![[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 | -
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- - |
- local typed declaration ** | -Π⢠-λW | -âV | -âβ | -no | -#i | -
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- - |
- global typed declaration *** | -Π⢠pλW | -no | -no | -no | -$p | -
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- - |
- native type annotation * | -Π⢠âW | -no | -no | -yes | -no | -
| {X | Π⢠X = V} | -local abbreviation * | -Π⢠+δV | -no | -local âδ | -yes | -#i | -
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- - |
- local definition ** | -Π⢠-δV | -no | -local âδ | -no | -#i | -
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- - |
- global definition *** | -Π⢠pδV | -no | -global âδ | -no | -$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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- + |
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| sizes | files | -329 | +362 | characters | -570962 | +431129 | nodes | -1619084 | +1829245 | ||||
| propositions | theorems | -108 | +123 | lemmas | -1122 | +1300 | total | -1230 | +1423 | ||||
| concepts | declared | -52 | +54 | defined | -76 | +84 | total | -128 | +138 |
| component | -plane | -files | -+ | component | +plane | +files | +
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- + |
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- + |
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||
| examples | +terms with special features | +ex_cpr_omega | +
+ + |
+
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||||||||
| + | + | + |
+ + |
+
+ + |
+
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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 |
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@@ -340,7 +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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@@ -431,8 +369,8 @@
strongly normalizing extended computation | -lcosx ( ? ⢠⧤â¬*[?,?,?] ? ) | -lcosx_cpxs | +lcosx ( ? ⢠~â¬*[?,?,?] ? ) | +lcosx_cpx |
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@@ -447,11 +385,9 @@
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- lsx ( ? ⢠ââ¬*[?,?,?,?] ? ) | -lsx_ldrop lsx_cpxs lsx_csx | -
- - |
+ lsx ( ? ⢠â¬*[?,?,?,?] ? ) | +lsx_alt ( ? ⢠â¬â¬*[?,?,?,?] ? ) | +lsx_drop lsx_lpx lsx_lpxs llsx_csx |
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@@ -481,7 +417,7 @@
csx ( â¦?,?⦠⢠â¬*[?,?] ? ) | csx_alt ( â¦?,?⦠⢠â¬â¬*[?,?] ? ) | -csx_lift csx_lpx csx_lpxs csx_fpbs | +csx_lift csx_lleq csx_lpx csx_lpxs csx_fpbs |
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@@ -491,8 +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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@@ -507,8 +443,8 @@
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- fpbc ( â¦?,?,?⦠â»â[?,?] â¦?,?,?⦠) | -fpbc_fpns fpbc_fpbs | +fpbc ( â¦?,?,?⦠â»â¡[?,?] â¦?,?,?⦠) | +fpbc_fleq fpbc_fpbs |
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@@ -524,10 +460,8 @@
fpbu ( â¦?,?,?⦠â»[?,?] â¦?,?,?⦠) | -fpbu_lift fpbu_fpns | -
- - |
+ fpbu_lift fpbu_lleq | +fpbu_fleq |
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@@ -541,21 +475,7 @@
fpbs ( â¦?,?,?⦠â¥[?,?] â¦?,?,?⦠) | fpbs_alt ( â¦?,?,?⦠â¥â¥[?,?] â¦?,?,?⦠) | -fpbs_lift fpbs_aaa fpbs_fpns fpbs_fpbs fpbs_ext | -
- - |
- ||||||
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- - |
- parallel computation for "big tree" normal forms | -fpns ( â¦?,?,?⦠⢠ââ¡*[?,?] â¦?,?,?⦠) | -fpns_fpns | -
- - |
+ fpbs_lift fpbs_fleq fpbs_aaa fpbs_fpbs fpbs_ext |
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@@ -580,8 +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 | +
+ + |
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@@ -594,7 +516,7 @@
cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) | -cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_cpys cpxs_lleq cpxs_aaa cpxs_cpxs | +cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs |
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@@ -608,8 +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 | +
+ + |
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@@ -635,8 +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 |
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@@ -688,10 +612,8 @@
context-sensitive extended reduction | lpx ( â¦?,?⦠⢠â¡[?,?] ? ) | -lpx_ldrop lpx_cpys lpx_lleq lpx_aaa | -
- - |
+ lpx_drop lpx_frees | +lpx_lleq lpx_aaa |
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@@ -704,7 +626,7 @@
cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) | -cpx_lift cpx_cpys cpx_lleq cpx_cix | +cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix |
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@@ -760,7 +682,7 @@
context-sensitive reduction | lpr ( �,?⦠⢠⡠? ) | -lpr_ldrop lpr_lpr | +lpr_drop lpr_lpr |
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@@ -776,7 +698,7 @@
cpr ( �,?⦠⢠? ⡠? ) | -cpr_lift cpr_cir | +cpr_lift cpr_llpx_sn cpr_cir |
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@@ -831,18 +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 |
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| 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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@@ -854,9 +776,9 @@
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- atomic arity assignment | -aaa ( â¦?,?⦠⢠? â ? ) | -aaa_lift aaa_lifts aaa_fqus aaa_da aaa_ssta aaa_aaa | +degree assignment | +da ( â¦?,?⦠⢠? âª[?,?] ? ) | +da_lift da_aaa da_sta da_da |
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@@ -868,9 +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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@@ -882,9 +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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@@ -896,9 +818,9 @@
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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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@@ -910,9 +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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@@ -925,7 +847,7 @@
restricted local env. ref. | -lsubr ( ? â ? ) | +lsubr ( ? â« ? ) | lsubr_lsubr |
@@ -935,11 +857,71 @@ |
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| substitution | -lazy equivalence for local environments | -lleq ( ? â[?,?] ? ) | -lleq_alt ( ? ââ[?,?] ? ) | -lleq_ldrop lleq_fqus lleq_lleq lleq_ext | +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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@@ -961,7 +943,7 @@
iterated structural successor for closures | -fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) | +fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) | fqus_alt fqus_fqus |
@@ -977,7 +959,7 @@ |
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- fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | +fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | fqup_fqup |
@@ -991,8 +973,8 @@ |
iterated local env. slicing | -ldrops ( â©*[?,?] ? â¡ ? ) | -ldrops_ldrop ldrops_ldrops | +drops ( â©*[?,?] ? â¡ ? ) | +drops_drop drops_drops |
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@@ -1041,10 +1023,10 @@
gr2_gr2 | ||||||||||||||||||||||||||||||||||||
| relocation | -contxt-sensitive extended ordinary substitution | -cpy ( â¦?,?⦠⢠? â¶[?,?] ? ) | -cpy_lift cpy_cpy | +substitution | +structural successor for closures | +fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) | +fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) |
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@@ -1056,9 +1038,13 @@
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- local env. ref. for extended substitution | -lsuby ( ? âÃ[?,?] ? ) | -lsuby_lsuby | +
+ + |
+ fqu ( â¦?,?,?⦠â â¦?,?,?⦠) | +
+ + |
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@@ -1070,9 +1056,9 @@
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- structural successor for closures | -fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) | -fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) | +global env. slicing | +gget ( â©[?] ? â¡ ? ) | +gget_gget |
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@@ -1084,13 +1070,23 @@
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- + | contxt-sensitive extended ordinary substitution | +cpy ( â¦?,?⦠⢠? â¶[?,?] ? ) | +cpy_lift cpy_nlift cpy_cpy | +
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- fqu ( â¦?,?,?⦠â â¦?,?,?⦠) | -+ |
+ + |
+ |||||||||||||||||||||||||
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+ local env. ref. for extended substitution | +lsuby ( ? â[?,?] ? ) | +lsuby_lsuby |
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@@ -1102,9 +1098,9 @@
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- global env. slicing | -gdrop ( â©[?] ? â¡ ? ) | -gdrop_gdrop | +pointwise extension of a relation | +lpx_sn | +lpx_sn_alt lpx_sn_tc lpx_sn_drop lpx_sn_lpx_sn |
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@@ -1117,8 +1113,8 @@
basic local env. slicing | -ldrop ( â©[?,?,?] ? â¡ ? ) | -ldrop_lpx_sn ldrop_leq ldrop_ldrop | +drop ( â©[?,?,?] ? â¡ ? ) | +drop_append drop_leq drop_drop |
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@@ -1148,7 +1144,7 @@
lift ( â§[?,?] ? â¡ ? ) | -lift_lift | +lift_neq lift_lift |
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@@ -1159,7 +1155,7 @@
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| grammar | equivalence for local environments | -leq ( ? â[?,?] ? ) | +leq ( ? ⩬[?,?] ? ) | leq_leq |
@@ -1168,26 +1164,12 @@ |
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- - |
- pointwise extension of a relation | -lpx_sn | -lpx_sn_tc lpx_sn_lpx_sn | -
- - |
-
- - |
- |||||||||||||||||||||||||||||||||||||||||||||||||||||
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same top term constructor | -tstc ( ? â ? ) | +tstc ( ? â ? ) | tstc_tstc tstc_vector |
@@ -1288,7 +1270,7 @@ |