![[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 | -293 | +367 | characters | -439998 | +431873 | nodes | -1286813 | +1830977 | ||||
| propositions | theorems | -91 | +128 | lemmas | -888 | +1302 | total | -979 | +1430 | ||||
| concepts | declared | -49 | +55 | defined | -85 | +82 | total | -134 | +137 |
| 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«Â¡[?,?] ? ) | +lsubsv_lsuba lsubsv_lsubd lsubsv_lstas lsubsv_cpds lsubsv_cpcs lsubsv_snv |
|
@@ -331,8 +277,24 @@
stratified native validity | +hsnv ( �,?⦠⢠? ¡[?,?,?] ) | +hsnv_aaa | +
+ + |
+
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
+ + |
+
+ + |
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_cpes snv_preserve |
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@@ -343,8 +305,8 @@
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| equivalence | decomposed extended equivalence | -cpes ( â¦?,?⦠⢠? â¢*â¬*[?,?] ? ) | -cpes_cpds | +cpes ( â¦?,?⦠⢠? â¢*â¬*[?,?,?,?] ? ) | +cpes_aaa cpes_cpcs cpes_cpes |
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@@ -380,7 +342,7 @@
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| computation | -context-sensitive extended evaluation | +evaluation for context-sensitive extended reduction | cpxe ( â¦?,?⦠⢠â¡*[?,?] ðâ¦?⦠) |
@@ -396,7 +358,7 @@ |
|
- context-sensitive evaluation | +evaluation for context-sensitive reduction | cpre ( â¦?,?⦠⢠â¡* ðâ¦?⦠) | cpre_cpre | @@ -413,7 +375,7 @@ | strongly normalizing "big tree" computation | fsb ( â¦?,?⦠⢠⦥[?,?] ? ) | fsb_alt ( â¦?,?⦠⢠⦥⦥[?,?] ? ) | -fsb_fleq fsb_csx | +fsb_aaa fsb_csx |
|
@@ -423,8 +385,8 @@
strongly normalizing extended computation | -csx_vector ( â¦?,?⦠⢠â¬*[?,?] ? ) | -csx_tstc_vector csx_aaa | +lcosx ( ? ⢠~â¬*[?,?,?] ? ) | +lcosx_cpx |
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@@ -439,9 +401,9 @@
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- csx ( â¦?,?⦠⢠â¬*[?,?] ? ) | -csx_alt ( â¦?,?⦠⢠â¬â¬*[?,?] ? ) | -csx_lift csx_lpx | +lsx ( ? ⢠â¬*[?,?,?,?] ? ) | +lsx_alt ( ? ⢠â¬â¬*[?,?,?,?] ? ) | +lsx_drop lsx_lpx lsx_lpxs llsx_csx |
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@@ -450,9 +412,11 @@
|
- parallel computation for "big tree" normal forms | -fpns ( â¦?,?,?⦠⢠ââ¡*[?,?] â¦?,?,?⦠) | -fpns_fpns | +
+ + |
+ csx_vector ( â¦?,?⦠⢠â¬*[?,?] ? ) | +csx_tstc_vector csx_aaa |
|
@@ -460,13 +424,27 @@
|||||||||||||||||||||||||||||||||||||||||
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+ + |
+
+ + |
+ csx ( â¦?,?⦠⢠â¬*[?,?] ? ) | +csx_alt ( â¦?,?⦠⢠â¬â¬*[?,?] ? ) | +csx_lift csx_lleq csx_lpx csx_lpxs csx_fpbs | +
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
|
"big tree" parallel computation | -fpbr ( â¦?,?,?⦠ââ¥[?,?] â¦?,?,?⦠) | -fpbr_fpbr | +fpbg ( â¦?,?,?⦠>â¡[?,?] â¦?,?,?⦠) | +fpbg_lift fpbg_fleq fpbg_fpbg |
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@@ -481,8 +459,8 @@
|
- fpbg ( â¦?,?,?⦠>[?,?] â¦?,?,?⦠) | -fpbg_lift fpbg_fpbg | +fpbc ( â¦?,?,?⦠â»â¡[?,?] â¦?,?,?⦠) | +fpbc_fleq fpbc_fpbs |
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@@ -490,6 +468,20 @@
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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+ + |
+
+ + |
+ fpbu ( â¦?,?,?⦠â»[?,?] â¦?,?,?⦠) | +fpbu_lift fpbu_lleq | +fpbu_fleq | +
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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@@ -499,7 +491,7 @@ |
fpbs ( â¦?,?,?⦠â¥[?,?] â¦?,?,?⦠) | fpbs_alt ( â¦?,?,?⦠â¥â¥[?,?] â¦?,?,?⦠) | -fpbs_lift fpbs_fleq fpbs_fpbs | +fpbs_lift fpbs_fleq fpbs_aaa fpbs_fpbs fpbs_ext |
|
@@ -509,7 +501,7 @@
decomposed extended computation | -cpds ( â¦?,?⦠⢠? â¢*â¡*[?,?] ? ) | +cpds ( â¦?,?⦠⢠? â¢*â¡*[?,?,?] ? ) | cpds_lift cpds_aaa cpds_cpds |
@@ -524,8 +516,10 @@ |
context-sensitive extended computation | lpxs ( â¦?,?⦠⢠â¡*[?,?] ? ) | -lpxs_alt ( â¦?,?⦠⢠â¡â¡*[?,?] ? ) | -lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs | +lpxs_drop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs | +
+ + |
|
@@ -538,7 +532,7 @@
cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) | -cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_aaa cpxs_cpxs | +cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs |
|
@@ -552,8 +546,10 @@
context-sensitive computation | lprs ( â¦?,?⦠⢠â¡* ? ) | -lprs_alt ( â¦?,?⦠⢠â¡â¡* ? ) | -lprs_ldrop lprs_cprs lprs_lprs | +lprs_drop lprs_cprs lprs_lprs | +
+ + |
|
@@ -579,8 +575,8 @@
local env. ref. for abstract candidates of reducibility | -lsubc ( ? ⢠? â[?] ? ) | -lsubc_ldrop lsubc_ldrops lsubc_lsuba | +lsubc ( ? ⢠? â«[?] ? ) | +lsubc_drop lsubc_drops lsubc_lsuba |
|
@@ -603,24 +599,8 @@
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| reduction | "big tree" parallel reduction | -fpbc ( â¦?,?,?⦠â»[?,?] â¦?,?,?⦠) | -fpbc_lift | -
- - |
-
- - |
- ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
- - |
-
- - |
fpb ( â¦?,?,?⦠â½[?,?] â¦?,?,?⦠) | -fpb_lift | +fpb_lift fpb_aaa |
|
@@ -632,8 +612,8 @@
|
- 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 |
@@ -648,10 +628,8 @@ |
context-sensitive extended reduction | lpx ( â¦?,?⦠⢠â¡[?,?] ? ) | -lpx_ldrop lpx_aaa lpx_lpx | -
- - |
+ lpx_drop lpx_frees | +lpx_lleq lpx_aaa |
|
@@ -664,7 +642,7 @@
cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) | -cpx_lift cpx_cix cpx_cpx | +cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix |
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@@ -676,9 +654,9 @@
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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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@@ -690,9 +668,9 @@
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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 |
|
@@ -704,8 +682,8 @@
|
- context-sensitive normal forms | -cnr ( â¦?,?⦠⢠ðâ¦?⦠) | +normal forms for context-sensitive reduction | +cnr ( â¦?,?⦠⢠⡠ðâ¦?⦠) | cnr_lift cnr_crr cnr_cir |
@@ -720,7 +698,7 @@ |
context-sensitive reduction | lpr ( �,?⦠⢠⡠? ) | -lpr_ldrop lpr_lpr | +lpr_drop lpr_lpr |
|
@@ -736,7 +714,7 @@
cpr ( �,?⦠⢠? ⡠? ) | -cpr_lift cpr_cir | +cpr_lift cpr_llpx_sn cpr_cir |
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@@ -748,9 +726,9 @@
|
- 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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@@ -762,9 +740,9 @@
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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 |
|
@@ -791,18 +769,18 @@
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 ( ? ⢠? â«âª[?,?] ? ) | +lsubd_da lsubd_lsubd |
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@@ -814,9 +792,9 @@
|
- 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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@@ -828,9 +806,9 @@
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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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@@ -842,9 +820,9 @@
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- local env. ref. for degree assignment | -lsubd ( ? ⢠? âªâ ? ) | -lsubd_da lsubd_lsubd | +parameters | +sh | +sd |
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@@ -856,9 +834,9 @@
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- degree assignment | -da ( â¦?,?⦠⢠? âª[?,?] ? ) | -da_lift da_da | +local env. ref. for atomic arity assignment | +lsuba ( ? ⢠? â«â ? ) | +lsuba_aaa lsuba_lsuba |
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@@ -870,9 +848,9 @@
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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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@@ -881,10 +859,82 @@
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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 | +
+ + |
+
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
+ + |
+
+ + |
+ lleq ( ? â¡[?,?] ? ) | +lleq_alt lleq_alt_rec lleq_leq lleq_drop lleq_fqus lleq_llor lleq_lleq | +
+ + |
+
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
+ + |
+ 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 | +
+ + |
+
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
+ + |
+ pointwise union for local environments | +llor ( ? â©[?,?] ? â¡ ? ) | +llor_alt llor_drop | +
+ + |
+
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
+ + |
+ context-sensitive exclusion from free variables | +frees ( ? ⢠? ϵ ð *[?]â¦?⦠) | +frees_append frees_leq frees_lift |
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@@ -892,12 +942,24 @@
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+ + |
+ contxt-sensitive extended multiple substitution | +cpys ( â¦?,?⦠⢠? â¶*[?,?] ? ) | +cpys_alt ( â¦?,?⦠⢠? â¶â¶*[?,?] ? ) | +cpys_lift cpys_cpys | +
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
|
iterated structural successor for closures | -fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) | +fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) | fqus_alt fqus_fqus |
@@ -913,7 +975,7 @@ |
|
- fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | +fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | fqup_fqup |
@@ -926,9 +988,9 @@ |
|
- 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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@@ -977,11 +1039,13 @@
gr2_gr2 | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| relocation | +substitution | structural successor for closures | -fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) | -fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) | -fquq_fquq | +fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) | +fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) | +
+ + |
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@@ -993,8 +1057,10 @@
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- fqu ( â¦?,?,?⦠â â¦?,?,?⦠) | -fqu_fqu | +fqu ( â¦?,?,?⦠â â¦?,?,?⦠) | +
+ + |
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@@ -1006,9 +1072,9 @@
|
- lazy equivalence for local environments | -lleq ( ? â[?] ? ) | -lleq_fleq | +global env. slicing | +gget ( â©[?] ? â¡ ? ) | +gget_gget |
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@@ -1020,9 +1086,37 @@
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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 | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||
|
+ + |
+ local env. ref. for extended substitution | +lsuby ( ? â[?,?] ? ) | +lsuby_lsuby | +
+ + |
+
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
+ + |
+ pointwise extension of a relation | +lpx_sn | +lpx_sn_alt lpx_sn_tc lpx_sn_drop lpx_sn_lpx_sn |
|
@@ -1035,8 +1129,8 @@
basic local env. slicing | -ldrop ( â©[?,?] ? â¡ ? ) | -ldrop_append ldrop_lpx_sn ldrop_ldrop | +drop ( â©[?,?,?] ? â¡ ? ) | +drop_append drop_leq drop_drop |
|
@@ -1066,7 +1160,7 @@
lift ( â§[?,?] ? â¡ ? ) | -lift_lift | +lift_neq lift_lift |
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@@ -1076,9 +1170,9 @@
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| grammar | -pointwise extension of a relation | -lpx_sn | -lpx_sn_tc lpx_sn_lpx_sn | +equivalence for local environments | +leq ( ? ⩬[?,?] ? ) | +leq_leq |
|
@@ -1091,7 +1185,7 @@
same top term constructor | -tstc ( ? â ? ) | +tstc ( ? â ? ) | tstc_tstc tstc_vector |
@@ -1105,8 +1199,8 @@ |
closures | -cl_shift ( ? @@ ? ) | -cl_weight ( â¯{?,?,?} ) | +cl_weight ( â¯{?,?,?} ) | +cl_restricted_weight ( â¯{?,?} ) |
|
@@ -1192,7 +1286,7 @@