X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fwww%2Flambdadelta%2Fbasic_2.html;h=7b6bf13cff9c472e442aaf8daf16ad2a60656d38;hb=ddd6cb6f4514d9ca97f857cafa218c170222f5aa;hp=df81e0374cc8b667b2677a46353de243cc1dc9b0;hpb=b9d48c1a4433b3a2b17483bc207b2092f7ac4fd2;p=helm.git diff --git a/helm/www/lambdadelta/basic_2.html b/helm/www/lambdadelta/basic_2.html index df81e0374..7b6bf13cf 100644 --- a/helm/www/lambdadelta/basic_2.html +++ b/helm/www/lambdadelta/basic_2.html @@ -6,8 +6,8 @@ - -
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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- + |
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sizes | files | -195 | +367 | characters | -365052 | +431873 | nodes | -984918 | +1830977 | ||||
propositions | theorems | -84 | +128 | lemmas | -781 | +1302 | total | -865 | +1430 | ||||
concepts | declared | -42 | +55 | defined | -70 | +82 | total | -112 | +137 |
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_cpr_omega | +
+ + |
+
+ + |
+
+ + |
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+ | + | + | + |
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- "big tree" parallel reduction | -ypr ( ? ⢠â¦?,?⦠â½[g] â¦?,?⦠) | -ysc ( ? ⢠â¦?,?⦠â»[g] â¦?,?⦠) | +
+ + |
+
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||
dynamic typing | +local env. ref. for stratified native validity | +lsubsv ( ? ⢠? â«Â¡[?,?] ? ) | +lsubsv_lsuba lsubsv_lsubd lsubsv_lstas lsubsv_cpds lsubsv_cpcs lsubsv_snv |
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@@ -324,9 +276,9 @@
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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 | +hsnv ( â¦?,?⦠⢠? ¡[?,?,?] ) | +hsnv_aaa |
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@@ -338,9 +290,11 @@
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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 | +
+ + |
+ snv ( �,?⦠⢠? ¡[?,?] ) | +snv_lift snv_aaa snv_da_lpr snv_lstas snv_lstas_lpr snv_lpr snv_cpes snv_preserve |
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@@ -350,9 +304,9 @@
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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_aaa cpes_cpcs cpes_cpes |
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@@ -364,11 +318,9 @@
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-
- - |
- fpcs ( â¦?,?⦠â¬* â¦?,?⦠) | -fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs | +context-sensitive equivalence | +cpcs ( â¦?,?⦠⢠? â¬* ? ) | +cpcs_aaa cpcs_cprs cpcs_cpcs |
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@@ -377,80 +329,122 @@
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+ | conversion | +context-sensitive conversion | +cpc ( �,?⦠⢠? ⬠? ) | +cpc_cpc | +
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- local env. ref. for stratified static type assignment | -lsubss ( ? â¢â[?] ? ) | -lsubss_ldrop lsubss_ssta lsubss_cpcs | -+ |
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- + | ||||||||||||||||||||||||||||||||||||||||||||
computation | +evaluation for context-sensitive extended reduction | +cpxe ( â¦?,?⦠⢠â¡*[?,?] ðâ¦?⦠) | +
+ + |
+
+ + |
+
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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 "big tree" computation | +fsb ( �,?⦠⢠⦥[?,?] ? ) | +fsb_alt ( �,?⦠⢠⦥⦥[?,?] ? ) | +fsb_aaa fsb_csx | +
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+ |
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- + | strongly normalizing extended computation | +lcosx ( ? ⢠~â¬*[?,?,?] ? ) | +lcosx_cpx | +
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- fpc ( �,?⦠⬠�,?⦠) | -fpc_fpc | -+ |
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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_tstc_vector csx_aaa | +
+ + |
+
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computation | -focalized computation | -lfprs ( â¦?⦠â¡* â¦?⦠) | -lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs | +
+ + |
+
+ + |
+ 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 |
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@@ -465,8 +459,8 @@
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- fprs ( â¦?,?⦠â¡* â¦?,?⦠) | -fprs_aaa fprs_fprs | +fpbc ( â¦?,?,?⦠â»â¡[?,?] â¦?,?,?⦠) | +fpbc_fleq fpbc_fpbs |
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@@ -478,12 +472,26 @@
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- decomposed extended computation | -dxprs ( â¦?,?⦠⢠? â¢*â¡*[?] ? ) | -dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxprs_dxprs | -+ |
+ + |
+ 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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@@ -492,9 +500,9 @@
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- weakly normalizing computation | -cpe ( ? ⢠â¡* ðâ¦?⦠) | -cpe_cpe | +decomposed extended computation | +cpds ( â¦?,?⦠⢠? â¢*â¡*[?,?,?] ? ) | +cpds_lift cpds_aaa cpds_cpds |
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@@ -506,9 +514,9 @@
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- strongly normalizing computation | -csn_vector ( ? ⢠â¬* ? ) | -csn_cpr_vector csn_tstc_vector csn_aaa | +context-sensitive extended computation | +lpxs ( â¦?,?⦠⢠â¡*[?,?] ? ) | +lpxs_drop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs |
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@@ -523,9 +531,11 @@
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- csn ( ? ⢠â¬* ? ) | -csn_alt ( ? ⢠â¬â¬* ? ) | -csn_lift csn_cpr csn_lfpr | +cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) | +cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs | +
+ + |
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@@ -535,9 +545,11 @@
context-sensitive computation | -lprs ( ? ⢠â¡* ? ) | -lprs_alt ( ? ⢠â¡â¡* ? ) | -lprs_ldrop lprs_aaa lprs_cprs lprs_lprs | +lprs ( â¦?,?⦠⢠â¡* ? ) | +lprs_drop lprs_cprs lprs_lprs | +
+ + |
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@@ -549,8 +561,8 @@
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- cprs ( ? ⢠? â¡* ?) | -cprs_lift cprs_tpss cprs_ltpss_dx cprs_ltpss_sn cprs_aaa cprs_lpr cprs_cprs cprs_tstc cprs_tstc_vector | +cprs ( â¦?,?⦠⢠? â¡* ?) | +cprs_lift cprs_cprs |
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@@ -563,8 +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 |
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@@ -578,7 +590,7 @@
support for abstract computation properties | acp | -acp_cr ( â¦?,?⦠ϵ[?] ã?ã ) | +acp_cr ( â¦?,?,?⦠ϵ[?] ã?ã ) | acp_aaa |
@@ -586,9 +598,9 @@ |
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 |
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@@ -600,9 +612,9 @@
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- context-sensitive reduction | -lpr ( ? ⢠⡠? ) | -lpr_ldrop lpr_cpss lpr_lpss lpr_aaa lpr_cpr lpr_lpr | +normal forms for context-sensitive extended reduction | +cnx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | +cnx_lift cnx_crx cnx_cix |
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@@ -610,6 +622,18 @@
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+ + |
+ context-sensitive extended reduction | +lpx ( â¦?,?⦠⢠â¡[?,?] ? ) | +lpx_drop lpx_frees | +lpx_lleq lpx_aaa | +
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||||
@@ -617,8 +641,8 @@ |
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- cpr ( ? ⢠? â¡ ? ) | -cpr_lift cpr_cif | +cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) | +cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix |
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@@ -630,46 +654,106 @@
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- 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 | -+ |
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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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- + | normal forms for context-sensitive reduction | +cnr ( â¦?,?⦠⢠⡠ðâ¦?⦠) | +cnr_lift cnr_crr cnr_cir | +
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- 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 | +
+ + |
+
+ + |
+ |||||||||||||||||||||||||||||||||||||||||||||||||
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+ 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 ( �,?⦠⢠? ⧫* ? ) |
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@@ -684,21 +768,19 @@
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- 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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@@ -710,9 +792,9 @@
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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 |
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@@ -724,9 +806,9 @@
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- 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 |
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@@ -749,10 +831,52 @@
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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 |
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@@ -767,8 +891,22 @@
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- 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 |
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@@ -780,9 +918,9 @@
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- local env. ref. for substitution | -lsubr ( ? â ? ) | -lsubr_lsubr | +pointwise union for local environments | +llor ( ? â©[?,?] ? â¡ ? ) | +llor_alt llor_drop |
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@@ -790,13 +928,39 @@
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+ + |
+ context-sensitive exclusion from free variables | +frees ( ? ⢠? ϵ ð *[?]â¦?⦠) | +frees_append frees_leq frees_lift | +
+ + |
+
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||||
+ + |
+ contxt-sensitive extended multiple substitution | +cpys ( â¦?,?⦠⢠? â¶*[?,?] ? ) | +cpys_alt ( â¦?,?⦠⢠? â¶â¶*[?,?] ? ) | +cpys_lift cpys_cpys | +
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||||
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iterated structural successor for closures | -fsups ( â¦?,?⦠â* â¦?,?⦠) | -fsups_fsups | +fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) | +fqus_alt fqus_fqus |
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@@ -811,8 +975,8 @@
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- fsupp ( â¦?,?⦠â+ â¦?,?⦠) | -fsupp_fsupp | +fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | +fqup_fqup |
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@@ -824,9 +988,9 @@
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- 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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@@ -875,9 +1039,25 @@
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¦?,?,?⦠) |
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@@ -893,8 +1073,50 @@
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 |
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@@ -907,8 +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 |
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@@ -938,7 +1160,7 @@
lift ( â§[?,?] ? â¡ ? ) | -lift_lift | +lift_neq lift_lift |
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@@ -948,9 +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 |
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@@ -963,7 +1185,7 @@
same top term constructor | -tstc ( ? â ? ) | +tstc ( ? â ? ) | tstc_tstc tstc_vector |
@@ -977,8 +1199,8 @@ |
closures | -cl_shift ( ? @@ ? ) | -cl_weight ( â¯{?,?} ) | +cl_weight ( â¯{?,?,?} ) | +cl_restricted_weight ( â¯{?,?} ) |
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@@ -1064,7 +1286,7 @@