![[Spacer]](http://lambdadelta.info/images/rainbow.png "lambdadelta rainbow rule")
| domain | -block | -leader | -applicator (with âθ)* | -reduction | -âζ * | -reference * | -
| {X | Π⢠X : W} | -local typed abstraction * | -Π⢠+λW | -âV | -âβ | -no | -#i | -
|
- - |
- local typed declaration ** | -Π⢠-λW | -âV | -âβ | -no | -#i | -
|
- - |
- global typed declaration *** | -Π⢠pλW | -no | -no | -no | -$p | -
|
- - |
- native type annotation * | -Π⢠âW | -no | -no | -yes | -no | -
| {X | Π⢠X = V} | -local abbreviation * | -Π⢠+δV | -no | -local âδ | -yes | -#i | -
|
- - |
- local definition ** | -Π⢠-δV | -no | -local âδ | -no | -#i | -
|
- - |
- global definition *** | -Π⢠pδV | -no | -global âδ | -no | -$p | -
| no | -sort **** | -Π⢠âk | -no | -no | -no | -no | -
| category | -objects | -+ | category | +objects | +
|
- + |
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- + |
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- + |
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- + |
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| sizes | files | -307 | +362 | characters | -488137 | +431125 | nodes | -1416510 | +1829252 | ||||
| propositions | theorems | -90 | +123 | lemmas | -956 | +1300 | total | -1046 | +1423 | ||||
| concepts | declared | -48 | +54 | defined | -75 | +84 | total | -123 | +138 |
| component | -plane | -files | -+ | component | +plane | +files | +
+ + |
+
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| examples | +terms with special features | +ex_cpr_omega | +
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- + |
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- + |
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| + | + | + |
+ + |
+
+ + |
+
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| dynamic typing | local env. ref. for stratified native validity | -lsubsv ( ? ⢠? ¡â[?,?] ? ) | -lsubsv_ldrop lsubsv_lsubd lsubsv_lsuba lsubsv_lsstas lsubsv_cpds lsubsv_cpcs lsubsv_snv | +lsubsv ( ? ⢠? ¡â«[?,?] ? ) | +lsubsv_lsuba lsubsv_lsubd lsubsv_lstas lsubsv_cpds lsubsv_cpcs lsubsv_snv |
|
@@ -332,7 +278,7 @@
stratified native validity | snv ( �,?⦠⢠? ¡[?,?] ) | -snv_lift snv_da_lpr snv_aaa snv_lsstas snv_lsstas_lpr snv_lpr snv_cpcs | +snv_lift snv_aaa snv_da_lpr snv_lstas snv_lstas_lpr snv_lpr snv_cpcs snv_preserve |
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@@ -380,7 +326,7 @@
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| computation | -context-sensitive extended evaluation | +evaluation for context-sensitive extended reduction | cpxe ( â¦?,?⦠⢠â¡*[?,?] ðâ¦?⦠) |
@@ -396,7 +342,7 @@ |
|
- context-sensitive evaluation | +evaluation for context-sensitive reduction | cpre ( â¦?,?⦠⢠â¡* ðâ¦?⦠) | cpre_cpre |
@@ -423,8 +369,8 @@
|
strongly normalizing extended computation | -lsx ( ? ⢠â¬*[?,?,?] ? ) | -lsx_cpxs lsx_csx | +lcosx ( ? ⢠~â¬*[?,?,?] ? ) | +lcosx_cpx |
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@@ -432,6 +378,20 @@
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+ + |
+
+ + |
+ lsx ( ? ⢠â¬*[?,?,?,?] ? ) | +lsx_alt ( ? ⢠â¬â¬*[?,?,?,?] ? ) | +lsx_drop lsx_lpx lsx_lpxs llsx_csx | +
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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@@ -457,7 +417,7 @@ |
csx ( â¦?,?⦠⢠â¬*[?,?] ? ) | csx_alt ( â¦?,?⦠⢠â¬â¬*[?,?] ? ) | -csx_lift csx_lpx csx_fpbs | +csx_lift csx_lleq csx_lpx csx_lpxs csx_fpbs |
|
@@ -467,8 +427,8 @@
"big tree" parallel computation | -fpbg ( â¦?,?,?⦠>â[?,?] â¦?,?,?⦠) | -fpbg_lift fpbg_fpns fpbg_fpbg | +fpbg ( â¦?,?,?⦠>â¡[?,?] â¦?,?,?⦠) | +fpbg_lift fpbg_fleq fpbg_fpbg |
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@@ -483,8 +443,8 @@
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- fpbc ( â¦?,?,?⦠â»â[?,?] â¦?,?,?⦠) | -fpbc_fpns fpbc_fpbs | +fpbc ( â¦?,?,?⦠â»â¡[?,?] â¦?,?,?⦠) | +fpbc_fleq fpbc_fpbs |
|
@@ -500,10 +460,8 @@
fpbu ( â¦?,?,?⦠â»[?,?] â¦?,?,?⦠) | -fpbu_lift fpbu_fpns | -
- - |
+ fpbu_lift fpbu_lleq | +fpbu_fleq |
|
@@ -517,21 +475,7 @@
fpbs ( â¦?,?,?⦠â¥[?,?] â¦?,?,?⦠) | fpbs_alt ( â¦?,?,?⦠â¥â¥[?,?] â¦?,?,?⦠) | -fpbs_lift fpbs_fpns fpbs_fpbs | -
- - |
- |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
- - |
- parallel computation for "big tree" normal forms | -fpns ( â¦?,?,?⦠⢠ââ¡*[?,?] â¦?,?,?⦠) | -fpns_fpns | -
- - |
+ fpbs_lift fpbs_fleq fpbs_aaa fpbs_fpbs fpbs_ext |
|
@@ -556,8 +500,10 @@
context-sensitive extended computation | lpxs ( â¦?,?⦠⢠â¡*[?,?] ? ) | -lpxs_alt ( â¦?,?⦠⢠â¡â¡*[?,?] ? ) | -lpxs_ldrop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs | +lpxs_drop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs | +
+ + |
|
@@ -570,7 +516,7 @@
cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) | -cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs | +cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs |
|
@@ -584,8 +530,10 @@
context-sensitive computation | lprs ( â¦?,?⦠⢠â¡* ? ) | -lprs_alt ( â¦?,?⦠⢠â¡â¡* ? ) | -lprs_ldrop lprs_cprs lprs_lprs | +lprs_drop lprs_cprs lprs_lprs | +
+ + |
|
@@ -611,8 +559,8 @@
local env. ref. for abstract candidates of reducibility | -lsubc ( ? ⢠? â[?] ? ) | -lsubc_ldrop lsubc_ldrops lsubc_lsuba | +lsubc ( ? ⢠? â«[?] ? ) | +lsubc_drop lsubc_drops lsubc_lsuba |
|
@@ -636,7 +584,7 @@
reduction | "big tree" parallel reduction | fpb ( â¦?,?,?⦠â½[?,?] â¦?,?,?⦠) | -fpb_lift | +fpb_lift fpb_aaa |
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@@ -648,8 +596,8 @@
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- context-sensitive extended normal forms | -cnx ( â¦?,?⦠⢠ð[?,?]â¦?⦠) | +normal forms for context-sensitive extended reduction | +cnx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | cnx_lift cnx_crx cnx_cix |
@@ -664,10 +612,8 @@ |
context-sensitive extended reduction | lpx ( â¦?,?⦠⢠â¡[?,?] ? ) | -lpx_leq lpx_ldrop lpx_lleq lpx_aaa | -
- - |
+ lpx_drop lpx_frees | +lpx_lleq lpx_aaa |
|
@@ -680,7 +626,7 @@
cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) | -cpx_leq cpx_lift cpx_cix | +cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix |
|
@@ -692,9 +638,9 @@
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- context-sensitive extended irreducible forms | -cix ( â¦?,?⦠⢠ð[?,?]â¦?⦠) | -cix_append cix_lift | +irreducible forms for context-sensitive extended reduction | +cix ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | +cix_lift |
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@@ -706,9 +652,9 @@
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- context-sensitive extended reducible forms | -crx ( â¦?,?⦠⢠ð[?,?]â¦?⦠) | -crx_append crx_lift | +reducible forms for context-sensitive extended reduction | +crx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | +crx_lift |
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@@ -720,8 +666,8 @@
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- context-sensitive normal forms | -cnr ( â¦?,?⦠⢠ðâ¦?⦠) | +normal forms for context-sensitive reduction | +cnr ( â¦?,?⦠⢠⡠ðâ¦?⦠) | cnr_lift cnr_crr cnr_cir |
@@ -736,7 +682,7 @@ |
context-sensitive reduction | lpr ( �,?⦠⢠⡠? ) | -lpr_ldrop lpr_lpr | +lpr_drop lpr_lpr |
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@@ -752,7 +698,7 @@
cpr ( �,?⦠⢠? ⡠? ) | -cpr_lift cpr_cir | +cpr_lift cpr_llpx_sn cpr_cir |
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@@ -764,9 +710,9 @@
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- context-sensitive irreducible forms | -cir ( â¦?,?⦠⢠ðâ¦?⦠) | -cir_append cir_lift | +irreducible forms for context-sensitive reduction | +cir ( â¦?,?⦠⢠⡠ðâ¦?⦠) | +cir_lift |
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@@ -778,9 +724,9 @@
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- context-sensitive reducible forms | -crr ( â¦?,?⦠⢠ðâ¦?⦠) | -crr_append crr_lift | +reducible forms for context-sensitive reduction | +crr ( â¦?,?⦠⢠⡠ðâ¦?⦠) | +crr_lift |
|
@@ -807,18 +753,18 @@
iterated static type assignment | -lsstas ( â¦?,?⦠⢠? â¢*[?,?,?] ? ) | -lsstas_alt ( â¦?,?⦠⢠? â¢â¢*[?,?,?] ? ) | -lsstas_lift lsstas_aaa lsstas_lsstas | +lstas ( â¦?,?⦠⢠? â¢*[?,?] ? ) | +lstas_alt ( â¦?,?⦠⢠? â¢â¢*[?,?] ? ) | +lstas_lift lstas_aaa lstas_da lstas_lstas |
|
| static typing | -local env. ref. for atomic arity assignment | -lsuba ( ? ⢠? ââ ? ) | -lsuba_ldrop lsuba_aaa lsuba_lsuba | +local env. ref. for degree assignment | +lsubd ( ? ⢠? âªâ« ? ) | +lsubd_da lsubd_lsubd |
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@@ -830,9 +776,9 @@
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- atomic arity assignment | -aaa ( â¦?,?⦠⢠? â ? ) | -aaa_lift aaa_lifts aaa_da aaa_ssta aaa_aaa | +degree assignment | +da ( â¦?,?⦠⢠? âª[?,?] ? ) | +da_lift da_aaa da_sta da_da |
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@@ -844,9 +790,9 @@
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- stratified static type assignment | -ssta ( â¦?,?⦠⢠? â¢[?,?] ? ) | -ssta_lift ssta_ssta | +static type assignment | +sta ( â¦?,?⦠⢠? â¢[?] ? ) | +sta_lift sta_lpx_sn sta_aaa sta_sta |
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@@ -858,9 +804,9 @@
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- local env. ref. for degree assignment | -lsubd ( ? ⢠? âªâ ? ) | -lsubd_da lsubd_lsubd | +parameters | +sh | +sd |
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@@ -872,9 +818,9 @@
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- degree assignment | -da ( â¦?,?⦠⢠? âª[?,?] ? ) | -da_lift da_da | +local env. ref. for atomic arity assignment | +lsuba ( ? ⢠? ââ« ? ) | +lsuba_aaa lsuba_lsuba |
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@@ -886,9 +832,9 @@
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- parameters | -sh | -sd | +atomic arity assignment | +aaa ( â¦?,?⦠⢠? â ? ) | +aaa_lift aaa_lifts aaa_fqus aaa_lleq aaa_aaa |
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@@ -897,10 +843,82 @@
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| substitution | -restricted local env. ref. | -lsubr ( ? â ? ) | -lsubr_lsubr | +
+ + |
+ restricted local env. ref. | +lsubr ( ? â« ? ) | +lsubr_lsubr | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| multiple substitution | +lazy equivalence | +fleq ( â¦?,?,?⦠â¡[?] â¦?,?,?⦠) | +fleq_fleq | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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+ + |
+
+ + |
+ lleq ( ? â¡[?,?] ? ) | +lleq_alt lleq_alt_rec lleq_leq lleq_drop lleq_fqus lleq_llor lleq_lleq | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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+ + |
+ lazy pointwise extension of a relation | +llpx_sn | +llpx_sn_alt llpx_sn_alt_rec llpx_sn_tc llpx_sn_leq llpx_sn_drop llpx_sn_lpx_sn llpx_sn_frees llpx_sn_llor | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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+ + |
+ pointwise union for local environments | +llor ( ? â©[?,?] ? â¡ ? ) | +llor_alt llor_drop | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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+ + |
+ context-sensitive exclusion from free variables | +frees ( ? ⢠? ϵ ð *[?]â¦?⦠) | +frees_append frees_leq frees_lift |
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@@ -908,13 +926,25 @@
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+ + |
+ contxt-sensitive extended multiple substitution | +cpys ( â¦?,?⦠⢠? â¶*[?,?] ? ) | +cpys_alt ( â¦?,?⦠⢠? â¶â¶*[?,?] ? ) | +cpys_lift cpys_cpys | +
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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iterated structural successor for closures | -fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) | -fqus_alt fqus_lleq fqus_fqus | +fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) | +fqus_alt fqus_fqus |
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@@ -929,8 +959,8 @@
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- fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | -fqup_lleq fqup_fqup | +fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | +fqup_fqup |
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@@ -942,9 +972,9 @@
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- generic local env. slicing | -ldrops ( â©*[?] ? â¡ ? ) | -ldrops_ldrop ldrops_ldrops | +iterated local env. slicing | +drops ( â©*[?,?] ? â¡ ? ) | +drops_drop drops_drops |
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@@ -993,11 +1023,13 @@
gr2_gr2 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| relocation | +substitution | structural successor for closures | -fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) | -fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) | -fquq_lleq | +fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) | +fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) | +
+ + |
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@@ -1009,8 +1041,10 @@
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- fqu ( â¦?,?,?⦠â â¦?,?,?⦠) | -fqu_lleq | +fqu ( â¦?,?,?⦠â â¦?,?,?⦠) | +
+ + |
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@@ -1022,9 +1056,9 @@
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- lazy equivalence for local environments | -lleq ( ? â[?,?] ? ) | -lleq_lleq | +global env. slicing | +gget ( â©[?] ? â¡ ? ) | +gget_gget |
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@@ -1036,9 +1070,9 @@
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- global env. slicing | -gdrop ( â©[?] ? â¡ ? ) | -gdrop_gdrop | +contxt-sensitive extended ordinary substitution | +cpy ( â¦?,?⦠⢠? â¶[?,?] ? ) | +cpy_lift cpy_nlift cpy_cpy |
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@@ -1050,9 +1084,9 @@
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- basic local env. slicing | -ldrop ( â©[?,?] ? â¡ ? ) | -ldrop_append ldrop_lpx_sn ldrop_leq ldrop_ldrop | +local env. ref. for extended substitution | +lsuby ( ? âÃ[?,?] ? ) | +lsuby_lsuby |
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@@ -1064,9 +1098,9 @@
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- basic term relocation | -lift_vector ( â§[?,?] ? â¡ ? ) | -lift_lift_vector | +pointwise extension of a relation | +lpx_sn | +lpx_sn_alt lpx_sn_tc lpx_sn_drop lpx_sn_lpx_sn |
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@@ -1078,11 +1112,9 @@
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-
- - |
- lift ( â§[?,?] ? â¡ ? ) | -lift_lift | +basic local env. slicing | +drop ( â©[?,?,?] ? â¡ ? ) | +drop_append drop_leq drop_drop |
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@@ -1091,26 +1123,40 @@
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| grammar | -equivalence for local environments | -leq ( ? â[?,?] ? ) | -+ |
|
- + | basic term relocation | +lift_vector ( â§[?,?] ? â¡ ? ) | +lift_lift_vector | +
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- + |
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| + |
|
- pointwise extension of a relation | -lpx_sn | -lpx_sn_tc lpx_sn_lpx_sn | +
+ + |
+ lift ( â§[?,?] ? â¡ ? ) | +lift_neq lift_lift | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| grammar | +equivalence for local environments | +leq ( ? ⩬[?,?] ? ) | +leq_leq |
|
@@ -1123,7 +1169,7 @@
same top term constructor | -tstc ( ? â ? ) | +tstc ( ? â ? ) | tstc_tstc tstc_vector |
@@ -1137,8 +1183,8 @@ |
closures | -cl_shift ( ? @@ ? ) | -cl_weight ( â¯{?,?,?} ) | +cl_weight ( â¯{?,?,?} ) | +cl_restricted_weight ( â¯{?,?} ) |
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@@ -1224,7 +1270,7 @@