![[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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- + |
|
| sizes | -files | -298 | -characters | -466817 | -nodes | -1359471 | +sizes | +files | +359 | +characters | +429712 | +nodes | +1856521 |
| propositions | -theorems | -89 | -lemmas | -910 | -total | -999 | +propositions | +theorems | +127 | +lemmas | +1273 | +total | +1400 |
| concepts | -declared | -50 | -defined | -73 | -total | -123 | +concepts | +declared | +54 | +defined | +83 | +total | +137 |
| component | -plane | -files | -+ | component | +plane | +files | +
|
- + |
|
- + |
|
| 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 | -+ | examples | +terms with special features | +ex_sta_ldec | +ex_cpr_omega | +
|
- + |
|
| + | + | + | + |
|
- stratified native validity | -snv ( �,?⦠⢠? ¡[?,?] ) | -snv_lift snv_da_lpr snv_aaa snv_lsstas snv_lsstas_lpr snv_lpr snv_cpcs | -+ |
|
- + |
|
| equivalence | -decomposed extended equivalence | -cpes ( â¦?,?⦠⢠? â¢*â¬*[?,?] ? ) | -cpes_cpds | -+ | dynamic typing | +local env. ref. for stratified native validity | +lsubsv ( ? ⢠? â«Â¡[?,?] ? ) | +lsubsv_lsuba lsubsv_lsubd lsubsv_lstas lsubsv_scpds lsubsv_cpcs lsubsv_snv | +
|
- + |
|
| + |
|
- context-sensitive equivalence | -cpcs ( â¦?,?⦠⢠? â¬* ? ) | -cpcs_aaa cpcs_cprs cpcs_cpcs | -+ | stratified native validity | +shnv ( â¦?,?⦠⢠? ¡[?,?,?] ) | +
|
- + |
+ + |
+
|
| conversion | -context-sensitive conversion | -cpc ( �,?⦠⢠? ⬠? ) | -cpc_cpc | -+ |
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- + |
|
- ||||
| computation | -context-sensitive extended evaluation | -cpxe ( â¦?,?⦠⢠â¡*[?,?] ðâ¦?⦠) | -+ | snv ( â¦?,?⦠⢠? ¡[?,?] ) | +snv_lift snv_aaa snv_da_lpr snv_lstas snv_lstas_lpr snv_lpr snv_scpes snv_preserve | +
+ + |
+
|
- + | |||
| equivalence | +decomposed extended equivalence | +scpes ( â¦?,?⦠⢠? â¢*â¬*[?,?,?,?] ? ) | +scpes_aaa scpes_cpcs scpes_scpes | +
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- + |
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|||||
| + |
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- context-sensitive evaluation | -cpre ( â¦?,?⦠⢠â¡* ðâ¦?⦠) | -cpre_cpre | -+ | context-sensitive equivalence | +cpcs ( â¦?,?⦠⢠? â¬* ? ) | +cpcs_aaa cpcs_cprs cpcs_cpcs | +
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- + |
|
| + | conversion | +context-sensitive conversion | +cpc ( �,?⦠⢠? ⬠? ) | +cpc_cpc | +
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- strongly normalizing "big tree" computation | -fsb ( �,?⦠⢠⦥[?,?] ? ) | -fsb_alt ( �,?⦠⢠⦥⦥[?,?] ? ) | -fsb_fleq fsb_csx | -+ |
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| + | computation | +evaluation for context-sensitive extended reduction | +cpxe ( â¦?,?⦠⢠â¡*[?,?] ðâ¦?⦠) | +
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- strongly normalizing extended computation | -csx_vector ( â¦?,?⦠⢠â¬*[?,?] ? ) | -csx_tstc_vector csx_aaa | -+ |
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- + |
|
| + |
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- + | evaluation for context-sensitive reduction | +cpre ( â¦?,?⦠⢠â¡* ðâ¦?⦠) | +cpre_cpre | +
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- csx ( â¦?,?⦠⢠â¬*[?,?] ? ) | -csx_alt ( â¦?,?⦠⢠â¬â¬*[?,?] ? ) | -csx_lift csx_lpx | -+ |
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| + |
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- parallel computation for "big tree" normal forms | -fpns ( â¦?,?,?⦠⢠ââ¡*[?,?] â¦?,?,?⦠) | -fpns_fpns | -+ | strongly normalizing "big tree" computation | +fsb ( â¦?,?⦠⢠⦥[?,?] ? ) | +fsb_alt ( â¦?,?⦠⢠⦥⦥[?,?] ? ) | +fsb_aaa fsb_csx | +
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- + |
|
+ + |
+ strongly normalizing extended computation | +lcosx ( ? ⢠~â¬*[?,?,?] ? ) | +lcosx_cpx | +
+ + |
+
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||||||
| + |
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- "big tree" parallel computation | -fpbr ( â¦?,?,?⦠ââ¥[?,?] â¦?,?,?⦠) | -fpbr_fpbr | -+ |
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- + | lsx ( ? ⢠â¬*[?,?,?,?] ? ) | +lsx_alt ( ? ⢠â¬â¬*[?,?,?,?] ? ) | +lsx_drop lsx_lpx lsx_lpxs llsx_csx | +
|
| + |
+ + |
+
+ + |
+ csx_vector ( â¦?,?⦠⢠â¬*[?,?] ? ) | +csx_tsts_vector csx_aaa | +
+ + |
+
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- + | ||||
|
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- fpbg ( �,?,?⦠>[?,?] �,?,?⦠) | -fpbg_lift fpbg_fpbg | -+ |
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- + | csx ( â¦?,?⦠⢠â¬*[?,?] ? ) | +csx_alt ( â¦?,?⦠⢠â¬â¬*[?,?] ? ) | +csx_lift csx_lleq csx_lpx csx_lpxs csx_fpbs | +
|
||
| + |
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- + | "big tree" parallel computation | +fpbg ( â¦?,?,?⦠>â¡[?,?] â¦?,?,?⦠) | +fpbg_lift fpbg_fleq fpbg_fpbg | +
|
- fpbs ( â¦?,?,?⦠â¥[?,?] â¦?,?,?⦠) | -fpbs_alt ( â¦?,?,?⦠â¥â¥[?,?] â¦?,?,?⦠) | -fpbs_lift fpbs_fleq fpbs_fpbs | -+ |
|
| + |
+ + |
+
|
- decomposed extended computation | -cpds ( â¦?,?⦠⢠? â¢*â¡*[?,?] ? ) | -cpds_lift cpds_aaa cpds_cpds | -+ | fpbc ( â¦?,?,?⦠â»â¡[?,?] â¦?,?,?⦠) | +fpbc_fleq fpbc_fpbs | +
|
- + |
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| + |
|
- context-sensitive extended computation | -lpxs ( â¦?,?⦠⢠â¡*[?,?] ? ) | -lpxs_alt ( â¦?,?⦠⢠â¡â¡*[?,?] ? ) | -lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs | -+ |
+ + |
+ 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 | +
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- + | ||||
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|
- cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) | -cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs | -+ | decomposed extended computation | +scpds ( â¦?,?⦠⢠? â¢*â¡*[?,?,?] ? ) | +scpds_lift scpds_aaa scpds_scpds | +
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- + |
|
||
| + |
|
- context-sensitive computation | -lprs ( â¦?,?⦠⢠â¡* ? ) | -lprs_alt ( â¦?,?⦠⢠â¡â¡* ? ) | -lprs_ldrop lprs_cprs lprs_lprs | -+ | context-sensitive extended computation | +lpxs ( â¦?,?⦠⢠â¡*[?,?] ? ) | +lpxs_drop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs | +
+ + |
+
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| + |
|
- + |
|
- cprs ( â¦?,?⦠⢠? â¡* ?) | -cprs_lift cprs_cprs | -+ | cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) | +cpxs_tsts cpxs_tsts_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs | +
|
- + |
|
| + |
|
- local env. ref. for abstract candidates of reducibility | -lsubc ( ? ⢠? â[?] ? ) | -lsubc_ldrop lsubc_ldrops lsubc_lsuba | -+ | context-sensitive computation | +lprs ( â¦?,?⦠⢠â¡* ? ) | +lprs_drop lprs_cprs lprs_lprs | +
|
- + |
|
| + |
|
- support for abstract computation properties | -acp | -acp_cr ( â¦?,?,?⦠ϵ[?] ã?ã ) | -acp_aaa | -+ |
+ + |
+ cprs ( â¦?,?⦠⢠? â¡* ?) | +cprs_lift cprs_cprs | +
+ + |
+
|
| reduction | -"big tree" parallel reduction | -fpbc ( â¦?,?,?⦠â»[?,?] â¦?,?,?⦠) | -fpbc_lift | -+ |
+ + |
+ local env. ref. for generic reducibility | +lsubc ( ? ⢠? â«[?] ? ) | +lsubc_drop lsubc_drops lsubc_lsuba | +
|
- + |
|
| + |
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- + | support for generic computation properties | +gcp | +gcp_cr ( â¦?,?,?⦠ϵ[?] ã?ã ) | +gcp_aaa | +
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- fpb ( â¦?,?,?⦠â½[?,?] â¦?,?,?⦠) | -fpb_lift | -+ | |
| reduction | +"big tree" parallel reduction | +fpb ( â¦?,?,?⦠â½[?,?] â¦?,?,?⦠) | +fpb_lift fpb_aaa | +
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- + |
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|||||
| + |
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- context-sensitive extended normal forms | -cnx ( â¦?,?⦠⢠ð[?,?]â¦?⦠) | -cnx_lift cnx_crx cnx_cix | -+ | normal forms for context-sensitive extended reduction | +cnx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | +cnx_lift cnx_crx cnx_cix | +
|
- + |
|
| + |
|
- context-sensitive extended reduction | -lpx ( â¦?,?⦠⢠â¡[?,?] ? ) | -lpx_ldrop lpx_lleq lpx_aaa | -+ | context-sensitive extended reduction | +lpx ( â¦?,?⦠⢠â¡[?,?] ? ) | +lpx_drop lpx_frees lpx_lleq lpx_aaa | +
|
- + |
|
| + |
|
- + |
|
- cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) | -cpx_lift cpx_lleq cpx_cix | -+ | cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) | +cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix | +
|
- + |
|
| + |
|
- 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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- 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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- + |
|
| + |
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- context-sensitive normal forms | -cnr ( â¦?,?⦠⢠ðâ¦?⦠) | -cnr_lift cnr_crr cnr_cir | -+ | normal forms for context-sensitive reduction | +cnr ( â¦?,?⦠⢠⡠ðâ¦?⦠) | +cnr_lift cnr_crr cnr_cir | +
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- + |
|
| + |
|
- context-sensitive reduction | -lpr ( �,?⦠⢠⡠? ) | -lpr_ldrop lpr_lpr | -+ | context-sensitive reduction | +lpr ( �,?⦠⢠⡠? ) | +lpr_drop lpr_lpr | +
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- + |
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| + |
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- + |
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- cpr ( �,?⦠⢠? ⡠? ) | -cpr_lift cpr_cir | -+ | cpr ( �,?⦠⢠? ⡠? ) | +cpr_lift cpr_llpx_sn cpr_cir | +
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- + |
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| + |
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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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- + |
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| + |
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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 | +
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- + |
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| unfold | -unfold | -unfold ( �,?⦠⢠? ⧫* ? ) | -+ | unfold | +unfold | +unfold ( �,?⦠⢠? ⧫* ? ) | +
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- + |
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- + |
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| + |
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- iterated static type assignment | -lsstas ( â¦?,?⦠⢠? â¢*[?,?,?] ? ) | -lsstas_alt ( â¦?,?⦠⢠? â¢â¢*[?,?,?] ? ) | -lsstas_lift lsstas_aaa lsstas_lsstas | -+ | iterated static type assignment | +lstas ( â¦?,?⦠⢠? â¢*[?,?] ? ) | +lstas_lift lstas_llpx_sn.ma lstas_aaa lstas_da lstas_lstas | +
+ + |
+
|
| static typing | -local env. ref. for atomic arity assignment | -lsuba ( ? ⢠? ââ ? ) | -lsuba_ldrop lsuba_aaa lsuba_lsuba | -+ | static typing | +local env. ref. for degree assignment | +lsubd ( ? ⢠? â«âª[?,?] ? ) | +lsubd_da lsubd_lsubd | +
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- + |
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| + |
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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_da | +
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- + |
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| + |
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- stratified static type assignment | -ssta ( â¦?,?⦠⢠? â¢[?,?] ? ) | -ssta_lift ssta_ssta | -+ | parameters | +sh | +sd | +
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- + |
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| + |
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- local env. ref. for degree assignment | -lsubd ( ? ⢠? âªâ ? ) | -lsubd_da lsubd_lsubd | -+ | local env. ref. for atomic arity assignment | +lsuba ( ? ⢠? â«â ? ) | +lsuba_aaa lsuba_lsuba | +
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- + |
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| + |
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- degree assignment | -da ( â¦?,?⦠⢠? âª[?,?] ? ) | -da_lift da_da | -+ | atomic arity assignment | +aaa ( â¦?,?⦠⢠? â ? ) | +aaa_lift aaa_lifts aaa_fqus aaa_lleq aaa_aaa | +
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- + |
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| + |
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- parameters | -sh | -sd | -+ | restricted local env. ref. | +lsubr ( ? â« ? ) | +lsubr_lsubr | +
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- + |
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| substitution | -restricted local env. ref. | -lsubr ( ? â ? ) | -lsubr_lsubr | -+ | multiple substitution | +lazy equivalence | +fleq ( â¦?,?,?⦠â¡[?] â¦?,?,?⦠) | +fleq_fleq | +
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- + |
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| + |
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- iterated structural successor for closures | -fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) | -fqus_alt fqus_lleq fqus_fqus | -+ |
|
- + | lleq ( ? â¡[?,?] ? ) | +lleq_alt lleq_alt_rec lleq_leq lleq_drop lleq_fqus lleq_llor lleq_lleq | +
+ + |
+
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| + |
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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 | +
|
- fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | -fqup_lleq fqup_fqup | -+ |
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- + |
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+ + |
+ pointwise union for local environments | +llor ( ? â©[?,?] ? â¡ ? ) | +llor_alt llor_drop | +
+ + |
+
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||||||
| + |
|
- generic local env. slicing | -ldrops ( â©*[?] ? â¡ ? ) | -ldrops_ldrop ldrops_ldrops | -+ | context-sensitive exclusion from free variables | +frees ( ? ⢠? ϵ ð *[?]â¦?⦠) | +frees_append frees_leq frees_lift | +
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- + |
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| + |
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- generic term relocation | -lifts_vector ( â§*[?] ? â¡ ? ) | -lifts_lift_vector | -+ | 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_alt fqus_fqus | +
+ + |
+
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|||||
| + |
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- + |
|
- lifts ( â§*[?] ? â¡ ? ) | -lifts_lift lifts_lifts | -+ | fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | +fqup_fqup | +
|
- + |
|
| + |
+ + |
+ iterated local env. slicing | +drops ( â©*[?,?] ? â¡ ? ) | +drops_drop drops_drops | +
+ + |
+
|
- support for generic relocation | -gr2 ( @â¦?,?⦠⡠? ) | -gr2_plus ( ? + ? ) | -gr2_minus ( ? â ? â¡ ? ) | -gr2_gr2 |
| relocation | -structural successor for closures | -fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) | -fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) | -fquq_lleq | -+ |
+ + |
+ generic term relocation | +lifts_vector ( â§*[?] ? â¡ ? ) | +lifts_lift_vector | +
+ + |
+
|
| + |
|
- + |
|
- fqu ( â¦?,?,?⦠â â¦?,?,?⦠) | -fqu_lleq | -+ | lifts ( â§*[?] ? â¡ ? ) | +lifts_lift lifts_lifts | +
+ + |
+
+ + |
+ |
|
+ + |
+ support for multiple relocation | +mr2 ( @â¦?,?⦠⡠? ) | +mr2_plus ( ? + ? ) | +mr2_minus ( ? â ? â¡ ? ) | +mr2_mr2 | +||||||
| substitution | +structural successor for closures | +fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) | +fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) | +
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- + |
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|||||
| + |
+ + |
+
+ + |
+ fqu ( â¦?,?,?⦠â â¦?,?,?⦠) | +
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- lazy equivalence for local environments | -lleq ( ? â[?,?] ? ) | -lleq_lleq | -+ |
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- + |
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| + |
|
- global env. slicing | -gdrop ( â©[?] ? â¡ ? ) | -gdrop_gdrop | -+ | global env. slicing | +gget ( â©[?] ? â¡ ? ) | +gget_gget | +
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- + |
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| + |
|
- basic local env. slicing | -ldrop ( â©[?,?] ? â¡ ? ) | -ldrop_append ldrop_lpx_sn ldrop_leq ldrop_ldrop | -+ | contxt-sensitive extended ordinary substitution | +cpy ( â¦?,?⦠⢠? â¶[?,?] ? ) | +cpy_lift cpy_nlift cpy_cpy | +
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- + |
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| + |
|
- basic term relocation | -lift_vector ( â§[?,?] ? â¡ ? ) | -lift_lift_vector | -+ | local env. ref. for extended substitution | +lsuby ( ? â[?,?] ? ) | +lsuby_lsuby | +
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- + |
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| + |
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- + | pointwise extension of a relation | +lpx_sn | +lpx_sn_alt lpx_sn_tc lpx_sn_drop lpx_sn_lpx_sn | +
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- lift ( â§[?,?] ? â¡ ? ) | -lift_lift | -+ |
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- + |
|
+ + |
+ basic local env. slicing | +drop ( â©[?,?,?] ? â¡ ? ) | +drop_append drop_leq drop_drop | +
+ + |
+
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||||||
| grammar | -equivalence for local environments | -leq ( ? â[?,?] ? ) | -+ |
|
- + | basic term relocation | +lift_vector ( â§[?,?] ? â¡ ? ) | +lift_lift_vector | +
|
- + |
|
| + |
+ + |
+
+ + |
+ lift ( â§[?,?] ? â¡ ? ) | +lift_neq lift_lift | +
|
- pointwise extension of a relation | -lpx_sn | -lpx_sn_tc lpx_sn_lpx_sn | -+ |
+ + |
+ |
| grammar | +equivalence for local environments | +leq ( ? ⩬[?,?] ? ) | +leq_leq | +
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- + |
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|||||
| + |
|
- same top term constructor | -tstc ( ? â ? ) | -tstc_tstc tstc_vector | -+ | same top term structure | +tsts ( ? â ? ) | +tsts_tsts tsts_vector | +
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- + |
|
| + |
|
- closures | -cl_shift ( ? @@ ? ) | -cl_weight ( â¯{?,?,?} ) | -+ | closures | +cl_weight ( â¯{?,?,?} ) | +cl_restricted_weight ( â¯{?,?} ) | +
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- + |
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| + |
|
- internal syntax | -genv | -+ | internal syntax | +genv | +
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- + |
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- + |
|
| + |
|
- + |
|
- lenv | -lenv_weight ( â¯{?} ) | -lenv_length ( |?| ) | -lenv_append ( ? @@ ? ) | +lenv | +lenv_weight ( â¯{?} ) | +lenv_length ( |?| ) | +lenv_append ( ? @@ ? ) |
| + |
|
- + |
|
- term | -term_weight ( â¯{?} ) | -term_simple ( ðâ¦?⦠) | -term_vector | +term | +term_weight ( â¯{?} ) | +term_simple ( ðâ¦?⦠) | +term_vector ( â¶?.? ) |
| + |
|
- + |
|
- item | -+ | item | +
|
- + |
|
- + |
|
| + |
|
- external syntax | -aarity | -+ | external syntax | +aarity | +
|
- + |
|
- + |
|