[ [ "strongly normalizing for lenvs on referred entries" ] "lfsx ( ? ⊢ ⬈*[?,?,?] 𝐒⦃?⦄ )" "lfsx_drops" + "lfsx_fqup" + "lfsx_lfpxs" + "lfsx_lfsx" * ]
[ [ "strongly normalizing for term vectors" ] "csx_vector ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )" "csx_cnx_vector" + "csx_csx_vector" * ]
[ [ "strongly normalizing for terms" ] "csx ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )" "csx_simple" + "csx_simple_theq" + "csx_drops" + "csx_lsubr" + "csx_lfdeq" + "csx_aaa" + "csx_gcp" + "csx_gcr" + "csx_lfpx" + "csx_cnx" + "csx_cpxs" + "csx_lfpxs" + "csx_csx" * ]
- [ [ "for lenvs on referred entries" ] "lfpxs ( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )" "lfpxs_length" + "lfpxs_drops" + "lfpxs_fqup" + "lfpxs_lfdeq" + "lfpxs_aaa" + "lfpxs_cpxs" + "lfpxs_lfpxs" * ]
+ [ [ "for lenvs on referred entries" ] "lfpxs ( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )" "lfpxs_length" + "lfpxs_drops" + "lfpxs_fqup" + "lfpxs_lfdeq" + "lfpxs_aaa" + "lfpxs_cpxs" + "lfpxs_lpxs" + "lfpxs_lfpxs" * ]
[ [ "for lenvs on all entries" ] "lpxs ( ⦃?,?⦄ ⊢ ⬈*[?] ? )" * ]
- [ [ "for terms" ] "cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" "cpxs_tdeq" + "cpxs_theq" + "cpxs_theq_vector" + "cpxs_drops" + "cpxs_fqus" + "cpxs_lsubr" + "cpxs_lfdeq" + "cpxs_aaa" + "cpxs_lfpx" + "cpxs_cnx" + "cpxs_cpxs" * ]
+ [ [ "for terms" ] "cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" "cpxs_tdeq" + "cpxs_theq" + "cpxs_theq_vector" + "cpxs_drops" + "cpxs_fqus" + "cpxs_lsubr" + "cpxs_lfdeq" + "cpxs_aaa" + "cpxs_lpx" + "cpxs_lfpx" + "cpxs_cnx" + "cpxs_cpxs" * ]
}
]
}
}
]
[ { "context-sensitive parallel r-transition" * } {
- [ [ "for lenvs on referred entries" ] "lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lfpr_length" + "lfpr_drops" + "lfpr_fquq" + "lfpr_fqup" + "lfpr_frees" + "lfpr_aaa" + "lfpr_lfpx" + "lfpr_lfpr" * ]
+ [ [ "for lenvs on referred entries" ] "lfpr ( ⦃?,?⦄ ⊢ ➡[?,?] ? )" "lfpr_length" + "lfpr_drops" + "lfpr_fquq" + "lfpr_fqup" + "lfpr_aaa" + "lfpr_lfpx" + "lfpr_lfpr" * ]
[ [ "for binders" ] "cpr_ext ( ⦃?,?⦄ ⊢ ? ➡[?] ? )" * ]
[ [ "for terms" ] "cpr ( ⦃?,?⦄ ⊢ ? ➡[?] ? )" "cpr_drops" * ]
}
]
[ { "uncounted context-sensitive parallel rt-transition" * } {
[ [ "normal form for terms" ] "cnx ( ⦃?,?⦄ ⊢ ⬈[?,?] 𝐍⦃?⦄ )" "cnx_simple" + "cnx_drops" + "cnx_cnx" * ]
- [ [ "for lenvs on referred entries" ] "lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )" "lfpx_length" + "lfpx_drops" + "lfpx_fqup" + "lfpx_frees" + "lfpx_lfdeq" + "lfpx_aaa" + "lfpx_cpx" + "lfpx_lfpx" * ]
+ [ [ "for lenvs on referred entries" ] "lfpx ( ⦃?,?⦄ ⊢ ⬈[?,?] ? )" "lfpx_length" + "lfpx_drops" + "lfpx_fqup" + "lfpx_lfdeq" + "lfpx_aaa" + "lfpx_cpx" + "lfpx_lfpx" * ]
[ [ "for lenvs on all entries" ] "lpx ( ⦃?,?⦄ ⊢ ⬈[?] ? )" * ]
[ [ "for binders" ] "cpx_ext ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )" * ]
- [ [ "for terms" ] "cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )" "cpx_simple" + "cpx_drops" + "cpx_fqus" + "cpx_lsubr" + "cpx_lfxs" * ]
+ [ [ "for terms" ] "cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )" "cpx_simple" + "cpx_drops" + "cpx_fqus" + "cpx_lsubr" + "cpx_lfxs" + "cpx_lfeq" * ]
}
]
[ { "counted context-sensitive parallel rt-transition" * } {
}
]
[ { "generic extension of a context-sensitive relation" * } {
- [ [ "for lenvs on referred entries" ] "lfxs ( ? ⦻*[?,?] ? )" "lfxs_length" + "lfxs_drops" + "lfxs_fqup" + "lfxs_lfxs" * ]
+ [ [ "for lenvs on referred entries" ] "lfxs ( ? ⦻*[?,?] ? )" "lfxs_length" + "lfxs_lex" + "lfxs_drops" + "lfxs_fqup" + "lfxs_lfxs" * ]
}
]
[ { "context-sensitive free variables" * } {
+ [ [ "inclusion for restricted closures" ] "fle ( ⦃?,?⦄ ⊆ ⦃?,?⦄ )" "fle_drops" + "fle_fqup" + "fle_fle" * ]
[ [ "restricted refinement for lenvs" ] "lsubf ( ⦃?,?⦄ ⫃𝐅* ⦃?,?⦄ )" "lsubf_lsubr" + "lsubf_frees" + "lsubf_lsubf" * ]
[ [ "for terms" ] "frees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )" "frees_drops" + "frees_fqup" + "frees_frees" * ]
}
]
class "orange"
[ { "relocation" * } {
- [ { "generic slicing for local environments" * } {
- [ [ "" ] "drops_vector ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )" * ]
- [ [ "" ] "drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )" "drops_lstar" + "drops_weight" + "drops_length" + "drops_cext2" + "drops_lexs" + "drops_lreq" + "drops_drops" * ]
+ [ { "generic slicing" * } {
+ [ [ "for lenvs" ] "drops ( ⬇*[?,?] ? ≡ ? ) ( ⬇*[?] ? ≡ ? )" "drops_lstar" + "drops_weight" + "drops_length" + "drops_cext2" + "drops_lexs" + "drops_lreq" + "drops_drops" + "drops_vector" * ]
}
]
[ { "generic relocation" * } {
- [ [ "" ] "lifts_bind ( ⬆*[?] ? ≡ ? )" "lifts_weight_bind" + "lifts_lifts_bind" * ]
- [ [ "" ] "lifts_vector ( ⬆*[?] ? ≡ ? )" "lifts_lifts_vector" * ]
- [ [ "" ] "lifts ( ⬆*[?] ? ≡ ? )" "lifts_simple" + "lifts_weight" + "lifts_tdeq" + "lifts_lifts" * ]
+ [ [ "for binders" ] "lifts_bind ( ⬆*[?] ? ≡ ? )" "lifts_weight_bind" + "lifts_lifts_bind" * ]
+ [ [ "for term vectors" ] "lifts_vector ( ⬆*[?] ? ≡ ? )" "lifts_lifts_vector" * ]
+ [ [ "for terms" ] "lifts ( ⬆*[?] ? ≡ ? )" "lifts_simple" + "lifts_weight" + "lifts_tdeq" + "lifts_lifts" * ]
}
]
- [ { "ranged equivalence for local environments" * } {
- [ [ "" ] "lreq ( ? ≡[?] ? )" "lreq_length" + "lreq_lreq" * ]
+ [ { "syntactic equivalence" * } {
+ [ [ "for lenvs on selected entries" ] "lreq ( ? ≡[?] ? )" "lreq_length" + "lreq_lreq" * ]
}
]
[ { "generic entrywise extension" * } {
- [ [ "" ] "lex ( ? ⦻[?] ? )" * ]
- [ [ "" ] "lexs ( ? ⦻*[?,?,?] ? )" "lexs_tc" + "lexs_length" + "lexs_lexs" * ]
+ [ [ "for lenvs of one contex-sensitive relation" ] "lex ( ? ⦻[?] ? )" "lex_tc" * ]
+ [ [ "for lenvs of two contex-sensitive relations" ] "lexs ( ? ⦻*[?,?,?] ? )" "lexs_tc" + "lexs_length" + "lexs_lexs" * ]
}
]
}
]
class "red"
[ { "syntax" * } {
- [ { "append for local environments" * } {
- [ [ "" ] "append ( ? @@ ? )" "append_length" * ]
+ [ { "equivalence up to exclusion binders" * } {
+ [ [ "for lenvs" ] "lveq ( ? ≋ⓧ*[?,?] ? )" "lveq_length" + "lveq_lveq" * ]
+ }
+ ]
+ [ { "append" * } {
+ [ [ "for lenvs" ] "append ( ? @@ ? )" "append_length" * ]
}
]
- [ { "head equivalence for terms" * } {
- [ [ "" ] "theq ( ? ⩳[?,?] ? )" "theq_simple" + "theq_tdeq" + "theq_theq" + "theq_simple_vector" * ]
+ [ { "head equivalence" * } {
+ [ [ "for terms" ] "theq ( ? ⩳[?,?] ? )" "theq_simple" + "theq_tdeq" + "theq_theq" + "theq_simple_vector" * ]
}
]
[ { "degree-based equivalence" * } {