@@ -293,7 +211,7 @@
Logical Structure of the Specification
The source files are grouped in planes and components
according to the following table.
- A notation file covering the whole specification is provided.
+ Notation files covering the whole specification are provided.
The notation for the relations or functions introduced in each file
is shown in parentheses (? are placeholders).
@@ -317,8 +235,8 @@
| 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«[?,?] ? ) |
+ lsubsv_lsuba lsubsv_lsubd lsubsv_lstas lsubsv_cpds lsubsv_cpcs lsubsv_snv |
|
@@ -332,7 +250,7 @@
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 |
|
@@ -380,7 +298,7 @@
| computation |
- context-sensitive extended evaluation |
+ evaluation for context-sensitive extended reduction |
cpxe ( â¦?,?⦠⢠â¡*[?,?] ðâ¦?⦠) |
@@ -396,7 +314,7 @@
|
|
- context-sensitive evaluation |
+ evaluation for context-sensitive reduction |
cpre ( â¦?,?⦠⢠â¡* ðâ¦?⦠) |
cpre_cpre |
@@ -413,7 +331,7 @@
| strongly normalizing "big tree" computation |
fsb ( �,?⦠⢠⦥[?,?] ? ) |
fsb_alt ( �,?⦠⢠⦥⦥[?,?] ? ) |
- fsb_fleq fsb_csx |
+ fsb_aaa fsb_csx |
|
@@ -423,6 +341,36 @@
strongly normalizing extended computation |
+ lcosx ( ? ⢠~â¬*[?,?,?] ? ) |
+ lcosx_cpx |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+
+
+ |
+ lsx ( ? ⢠â¬*[?,?,?,?] ? ) |
+ lsx_alt ( ? ⢠â¬â¬*[?,?,?,?] ? ) |
+ lsx_ldrop lsx_lpx lsx_lpxs llsx_csx |
+
+
+ |
+
+
+
+
+ |
+
+
+ |
csx_vector ( â¦?,?⦠⢠â¬*[?,?] ? ) |
csx_tstc_vector csx_aaa |
@@ -441,7 +389,7 @@
|
csx ( â¦?,?⦠⢠â¬*[?,?] ? ) |
csx_alt ( â¦?,?⦠⢠â¬â¬*[?,?] ? ) |
- csx_lift csx_lpx |
+ csx_lift csx_lleq csx_lpx csx_lpxs csx_fpbs |
|
@@ -451,8 +399,8 @@
"big tree" parallel computation |
- fpbr ( â¦?,?,?⦠ââ¥[?,?] â¦?,?,?⦠) |
- fpbr_fpbr |
+ fpbg ( â¦?,?,?⦠>â¡[?,?] â¦?,?,?⦠) |
+ fpbg_lift fpbg_fleq fpbg_fpbg |
|
@@ -467,8 +415,8 @@
|
- fpbg ( �,?,?⦠>[?,?] �,?,?⦠) |
- fpbg_lift fpbg_fpbg |
+ fpbc ( â¦?,?,?⦠â»â¡[?,?] â¦?,?,?⦠) |
+ fpbc_fleq fpbc_fpbs |
|
@@ -476,6 +424,20 @@
+
+
+
+ |
+
+
+ |
+ fpbu ( â¦?,?,?⦠â»[?,?] â¦?,?,?⦠) |
+ fpbu_lift fpbu_lleq |
+ fpbu_fleq |
+
+
+ |
+
@@ -485,7 +447,7 @@
|
fpbs ( â¦?,?,?⦠â¥[?,?] â¦?,?,?⦠) |
fpbs_alt ( â¦?,?,?⦠â¥â¥[?,?] â¦?,?,?⦠) |
- fpbs_lift fpbs_fleq fpbs_fpbs |
+ fpbs_lift fpbs_fleq fpbs_aaa fpbs_fpbs fpbs_ext |
|
@@ -510,8 +472,10 @@
context-sensitive extended computation |
lpxs ( â¦?,?⦠⢠â¡*[?,?] ? ) |
- lpxs_alt ( â¦?,?⦠⢠â¡â¡*[?,?] ? ) |
- lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs |
+ lpxs_ldrop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs |
+
+
+ |
|
@@ -524,7 +488,7 @@
cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) |
- cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_aaa cpxs_cpxs |
+ cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs |
|
@@ -538,8 +502,10 @@
context-sensitive computation |
lprs ( â¦?,?⦠⢠â¡* ? ) |
- lprs_alt ( â¦?,?⦠⢠â¡â¡* ? ) |
lprs_ldrop lprs_cprs lprs_lprs |
+
+
+ |
|
@@ -565,7 +531,7 @@
local env. ref. for abstract candidates of reducibility |
- lsubc ( ? ⢠? â[?] ? ) |
+ lsubc ( ? ⢠? â«[?] ? ) |
lsubc_ldrop lsubc_ldrops lsubc_lsuba |
@@ -589,24 +555,8 @@
|
| reduction |
"big tree" parallel reduction |
- fpbc ( â¦?,?,?⦠â»[?,?] â¦?,?,?⦠) |
- fpbc_lift |
-
-
- |
-
-
- |
-
-
-
-
- |
-
-
- |
fpb ( â¦?,?,?⦠â½[?,?] â¦?,?,?⦠) |
- fpb_lift |
+ fpb_lift fpb_aaa |
|
@@ -618,8 +568,8 @@
|
- context-sensitive extended normal forms |
- cnx ( â¦?,?⦠⢠ð[?,?]â¦?⦠) |
+ normal forms for context-sensitive extended reduction |
+ cnx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) |
cnx_lift cnx_crx cnx_cix |
@@ -634,10 +584,8 @@
|
context-sensitive extended reduction |
lpx ( â¦?,?⦠⢠â¡[?,?] ? ) |
- lpx_ldrop lpx_aaa |
-
-
- |
+ lpx_ldrop lpx_frees |
+ lpx_lleq lpx_aaa |
|
@@ -650,7 +598,7 @@
cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) |
- cpx_lift cpx_cix |
+ cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix |
|
@@ -662,9 +610,9 @@
|
- 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 |
|
@@ -676,9 +624,9 @@
|
- 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 |
|
@@ -690,8 +638,8 @@
|
- context-sensitive normal forms |
- cnr ( â¦?,?⦠⢠ðâ¦?⦠) |
+ normal forms for context-sensitive reduction |
+ cnr ( â¦?,?⦠⢠⡠ðâ¦?⦠) |
cnr_lift cnr_crr cnr_cir |
@@ -722,7 +670,7 @@
|
cpr ( �,?⦠⢠? ⡠? ) |
- cpr_lift cpr_cir |
+ cpr_lift cpr_llpx_sn cpr_cir |
|
@@ -734,9 +682,9 @@
|
- context-sensitive irreducible forms |
- cir ( â¦?,?⦠⢠ðâ¦?⦠) |
- cir_append cir_lift |
+ irreducible forms for context-sensitive reduction |
+ cir ( â¦?,?⦠⢠⡠ðâ¦?⦠) |
+ cir_lift |
|
@@ -748,9 +696,9 @@
|
- context-sensitive reducible forms |
- crr ( â¦?,?⦠⢠ðâ¦?⦠) |
- crr_append crr_lift |
+ reducible forms for context-sensitive reduction |
+ crr ( â¦?,?⦠⢠⡠ðâ¦?⦠) |
+ crr_lift |
|
@@ -777,18 +725,18 @@
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 |
|
| static typing |
- local env. ref. for atomic arity assignment |
- lsuba ( ? ⢠? ââ ? ) |
- lsuba_ldrop lsuba_aaa lsuba_lsuba |
+ local env. ref. for degree assignment |
+ lsubd ( ? ⢠? âªâ« ? ) |
+ lsubd_da lsubd_lsubd |
|
@@ -800,9 +748,9 @@
|
- 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_sta da_da |
|
@@ -814,9 +762,9 @@
|
- 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 |
|
@@ -828,9 +776,9 @@
|
- local env. ref. for degree assignment |
- lsubd ( ? ⢠? âªâ ? ) |
- lsubd_da lsubd_lsubd |
+ parameters |
+ sh |
+ sd |
|
@@ -842,9 +790,9 @@
|
- degree assignment |
- da ( â¦?,?⦠⢠? âª[?,?] ? ) |
- da_lift da_da |
+ local env. ref. for atomic arity assignment |
+ lsuba ( ? ⢠? ââ« ? ) |
+ lsuba_aaa lsuba_lsuba |
|
@@ -856,9 +804,23 @@
|
- parameters |
- sh |
- sd |
+ atomic arity assignment |
+ aaa ( â¦?,?⦠⢠? â ? ) |
+ aaa_lift aaa_lifts aaa_fqus aaa_lleq aaa_aaa |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ restricted local env. ref. |
+ lsubr ( ? â« ? ) |
+ lsubr_lsubr |
|
@@ -867,10 +829,10 @@
- | substitution |
- restricted local env. ref. |
- lsubr ( ? â ? ) |
- lsubr_lsubr |
+ multiple substitution |
+ lazy equivalence |
+ fleq ( â¦?,?,?⦠â¡[?] â¦?,?,?⦠) |
+ fleq_fleq |
|
@@ -878,12 +840,82 @@
+
+
+
+ |
+
+
+ |
+ lleq ( ? â¡[?,?] ? ) |
+ lleq_alt lleq_alt_rec lleq_leq lleq_ldrop 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_ldrop llpx_sn_lpx_sn llpx_sn_frees llpx_sn_llor |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ pointwise union for local environments |
+ llor ( ? â©[?,?] ? â¡ ? ) |
+ llor_alt llor_ldrop |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ context-sensitive exclusion from free variables |
+ frees ( ? ⢠? ϵ ð
*[?]�⦠) |
+ frees_append frees_leq frees_lift |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ 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 ( â¦?,?,?⦠â* â¦?,?,?⦠) |
fqus_alt fqus_fqus |
@@ -899,7 +931,7 @@
|
|
- fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) |
+ fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) |
fqup_fqup |
@@ -912,8 +944,8 @@
|
|
- generic local env. slicing |
- ldrops ( â©*[?] ? â¡ ? ) |
+ iterated local env. slicing |
+ ldrops ( â©*[?,?] ? â¡ ? ) |
ldrops_ldrop ldrops_ldrops |
@@ -963,11 +995,13 @@
| gr2_gr2 |
- | relocation |
+ substitution |
structural successor for closures |
- fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) |
- fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) |
- fquq_fquq |
+ fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) |
+ fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) |
+
+
+ |
|
@@ -979,8 +1013,10 @@
|
- fqu ( â¦?,?,?⦠â â¦?,?,?⦠) |
- fqu_fqu |
+ fqu ( â¦?,?,?⦠â â¦?,?,?⦠) |
+
+
+ |
|
@@ -992,9 +1028,9 @@
|
- lazy equivalence for local environments |
- lleq ( ? â[?] ? ) |
- lleq_fleq |
+ global env. slicing |
+ gget ( â©[?] ? â¡ ? ) |
+ gget_gget |
|
@@ -1006,9 +1042,37 @@
|
- global env. slicing |
- gdrop ( â©[?] ? â¡ ? ) |
- gdrop_gdrop |
+ contxt-sensitive extended ordinary substitution |
+ cpy ( â¦?,?⦠⢠? â¶[?,?] ? ) |
+ cpy_lift cpy_nlift cpy_cpy |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ local env. ref. for extended substitution |
+ lsuby ( ? âÃ[?,?] ? ) |
+ lsuby_lsuby |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ pointwise extension of a relation |
+ lpx_sn |
+ lpx_sn_alt lpx_sn_tc lpx_sn_ldrop lpx_sn_lpx_sn |
|
@@ -1021,8 +1085,8 @@
basic local env. slicing |
- ldrop ( â©[?,?] ? â¡ ? ) |
- ldrop_append ldrop_lpx_sn ldrop_ldrop |
+ ldrop ( â©[?,?,?] ? â¡ ? ) |
+ ldrop_append ldrop_leq ldrop_ldrop |
|
@@ -1052,7 +1116,7 @@
lift ( â§[?,?] ? â¡ ? ) |
- lift_lift |
+ lift_neq lift_lift |
|
@@ -1062,9 +1126,9 @@
| grammar |
- pointwise extension of a relation |
- lpx_sn |
- lpx_sn_tc lpx_sn_lpx_sn |
+ equivalence for local environments |
+ leq ( ? â[?,?] ? ) |
+ leq_leq |
|
@@ -1091,8 +1155,8 @@
closures |
- cl_shift ( ? @@ ? ) |
- cl_weight ( â¯{?,?,?} ) |
+ cl_weight ( â¯{?,?,?} ) |
+ cl_restricted_weight ( â¯{?,?} ) |
|
@@ -1208,6 +1272,6 @@
- Last update: Fri, 01 Nov 2013 17:48:10 +0100
+ Last update: Wed, 18 Jun 2014 17:05:27 +0200
![[Spacer]](http://lambdadelta.info/images/rainbow.png "lambdadelta rainbow rule")