140 [ "cix ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐈⦃?⦄ )" "cix_lift" * ]
143 [ { "reducible forms for context-sensitive extended reduction" * } {
144 [ "crx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐑⦃?⦄ )" "crx_lift" * ]
147 [ { "normal forms for context-sensitive reduction" * } {
148 [ "cnr ( ⦃?,?⦄ ⊢ ➡ 𝐍⦃?⦄ )" "cnr_lift" + "cnr_crr" + "cnr_cir" * ]
151 [ { "context-sensitive reduction" * } {
152 [ "lpr ( ⦃?,?⦄ ⊢ ➡ ? )" "lpr_ldrop" + "lpr_lpr" * ]
153 [ "cpr ( ⦃?,?⦄ ⊢ ? ➡ ? )" "cpr_lift" + "cpr_llpx_sn" + "cpr_cir" * ]
156 [ { "irreducible forms for context-sensitive reduction" * } {
157 [ "cir ( ⦃?,?⦄ ⊢ ➡ 𝐈⦃?⦄ )" "cir_lift" * ]
160 [ { "reducible forms for context-sensitive reduction" * } {
161 [ "crr ( ⦃?,?⦄ ⊢ ➡ 𝐑⦃?⦄ )" "crr_lift" * ]
169 [ "unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )" * ]
172 [ { "iterated static type assignment" * } {
173 [ "lsstas ( ⦃?,?⦄ ⊢ ? •*[?,?,?] ? )" "lsstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?,?] ? )" "lsstas_lift" + "lsstas_aaa" + "lsstas_lsstas" * ]
179 [ { "static typing" * } {
180 [ { "local env. ref. for atomic arity assignment" * } {
181 [ "lsuba ( ? ⊢ ? ⁝⫃ ? )" "lsuba_ldrop" + "lsuba_aaa" + "lsuba_lsuba" * ]
184 [ { "atomic arity assignment" * } {
185 [ "aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )" "aaa_lift" + "aaa_lifts" + "aaa_fqus" + "aaa_lleq" + "aaa_da" + "aaa_ssta" + "aaa_aaa" * ]
188 [ { "stratified static type assignment" * } {
189 [ "ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )" "ssta_lift" + "ssta_lpx_sn" + "ssta_ssta" * ]
192 [ { "local env. ref. for degree assignment" * } {
193 [ "lsubd ( ? ⊢ ? ▪⫃ ? )" "lsubd_da" + "lsubd_lsubd" * ]
196 [ { "degree assignment" * } {
197 [ "da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )" "da_lift" + "da_da" * ]
200 [ { "parameters" * } {
204 [ { "restricted local env. ref." * } {
205 [ "lsubr ( ? ⫃ ? )" "lsubr_lsubr" * ]
211 [ { "substitution" * } {
212 [ { "lazy equivalence" * } {
213 [ "fleq ( ⦃?,?,?⦄ ⋕[?] ⦃?,?,?⦄ )" "fleq_fleq" * ]
214 [ "lleq ( ? ⋕[?,?] ? )" "lleq_alt" + "lleq_alt_rec" + "lleq_leq" + "lleq_ldrop" + "lleq_fqus" + "lleq_llor" + "lleq_lleq" * ]
217 [ { "lazy pointwise extension of a relation" * } {
218 [ "llpx_sn" "llpx_sn_alt" + "llpx_sn_alt_rec" + "llpx_sn_tc" + "llpx_sn_leq" + "llpx_sn_ldrop" + "llpx_sn_lpx_sn" + "llpx_sn_llor" * ]
221 [ { "pointwise union for local environments" * } {
222 [ "llor ( ? ⩖[?] ? ≡ ? )" * ]
225 [ { "context-sensitive exclusion from free variables" * } {
226 [ "cofrees ( ? ⊢ ? ~ϵ 𝐅*[?]⦃?⦄ )" "cofrees_alt" + "cofrees_lift" * ]
229 [ { "contxt-sensitive extended multiple substitution" * } {
230 [ "cpys ( ⦃?,?⦄ ⊢ ? ▶*[?,?] ? )" "cpys_alt ( ⦃?,?⦄ ⊢ ? ▶▶*[?,?] ? )" "cpys_lift" + "cpys_cpys" * ]
233 [ { "iterated structural successor for closures" * } {
234 [ "fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )" "fqus_alt" + "fqus_fqus" * ]
235 [ "fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )" "fqup_fqup" * ]
238 [ { "iterated local env. slicing" * } {
239 [ "ldrops ( ⇩*[?,?] ? ≡ ? )" "ldrops_ldrop" + "ldrops_ldrops" * ]
242 [ { "generic term relocation" * } {
243 [ "lifts_vector ( ⇧*[?] ? ≡ ? )" "lifts_lift_vector" * ]
244 [ "lifts ( ⇧*[?] ? ≡ ? )" "lifts_lift" + "lifts_lifts" * ]
247 [ { "support for generic relocation" * } {
248 [ "gr2 ( @⦃?,?⦄ ≡ ? )" "gr2_plus ( ? + ? )" "gr2_minus ( ? ▭ ? ≡ ? )" "gr2_gr2" * ]
254 [ { "relocation" * } {
255 [ { "structural successor for closures" * } {
256 [ "fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )" "fquq_alt ( ⦃?,?,?⦄ ⊐⊐⸮ ⦃?,?,?⦄ )" * ]
257 [ "fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )" * ]
260 [ { "global env. slicing" * } {
261 [ "gget ( ⇩[?] ? ≡ ? )" "gget_gget" * ]
264 [ { "contxt-sensitive extended ordinary substitution" * } {
265 [ "cpy ( ⦃?,?⦄ ⊢ ? ▶[?,?] ? )" "cpy_lift" + "cpy_nlift" + "cpy_cpy" * ]
268 [ { "local env. ref. for extended substitution" * } {
269 [ "lsuby ( ? ⊑×[?,?] ? )" "lsuby_lsuby" * ]
272 [ { "pointwise extension of a relation" * } {
273 [ "lpx_sn" "lpx_sn_alt" + "lpx_sn_tc" + "lpx_sn_ldrop" + "lpx_sn_lpx_sn" * ]
276 [ { "basic local env. slicing" * } {
277 [ "ldrop ( ⇩[?,?,?] ? ≡ ? )" "ldrop_leq" + "ldrop_ldrop" * ]
280 [ { "basic term relocation" * } {
281 [ "lift_vector ( ⇧[?,?] ? ≡ ? )" "lift_lift_vector" * ]
282 [ "lift ( ⇧[?,?] ? ≡ ? )" "lift_neq" + "lift_lift" * ]
289 [ { "equivalence for local environments" * } {
290 [ "leq ( ? ≃[?,?] ? )" "leq_leq" * ]
293 [ { "same top term constructor" * } {
294 [ "tstc ( ? ≃ ? )" "tstc_tstc" + "tstc_vector" * ]
298 [ "cl_weight ( ♯{?,?,?} )" "cl_restricted_weight ( ♯{?,?} )" * ]
301 [ { "internal syntax" * } {
303 [ "lenv" "lenv_weight ( ♯{?} )" "lenv_length ( |?| )" "lenv_append ( ? @@ ? )" * ]
304 [ "term" "term_weight ( ♯{?} )" "term_simple ( 𝐒⦃?⦄ )" "term_vector" * ]
308 [ { "external syntax" * } {
316 class "component" { 0 }