![[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 | -250 | -characters | -484808 | -nodes | -1304888 | +sizes | +files | +358 | +characters | +430798 | +nodes | +1858367 |
| propositions | -theorems | -84 | -lemmas | -1112 | -total | -1196 | +propositions | +theorems | +130 | +lemmas | +1283 | +total | +1413 |
| concepts | -declared | -45 | -defined | -83 | -total | -128 | +concepts | +declared | +54 | +defined | +89 | +total | +143 |
| component | -plane | -files | -
- - |
- + | component | +plane | +files | +
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- + |
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- + |
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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_sta_ldec ex_cpr_omega ex_fpbg_refl | +
+ + |
+
+ + |
+
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| + | + | + | + |
+ + |
+
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- "big tree" parallel reduction | -ypr ( ? ⢠â¦?,?⦠â½[g] â¦?,?⦠) | -ysc ( ? ⢠â¦?,?⦠â»[g] â¦?,?⦠) | -+ |
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- + | |
| dynamic typing | +local env. ref. for stratified native validity | +lsubsv ( ? ⢠? â«Â¡[?,?] ? ) | +lsubsv_lsuba lsubsv_lsubd lsubsv_lstas lsubsv_scpds lsubsv_cpcs lsubsv_snv | +
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- + |
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||||||
| + |
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- local env. ref. for stratified native validity | -lsubsv ( ? ⢠? ¡â[?] ? ) | -lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv | -+ | stratified native validity | +shnv ( â¦?,?⦠⢠? ¡[?,?,?] ) | +
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- + |
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- + |
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| + |
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- 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 | -+ |
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- + | snv ( �,?⦠⢠? ¡[?,?] ) | +snv_lift snv_aaa snv_da_lpr snv_lstas snv_lstas_lpr snv_lpr snv_scpes snv_preserve | +
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- + |
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| equivalence | -focalized equivalence | -lfpcs ( â¦?⦠â¬* â¦?⦠) | -lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs | -+ | 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 equivalence | +cpcs ( â¦?,?⦠⢠? â¬* ? ) | +cpcs_aaa cpcs_cprs cpcs_cpcs | +
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- fpcs ( â¦?,?⦠â¬* â¦?,?⦠) | -fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs | -+ |
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- + | |
| conversion | +context-sensitive conversion | +cpc ( �,?⦠⢠? ⬠? ) | +cpc_cpc | +
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- + |
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- - |
- 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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- + |
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- + |
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| + |
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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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-
- - |
- + |
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| conversion | -focalized conversion | -lfpc ( �⦠⬠�⦠) | -lfpc_lfpc | -+ |
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-
- - |
- + | strongly normalizing qrst-computation | +fsb ( �,?⦠⢠⦥[?,?] ? ) | +fsb_alt ( �,?⦠⢠⦥⦥[?,?] ? ) | +fsb_aaa fsb_csx | +
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| + |
+ + |
+ strongly normalizing extended computation | +lcosx ( ? ⢠~â¬*[?,?,?] ? ) | +lcosx_cpx | +
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- + |
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- fpc ( �,?⦠⬠�,?⦠) | -fpc_fpc | -+ | ||
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- + |
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- + | lsx ( ? ⢠â¬*[?,?,?,?] ? ) | +lsx_alt ( ? ⢠â¬â¬*[?,?,?,?] ? ) | +lsx_drop lsx_lpx lsx_lpxs llsx_csx | +
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|||||
| + |
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- context-sensitive conversion | -cpc ( ? ⢠? ⬠? ) | -cpc_cpc | -+ |
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- + | csx_vector ( â¦?,?⦠⢠â¬*[?,?] ? ) | +csx_tsts_vector csx_aaa | +
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- + |
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| computation | -focalized computation | -lfprs ( â¦?⦠â¡* â¦?⦠) | -lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs | -+ |
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- + |
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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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| + |
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- + | parallel qrst-computation | +fpbg ( â¦?,?,?⦠>â¡[?,?] â¦?,?,?⦠) | +fpbg_lift fpbg_fleq fpbg_fpbs fpbg_fpbg | +
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- fprs ( â¦?,?⦠â¡* â¦?,?⦠) | -fprs_aaa fprs_fprs | -+ |
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- + | |
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- + |
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- ||||||||||
| + | fpbs ( â¦?,?,?⦠â¥[?,?] â¦?,?,?⦠) | +fpbs_alt ( â¦?,?,?⦠â¥â¥[?,?] â¦?,?,?⦠) | +fpbs_lift fpbs_aaa fpbs_fpb fpbs_fpbs | +
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- decomposed extended computation | -dxprs ( â¦?,?⦠⢠? â¢*â¡*[?] ? ) | -dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxprs_dxprs | -+ | ||||
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- + | decomposed extended computation | +scpds ( â¦?,?⦠⢠? â¢*â¡*[?,?,?] ? ) | +scpds_lift scpds_aaa scpds_scpds | +
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- + |
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|||||
| + |
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- weakly normalizing computation | -cpe ( ? ⢠â¡* ðâ¦?⦠) | -cpe_cpe | -+ | context-sensitive extended computation | +lpxs ( â¦?,?⦠⢠â¡*[?,?] ? ) | +lpxs_drop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs | +
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-
- - |
- + |
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| + |
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- strongly normalizing computation | -csn_vector ( ? ⢠â¬* ? ) | -csn_cpr_vector csn_tstc_vector csn_aaa | -+ |
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- + | cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) | +cpxs_tsts cpxs_tsts_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs | +
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- + |
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- - |
- + |
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- csn ( ? ⢠â¬* ? ) | -csn_alt ( ? ⢠â¬â¬* ? ) | -csn_lift csn_cpr csn_lfpr | -+ | context-sensitive computation | +lprs ( â¦?,?⦠⢠â¡* ? ) | +lprs_drop lprs_cprs lprs_lprs | +
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- + |
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| + |
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- context-sensitive computation | -cprs (? ⢠? â¡* ?) | -cprs_lift cprs_tpss cprs_ltpss_dx cprs_ltpss_sn cprs_delift cprs_aaa cprs_ltpr cprs_lfpr cprs_cprs cprs_lfprs cprs_tstc cprs_tstc_vector | -+ |
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- + | cprs ( â¦?,?⦠⢠? â¡* ?) | +cprs_lift cprs_cprs | +
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- + |
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| + |
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- context-free computation | -ltprs ( ? â¡* ? ) | -ltprs_alt ( ? â¡â¡* ? ) | -ltprs_ldrop ltprs_ltprs | -+ | local env. ref. for generic reducibility | +lsubc ( ? ⢠? â«[?] ? ) | +lsubc_drop lsubc_drops lsubc_lsuba | +
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- + |
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- - |
- + |
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- tprs ( ? â¡* ?) | -tprs_lift tprs_tprs | -+ | support for generic computation properties | +gcp | +gcp_cr ( â¦?,?,?⦠ϵ[?] ã?ã ) | +gcp_aaa | +
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-
- - |
- + |
| reduction | +parallel qrst-reduction | +fpbq ( â¦?,?,?⦠â½[?,?] â¦?,?,?⦠) | +fpbq_alt ( â¦?,?,?⦠â½â½[?,?] â¦?,?,?⦠) | +fpbq_lift fpbq_aaa | +
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| + |
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- local env. ref. for abstract candidates of reducibility | -lsubc ( ? â[?] ? ) | -lsubc_ldrop lsubc_ldrops lsubc_lsuba | -+ |
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- + | fpb ( â¦?,?,?⦠â»[?,?] â¦?,?,?⦠) | +fpb_lift fpb_lleq fpb_fleq | +
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- + |
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| + |
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- support for abstract computation properties | -acp | -acp_cr ( â¦?,?⦠ϵ[?] ã?ã ) | -acp_aaa | -+ | normal forms for context-sensitive extended reduction | +cnx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | +cnx_lift cnx_crx cnx_cix | +
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- + |
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| reducibility | -context-sensitive focalized reduction | -cfpr ( ? ⢠�,?⦠⡠�,?⦠) | -cnfpr_ltpss cfpr_aaa cfpr_cpr cfpr_cfpr | -+ |
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- + | context-sensitive extended reduction | +lpx ( â¦?,?⦠⢠â¡[?,?] ? ) | +lpx_drop lpx_frees lpx_lleq lpx_aaa | +
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- + |
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| + |
+ + |
+
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- context-free focalized reduction | -lfpr ( â¦?⦠⡠â¦?⦠) | -lfpr_alt ( â¦?⦠â¡â¡ â¦?⦠) | -lfpr_aaa lfpr_cpr lfpr_fpr lfpr_lfpr | -+ | cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) | +cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix | +
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- + |
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| + |
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- + | irreducible forms for context-sensitive extended reduction | +cix ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | +cix_lift | +
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- fpr ( �,?⦠⡠�,?⦠) | -fpr_cpr fpr_fpr | -+ |
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- + | |
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- + | 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 | -cnf ( ? ⢠ðâ¦?⦠) | -cnf_lift cnf_cif | -+ | |||||||
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- + | normal forms for context-sensitive reduction | +cnr ( â¦?,?⦠⢠⡠ðâ¦?⦠) | +cnr_lift cnr_crr cnr_cir | +
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- + |
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| + |
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- context-sensitive reduction | -cpr ( ? ⢠? ⡠? ) | -cpr_lift cpr_tpss cpr_ltpss_dx cpr_ltpss_sn cpr_delift cpr_aaa cpr_ltpr cpr_cpr | -+ | context-sensitive reduction | +lpr ( �,?⦠⢠⡠? ) | +lpr_drop lpr_lpr | +
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-
- - |
- + |
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| + |
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- context-sensitive reducible forms | -crf ( ? ⢠ðâ¦?⦠) | -crf_append | -cif ( ? ⢠ðâ¦?⦠) | -cif_append | -+ |
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- ||||
| + | cpr ( �,?⦠⢠? ⡠? ) | +cpr_lift cpr_llpx_sn cpr_cir | +
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- context-free normal forms | -thnf ( ððâ¦?⦠) | -+ |
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- + | ||||
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- + | irreducible forms for context-sensitive reduction | +cir ( â¦?,?⦠⢠⡠ðâ¦?⦠) | +cir_lift | +
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- + |
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| + |
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- context-free reduction | -ltpr ( ? â¡ ? ) | -ltpr_ldrop ltpr_tps ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr | -+ | reducible forms for context-sensitive reduction | +crr ( â¦?,?⦠⢠⡠ðâ¦?⦠) | +crr_lift | +
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- + |
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- + |
| unfold | +unfold | +unfold ( �,?⦠⢠? ⧫* ? ) | +
+ + |
+
+ + |
+
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| + |
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- + | iterated static type assignment | +lstas ( â¦?,?⦠⢠? â¢*[?,?] ? ) | +lstas_lift lstas_llpx_sn.ma lstas_aaa lstas_da lstas_lstas | +
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- tpr ( ? â¡ ? ) | -tpr_lift tpr_tps tpr_tpss tpr_delift tpr_tpr | -+ |
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- + | |
| static typing | +local env. ref. for degree assignment | +lsubd ( ? ⢠? â«âª[?,?] ? ) | +lsubd_da lsubd_lsubd | +
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- + |
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| unwind | -iterated stratified static type assignment | -sstas ( â¦?,?⦠⢠? â¢*[?] ? ) | -sstas_lift sstas_ltpss_dx sstas_ltpss_sn sstas_aaa sstas_sstas | -+ |
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- + | degree assignment | +da ( â¦?,?⦠⢠? âª[?,?] ? ) | +da_lift da_aaa da_da | +
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- + |
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| static typing | -stratified static type assignment | -ssta ( â¦?,?⦠⢠? â¢[?,?] ? ) | -ssta_lift ssta_ltpss_dx ssta_ltpss_sn ssta_aaa ssta_ssta | -+ |
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- + | parameters | +sh | +sd | +
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- + |
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| + |
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- local env. ref. for atomic arity assignment | -lsuba ( ? ââ ? ) | -lsuba_ldrop lsuba_aaa lsuba_lsuba | -+ | local env. ref. for atomic arity assignment | +lsuba ( ? ⢠? â«â ? ) | +lsuba_aaa lsuba_lsuba | +
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-
- - |
- + |
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- - |
- atomic arity assignment | -aaa ( ? ⢠? â ? ) | -aaa_lift aaa_lifts aaa_ltpss_dx aaa_ltpss_sn aaa_aaa | -+ |
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- + | 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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- + |
| multiple substitution | +lazy equivalence | +fleq ( â¦?,?,?⦠â¡[?] â¦?,?,?⦠) | +fleq_fleq | +
+ + |
+
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| unfold | -basic local env. thinning | -thin ( ? â¼*[?,?] â¡ ? ) | -thin_ldrop thin_delift | -+ |
+ + |
+
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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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- + |
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| + |
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- inverse basic term relocation | -delift ( ? ⢠? â¼*[?,?] â¡ ? ) | -delift_alt ( ? ⢠? â¼â¼*[?,?] â¡ ? ) | -delift_lift delift_tpss delift_ltpss delift_delift | -+ | 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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- + |
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| + |
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- partial unfold | -ltpss_sn ( ? ⢠â¶*[?,?] ? ) | -ltpss_sn_alt ( ? ⢠â¶â¶*[?,?] ? ) | -ltpss_sn_ldrop ltpss_sn_tps ltpss_sn_tpss ltpss_sn_ltpss_sn | -+ | pointwise union for local environments | +llor ( ? â[?,?] ? â¡ ? ) | +llor_alt llor_drop | +
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- + |
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| + |
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- + | context-sensitive exclusion from free variables | +frees ( ? ⢠? ϵ ð *[?]â¦?⦠) | +frees_append frees_leq frees_lift | +
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- ltpss_dx ( ? â¶*[?,?] ? ) | -ltpss_dx_ldrop ltpss_dx_tps ltpss_dx_tpss ltpss_dx_ltpss_dx | -+ |
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- + | |
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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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| + |
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- + | iterated structural successor for closures | +fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) | +fqus_alt fqus_fqus | +
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- tpss ( ? ⢠? â¶*[?,?] ? ) | -tpss_alt ( ? ⢠? â¶â¶*[?,?] ? ) | -tpss_lift | -tpss_tpss | -+ |
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| + |
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- generic local env. slicing | -ldrops ( â©*[?] ? â¡ ? ) | -ldrops_ldrop ldrops_ldrops | -+ |
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- + | fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | +fqup_fqup | +
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- + |
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| + |
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- iterated restricted structural predecessor for closures | -frsups ( â¦?,?⦠â§* â¦?,?⦠) | -frsups_frsups | -+ | iterated local env. slicing | +drops ( â¬*[?,?] ? â¡ ? ) | +drops_drop drops_drops | +
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-
- - |
- + |
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- - |
-
- - |
- frsupp ( â¦?,?⦠â§+ â¦?,?⦠) | -frsupp_frsupp | -+ |
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- + | generic term relocation | +lifts_vector ( â¬*[?] ? â¡ ? ) | +lifts_lift_vector | +
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- + |
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| + |
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- generic term relocation | -lifts_vector ( â§*[?] ? â¡ ? ) | -lifts_lift_vector | -+ |
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- + | lifts ( â¬*[?] ? â¡ ? ) | +lifts_lift lifts_lifts | +
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- + |
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| + |
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-
- - |
- 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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| + |
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- support for generic relocation | -gr2 ( @â¦?,?⦠⡠? ) | -gr2_plus ( ? + ? ) | -gr2_minus ( ? â ? â¡ ? ) | -gr2_gr2 | -+ |
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- ||||
| substitution | -parallel substitution | -tps ( ? ⢠? â¶[?,?] ? ) | -tps_lift tps_tps | -+ | fqu ( â¦?,?,?⦠â â¦?,?,?⦠) | +
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- + |
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- + |
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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 ldrop_lbotr ldrop_ldrop | -+ |
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- + | contxt-sensitive extended ordinary substitution | +cpy ( â¦?,?⦠⢠? â¶[?,?] ? ) | +cpy_lift cpy_nlift cpy_cpy | +
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- + |
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| + |
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- local env. ref. for substitution | -lsubr ( ? â[?,?] ? ) | -(lsubr_lsubr) | -lsubr_lbotr ( â[?,?] ? ) | -+ | local env. ref. for extended substitution | +lsuby ( ? â[?,?] ? ) | +lsuby_lsuby | +
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- + |
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| + |
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- restricted structural predecessor for closures | -frsup ( �,?⦠⧠�,?⦠) | -+ | pointwise extension of a relation | +lpx_sn | +lpx_sn_alt lpx_sn_tc lpx_sn_drop lpx_sn_lpx_sn | +
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- + |
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- + | |
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- + | basic local env. slicing | +drop ( â¬[?,?,?] ? â¡ ? ) | +drop_append drop_leq drop_drop | +
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- |||||||
| + |
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- basic term relocation | -lift_vector ( â§[?,?] ? â¡ ? ) | -lift_lift_vector | -+ | |||||||
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- + | basic term relocation | +lift_vector ( â¬[?,?] ? â¡ ? ) | +lift_lift_vector | +
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- + |
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- - |
- + |
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- lift ( â§[?,?] ? â¡ ? ) | -lift_lift | -+ |
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- + | lift ( â¬[?,?] ? â¡ ? ) | +lift_neq lift_lift | +
|
- + |
|
| grammar | -same head term form | -tshf ( ? â ? ) | -(tshf_tshf) | -+ | grammar | +equivalence for local environments | +leq ( ? ⩬[?,?] ? ) | +leq_leq | +
|
-
- - |
- + |
|
| + |
|
- same top term constructor | -tstc ( ? â ? ) | -tstc_tstc tstc_vector | -+ | same top term structure | +tsts ( ? â ? ) | +tsts_tsts tsts_vector | +
|
-
- - |
- + |
|
|
- - |
- closures | -cl_shift ( ? @@ ? ) | -cl_weight ( â¯{?,?} ) | -+ |
|
- + | closures | +cl_weight ( â¯{?,?,?} ) | +cl_restricted_weight ( â¯{?,?} ) | +
|
- + |
|
| + |
|
- internal syntax | -genv | -+ | internal syntax | +genv | +
|
- + |
|
-
- - |
- + |
|
| + |
|
- + |
|
- lenv | -lenv_weight ( â¯{?} ) | -lenv_length ( |?| ) | -lenv_append ( ? @@ ? ) | -lenv_px lenv_px_bi | +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 | +
|
- + |
|
- + |
|