![[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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- + |
|
| sizes | files | -187 | +362 | characters | -363451 | +431129 | nodes | -982229 | +1829245 | ||||
| propositions | theorems | -85 | +123 | lemmas | -781 | +1300 | total | -866 | +1423 | ||||
| concepts | declared | -42 | +54 | defined | -70 | +84 | total | -112 | +138 |
| component | -plane | -files | -+ | component | +plane | +files | +
|
- + |
|
- + |
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| dynamic typing | -"big tree" parallel computation | -yprs ( ? ⢠â¦?,?⦠â¥[g] â¦?,?⦠) | -yprs_yprs | -ygt ( ? ⢠â¦?,?⦠>[g] â¦?,?⦠) | -ygt_ygt | -|||||||||||||||||||||||||||||||||||||||||
| + | examples | +terms with special features | +ex_cpr_omega | +
|
- "big tree" parallel reduction | -ypr ( ? ⢠â¦?,?⦠â½[g] â¦?,?⦠) | -ysc ( ? ⢠â¦?,?⦠â»[g] â¦?,?⦠) | -+ |
|
- + |
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| + | + | + | + |
+ + |
+
+ + |
+
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+ ||||||||||||||||||||||||||||||||||||||||
| dynamic typing | local env. ref. for stratified native validity | -lsubsv ( ? ⢠? ¡â[?] ? ) | -lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv | +lsubsv ( ? ⢠? â«Â¡[?,?] ? ) | +lsubsv_lsuba lsubsv_lsubd lsubsv_lstas lsubsv_cpds lsubsv_cpcs lsubsv_snv |
|
@@ -339,8 +277,8 @@
stratified native validity | -snv ( �,?⦠⢠? ¡[?] ) | -snv_lift snv_ltpss_dx snv_ltpss_sn snv_aaa snv_ssta snv_sstas snv_ssta_ltpr snv_ltpr snv_cpcs | +snv ( �,?⦠⢠? ¡[?,?] ) | +snv_lift snv_aaa snv_da_lpr snv_lstas snv_lstas_lpr snv_lpr snv_cpcs snv_preserve |
|
@@ -350,9 +288,9 @@
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| equivalence | -focalized equivalence | -lfpcs ( â¦?⦠â¬* â¦?⦠) | -lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs | +decomposed extended equivalence | +cpes ( â¦?,?⦠⢠? â¢*â¬*[?,?] ? ) | +cpes_cpds |
|
@@ -364,11 +302,9 @@
|
-
- - |
- fpcs ( â¦?,?⦠â¬* â¦?,?⦠) | -fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs | +context-sensitive equivalence | +cpcs ( â¦?,?⦠⢠? â¬* ? ) | +cpcs_aaa cpcs_cprs cpcs_cpcs |
|
@@ -377,80 +313,138 @@
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| + | conversion | +context-sensitive conversion | +cpc ( �,?⦠⢠? ⬠? ) | +cpc_cpc | +
|
- local env. ref. for stratified static type assignment | -lsubss ( ? â¢â[?] ? ) | -lsubss_ldrop lsubss_ssta lsubss_cpcs | -+ |
|
- + | |||||||||||||||||||||||||||||||||||
| computation | +evaluation for context-sensitive extended reduction | +cpxe ( â¦?,?⦠⢠â¡*[?,?] ðâ¦?⦠) | +
+ + |
+
+ + |
+
|
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| + |
|
- context-sensitive equivalence | -cpcs ( ? ⢠? â¬* ? ) | -cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs | -+ | evaluation for context-sensitive reduction | +cpre ( â¦?,?⦠⢠â¡* ðâ¦?⦠) | +cpre_cpre | +
|
- + |
|
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| conversion | -focalized conversion | -lfpc ( �⦠⬠�⦠) | -lfpc_lfpc | -+ |
|
- + | strongly normalizing "big tree" computation | +fsb ( �,?⦠⢠⦥[?,?] ? ) | +fsb_alt ( �,?⦠⢠⦥⦥[?,?] ? ) | +fsb_aaa fsb_csx | +
|
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| + |
|
- + | strongly normalizing extended computation | +lcosx ( ? ⢠~â¬*[?,?,?] ? ) | +lcosx_cpx | +
|
- fpc ( �,?⦠⬠�,?⦠) | -fpc_fpc | -+ |
|
- + | |||||||||||||||||||||||||||||||||||
|
+ + |
+
+ + |
+ lsx ( ? ⢠â¬*[?,?,?,?] ? ) | +lsx_alt ( ? ⢠â¬â¬*[?,?,?,?] ? ) | +lsx_drop lsx_lpx lsx_lpxs llsx_csx | +
|
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| + |
|
- context-sensitive conversion | -cpc ( ? ⢠? ⬠? ) | -cpc_cpc | -+ |
|
- + | csx_vector ( â¦?,?⦠⢠â¬*[?,?] ? ) | +csx_tstc_vector csx_aaa | +
+ + |
+
|
|||||||||||||||||||||||||||||||||||
| computation | -decomposed extended computation | -dxprs ( â¦?,?⦠⢠? â¢*â¡*[?] ? ) | -dxprs_lift dxprs_lpss dxprs_aaa dxprs_dxprs | +
+ + |
+
+ + |
+ csx ( â¦?,?⦠⢠â¬*[?,?] ? ) | +csx_alt ( â¦?,?⦠⢠â¬â¬*[?,?] ? ) | +csx_lift csx_lleq csx_lpx csx_lpxs csx_fpbs | +
+ + |
+ |||||||||||||||||||||||||||||||||||||
|
+ + |
+ "big tree" parallel computation | +fpbg ( â¦?,?,?⦠>â¡[?,?] â¦?,?,?⦠) | +fpbg_lift fpbg_fleq fpbg_fpbg | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||
|
+ + |
+
+ + |
+ fpbc ( â¦?,?,?⦠â»â¡[?,?] â¦?,?,?⦠) | +fpbc_fleq fpbc_fpbs |
|
@@ -462,9 +456,37 @@
|
- weakly normalizing computation | -cpe ( ? ⢠â¡* ðâ¦?⦠) | -cpe_cpe | +
+ + |
+ fpbu ( â¦?,?,?⦠â»[?,?] â¦?,?,?⦠) | +fpbu_lift fpbu_lleq | +fpbu_fleq | +
+ + |
+ |||||||||||||||||||||||||||||||||
|
+ + |
+
+ + |
+ fpbs ( â¦?,?,?⦠â¥[?,?] â¦?,?,?⦠) | +fpbs_alt ( â¦?,?,?⦠â¥â¥[?,?] â¦?,?,?⦠) | +fpbs_lift fpbs_fleq fpbs_aaa fpbs_fpbs fpbs_ext | +
+ + |
+ |||||||||||||||||||||||||||||||||||||||||
|
+ + |
+ decomposed extended computation | +cpds ( â¦?,?⦠⢠? â¢*â¡*[?,?] ? ) | +cpds_lift cpds_aaa cpds_cpds |
|
@@ -476,9 +498,9 @@
|
- strongly normalizing computation | -csn_vector ( ? ⢠â¬* ? ) | -csn_tstc_vector csn_aaa | +context-sensitive extended computation | +lpxs ( â¦?,?⦠⢠â¡*[?,?] ? ) | +lpxs_drop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs |
|
@@ -493,9 +515,11 @@
|
- csn ( ? ⢠â¬* ? ) | -csn_alt ( ? ⢠â¬â¬* ? ) | -csn_lift csn_lpr | +cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) | +cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs | +
+ + |
|
@@ -505,9 +529,11 @@
context-sensitive computation | -lprs ( ? ⢠â¡* ? ) | -lprs_alt ( ? ⢠â¡â¡* ? ) | -lprs_ldrop lprs_lpss lprs_aaa lprs_cprs lprs_lprs | +lprs ( â¦?,?⦠⢠â¡* ? ) | +lprs_drop lprs_cprs lprs_lprs | +
+ + |
|
@@ -519,8 +545,8 @@
|
- cprs ( ? ⢠? â¡* ?) | -cprs_tstc cprs_tstc_vector cprs_lift cprs_lpss cprs_aaa cprs_cprs | +cprs ( â¦?,?⦠⢠? â¡* ?) | +cprs_lift cprs_cprs |
|
@@ -533,8 +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 |
|
@@ -548,7 +574,7 @@
support for abstract computation properties | acp | -acp_cr ( â¦?,?⦠ϵ[?] ã?ã ) | +acp_cr ( â¦?,?,?⦠ϵ[?] ã?ã ) | acp_aaa |
@@ -556,9 +582,9 @@ |
| reduction | -context-sensitive normal forms | -cnf ( ? ⢠ðâ¦?⦠) | -cnf_liftt cnf_crf cnf_cif | +"big tree" parallel reduction | +fpb ( â¦?,?,?⦠â½[?,?] â¦?,?,?⦠) | +fpb_lift fpb_aaa |
|
@@ -570,9 +596,9 @@
|
- context-sensitive reduction | -lpr ( ? ⢠⡠? ) | -lpr_ldrop lpr_lpss lpr_aaa lpr_lpr | +normal forms for context-sensitive extended reduction | +cnx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | +cnx_lift cnx_crx cnx_cix |
|
@@ -580,6 +606,18 @@
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|
+ + |
+ context-sensitive extended reduction | +lpx ( â¦?,?⦠⢠â¡[?,?] ? ) | +lpx_drop lpx_frees | +lpx_lleq lpx_aaa | +
+ + |
+ |||||||||||||||||||||||||||||||||||||||||
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@@ -587,8 +625,8 @@ |
|
- cpr ( ? ⢠? â¡ ? ) | -cpr_lift cpr_cif | +cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) | +cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix |
|
@@ -600,46 +638,106 @@
|
- context-sensitive reducible forms | -crf ( ? ⢠ðâ¦?⦠) | -crf_append | -cif ( ? ⢠ðâ¦?⦠) | -cif_append | +irreducible forms for context-sensitive extended reduction | +cix ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | +cix_lift | +
+ + |
+
+ + |
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| unfold | -restricted parallel computation | -lpqs ( ? ⢠â¤* ? ) | -lpqs_ldrop lpqs_cpqs lpqs_lpqs | -+ |
|
- + | reducible forms for context-sensitive extended reduction | +crx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | +crx_lift | +
+ + |
+
|
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| + |
|
- + | normal forms for context-sensitive reduction | +cnr ( â¦?,?⦠⢠⡠ðâ¦?⦠) | +cnr_lift cnr_crr cnr_cir | +
|
- cpqs ( ? ⢠? â¤* ? ) | -cpqs_lift | -+ |
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- + | |||||||||||||||||||||||||||||||||||
|
+ + |
+ context-sensitive reduction | +lpr ( �,?⦠⢠⡠? ) | +lpr_drop lpr_lpr | +
+ + |
+
|
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| + |
+ + |
+
+ + |
+ cpr ( �,?⦠⢠? ⡠? ) | +cpr_lift cpr_llpx_sn cpr_cir | +
+ + |
+
+ + |
+ ||||||||||||||||||||||||||||||||||||||||
|
+ + |
+ irreducible forms for context-sensitive reduction | +cir ( â¦?,?⦠⢠⡠ðâ¦?⦠) | +cir_lift | +
+ + |
+
|
+ |||||||||||||||||||||||||||||||||||||||||
|
+ + |
+ reducible forms for context-sensitive reduction | +crr ( â¦?,?⦠⢠⡠ðâ¦?⦠) | +crr_lift | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||
| unfold | unfold | -unfold ( ? ⢠? ⧫* ? ) | +unfold ( �,?⦠⢠? ⧫* ? ) |
|
@@ -654,21 +752,19 @@
|
- iterated stratified static type assignment | -sstas ( â¦?,?⦠⢠? â¢*[?] ? ) | -sstas_lift sstas_lpss sstas_aaa sstas_sstas | -
- - |
+ iterated static type assignment | +lstas ( â¦?,?⦠⢠? â¢*[?,?] ? ) | +lstas_alt ( â¦?,?⦠⢠? â¢â¢*[?,?] ? ) | +lstas_lift lstas_aaa lstas_da lstas_lstas |
|
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| static typing | -stratified static type assignment | -ssta ( â¦?,?⦠⢠? â¢[?,?] ? ) | -ssta_lift ssta_lpss ssta_aaa ssta_ssta | +local env. ref. for degree assignment | +lsubd ( ? ⢠? â«âª[?,?] ? ) | +lsubd_da lsubd_lsubd |
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@@ -680,9 +776,9 @@
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- local env. ref. for atomic arity assignment | -lsuba ( ? ââ ? ) | -lsuba_ldrop lsuba_aaa lsuba_lsuba | +degree assignment | +da ( â¦?,?⦠⢠? âª[?,?] ? ) | +da_lift da_aaa da_sta da_da |
|
@@ -694,9 +790,9 @@
|
- atomic arity assignment | -aaa ( ? ⢠? â ? ) | -aaa_lift aaa_lifts aaa_lpss aaa_aaa | +static type assignment | +sta ( â¦?,?⦠⢠? â¢[?] ? ) | +sta_lift sta_lpx_sn sta_aaa sta_sta |
|
@@ -719,10 +815,52 @@
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| substitution | -parallel substitution | -lpss ( ? ⢠â¶* ? ) | -lpss_ldrop lpss_cpss lpss_lpss | +
+ + |
+ local env. ref. for atomic arity assignment | +lsuba ( ? ⢠? â«â ? ) | +lsuba_aaa lsuba_lsuba | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||
|
+ + |
+ atomic arity assignment | +aaa ( â¦?,?⦠⢠? â ? ) | +aaa_lift aaa_lifts aaa_fqus aaa_lleq aaa_aaa | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||
|
+ + |
+ restricted local env. ref. | +lsubr ( ? â« ? ) | +lsubr_lsubr | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||
| multiple substitution | +lazy equivalence | +fleq ( â¦?,?,?⦠â¡[?] â¦?,?,?⦠) | +fleq_fleq |
|
@@ -737,8 +875,36 @@
|
- cpss ( ? ⢠? â¶* ? ) | -cpss_lift | +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 |
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@@ -750,9 +916,9 @@
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- local env. ref. for substitution | -lsubr ( ? â ? ) | -lsubr_lsubr | +context-sensitive exclusion from free variables | +frees ( ? ⢠? ϵ ð *[?]â¦?⦠) | +frees_append frees_leq frees_lift |
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@@ -760,13 +926,25 @@
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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 | -fsups ( â¦?,?⦠â* â¦?,?⦠) | -fsups_fsups | +fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) | +fqus_alt fqus_fqus |
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@@ -781,8 +959,8 @@
|
- fsupp ( â¦?,?⦠â+ â¦?,?⦠) | -fsupp_fsupp | +fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | +fqup_fqup |
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@@ -794,9 +972,9 @@
|
- generic local env. slicing | -ldrops ( â©*[?] ? â¡ ? ) | -ldrops_ldrop ldrops_ldrops | +iterated local env. slicing | +drops ( â©*[?,?] ? â¡ ? ) | +drops_drop drops_drops |
|
@@ -845,9 +1023,25 @@
gr2_gr2 | |||||||||||||||||||||||||
| relocation | +substitution | structural successor for closures | -fsup ( â¦?,?⦠â â¦?,?⦠) | +fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) | +fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||
|
+ + |
+
+ + |
+ fqu ( â¦?,?,?⦠â â¦?,?,?⦠) |
|
@@ -863,8 +1057,50 @@
global env. slicing | -gdrop ( â©[?] ? â¡ ? ) | -gdrop_gdrop | +gget ( â©[?] ? â¡ ? ) | +gget_gget | +
+ + |
+
+ + |
+ ||||||||||||||||||||||||||||||||||||
|
+ + |
+ 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 |
|
@@ -877,8 +1113,8 @@
basic local env. slicing | -ldrop ( â©[?,?] ? â¡ ? ) | -ldrop_append ldrop_lpx_sn ldrop_ldrop | +drop ( â©[?,?,?] ? â¡ ? ) | +drop_append drop_leq drop_drop |
|
@@ -908,7 +1144,7 @@
lift ( â§[?,?] ? â¡ ? ) | -lift_lift | +lift_neq lift_lift |
|
@@ -918,9 +1154,9 @@
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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 |
|
@@ -933,7 +1169,7 @@
same top term constructor | -tstc ( ? â ? ) | +tstc ( ? â ? ) | tstc_tstc tstc_vector |
@@ -947,8 +1183,8 @@ |
closures | -cl_shift ( ? @@ ? ) | -cl_weight ( â¯{?,?} ) | +cl_weight ( â¯{?,?,?} ) | +cl_restricted_weight ( â¯{?,?} ) |
|
@@ -1034,7 +1270,7 @@