@@ -277,7 +204,7 @@
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).
@@ -300,33 +227,9 @@
| dynamic typing |
- "big tree" parallel computation |
- yprs ( ? ⢠â¦?,?⦠â¥[g] â¦?,?⦠) |
- yprs_yprs |
- ygt ( ? ⢠�,?⦠>[g] �,?⦠) |
- ygt_ygt |
-
-
-
-
- |
- "big tree" parallel reduction |
- ypr ( ? ⢠â¦?,?⦠â½[g] â¦?,?⦠) |
- ysc ( ? ⢠â¦?,?⦠â»[g] â¦?,?⦠) |
-
-
- |
-
-
- |
-
-
-
-
- |
local env. ref. for stratified native validity |
- lsubsv ( ? ⢠? ¡â[?] ? ) |
- lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv |
+ lsubsv ( ? ⢠? ¡â«[?,?] ? ) |
+ lsubsv_ldrop lsubsv_lsubd lsubsv_lsuba lsubsv_lsstas lsubsv_cpds lsubsv_cpcs lsubsv_snv |
|
@@ -339,8 +242,8 @@
stratified native validity |
- snv ( �,?⦠⢠? ¡[?] ) |
- snv_lift snv_lpss snv_aaa snv_ssta snv_sstas snv_ssta_lpr snv_lpr snv_cpcs |
+ snv ( �,?⦠⢠? ¡[?,?] ) |
+ snv_lift snv_da_lpr snv_aaa snv_lsstas snv_lsstas_lpr snv_lpr snv_cpcs |
|
@@ -350,9 +253,9 @@
| equivalence |
- local env. ref. for stratified static type assignment |
- lsubss ( ? â¢â[?] ? ) |
- lsubss_ldrop lsubss_ssta lsubss_cpcs |
+ decomposed extended equivalence |
+ cpes ( â¦?,?⦠⢠? â¢*â¬*[?,?] ? ) |
+ cpes_cpds |
|
@@ -365,8 +268,8 @@
context-sensitive equivalence |
- cpcs ( ? ⢠? â¬* ? ) |
- cpcs_lpss cpcs_aaa cpcs_cprs cpcs_cpcs |
+ cpcs ( â¦?,?⦠⢠? â¬* ? ) |
+ cpcs_aaa cpcs_cprs cpcs_cpcs |
|
@@ -377,7 +280,7 @@
| conversion |
context-sensitive conversion |
- cpc ( ? ⢠? ⬠? ) |
+ cpc ( �,?⦠⢠? ⬠? ) |
cpc_cpc |
@@ -388,9 +291,51 @@
|
| computation |
- decomposed extended computation |
- dxprs ( â¦?,?⦠⢠? â¢*â¡*[?] ? ) |
- dxprs_lift dxprs_lpss dxprs_aaa dxprs_dxprs |
+ evaluation for context-sensitive extended reduction |
+ cpxe ( â¦?,?⦠⢠â¡*[?,?] ðâ¦?⦠) |
+
+
+ |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ evaluation for context-sensitive reduction |
+ cpre ( â¦?,?⦠⢠â¡* ðâ¦?⦠) |
+ cpre_cpre |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ strongly normalizing "big tree" computation |
+ fsb ( �,?⦠⢠⦥[?,?] ? ) |
+ fsb_alt ( �,?⦠⢠⦥⦥[?,?] ? ) |
+ fsb_aaa fsb_csx |
+
+
+ |
+
+
+
+
+ |
+ strongly normalizing extended computation |
+ lcosx ( ? ⢠~â¬*[?,?,?] ? ) |
+ lcosx_cpx |
|
@@ -402,9 +347,25 @@
|
- weakly normalizing computation |
- cpe ( ? ⢠â¡* ðâ¦?⦠) |
- cpe_cpe |
+
+
+ |
+ lsx ( ? ⢠â¬*[?,?,?,?] ? ) |
+ lsx_alt ( ? ⢠â¬â¬*[?,?,?,?] ? ) |
+ lsx_ldrop lsx_lpx lsx_lpxs llsx_csx |
+
+
+ |
+
+
+
+
+ |
+
+
+ |
+ csx_vector ( â¦?,?⦠⢠â¬*[?,?] ? ) |
+ csx_tstc_vector csx_aaa |
|
@@ -416,9 +377,23 @@
|
- strongly normalizing computation |
- csn_vector ( ? ⢠â¬* ? ) |
- csn_tstc_vector csn_aaa |
+
+
+ |
+ 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 |
|
@@ -433,9 +408,83 @@
|
- csn ( ? ⢠â¬* ? ) |
- csn_alt ( ? ⢠â¬â¬* ? ) |
- csn_lift csn_lpr |
+ fpbc ( â¦?,?,?⦠â»â[?,?] â¦?,?,?⦠) |
+ fpbc_fleq fpbc_fpbs |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+
+
+ |
+ 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 |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ context-sensitive extended computation |
+ lpxs ( â¦?,?⦠⢠â¡*[?,?] ? ) |
+ lpxs_ldrop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+
+
+ |
+ cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) |
+ cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs |
+
+
+ |
|
@@ -445,9 +494,11 @@
context-sensitive computation |
- lprs ( ? ⢠â¡* ? ) |
- lprs_alt ( ? ⢠â¡â¡* ? ) |
- lprs_ldrop lprs_lpss lprs_aaa lprs_cprs lprs_lprs |
+ lprs ( â¦?,?⦠⢠â¡* ? ) |
+ lprs_ldrop lprs_cprs lprs_lprs |
+
+
+ |
|
@@ -459,8 +510,8 @@
|
- cprs ( ? ⢠? â¡* ?) |
- cprs_tstc cprs_tstc_vector cprs_lift cprs_lpss cprs_aaa cprs_cprs |
+ cprs ( â¦?,?⦠⢠? â¡* ?) |
+ cprs_lift cprs_cprs |
|
@@ -473,7 +524,7 @@
local env. ref. for abstract candidates of reducibility |
- lsubc ( ? â[?] ? ) |
+ lsubc ( ? ⢠? â«[?] ? ) |
lsubc_ldrop lsubc_ldrops lsubc_lsuba |
@@ -488,7 +539,7 @@
|
support for abstract computation properties |
acp |
- acp_cr ( â¦?,?⦠ϵ[?] ã?ã ) |
+ acp_cr ( â¦?,?,?⦠ϵ[?] ã?ã ) |
acp_aaa |
@@ -496,9 +547,37 @@
|
| reduction |
+ "big tree" parallel reduction |
+ fpb ( â¦?,?,?⦠â½[?,?] â¦?,?,?⦠) |
+ fpb_lift fpb_aaa |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ 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_aaa |
+ lpx ( â¦?,?⦠⢠â¡[?,?] ? ) |
+ lpx_ldrop lpx_lleq lpx_aaa |
|
@@ -513,8 +592,8 @@
|
- cpx ( â¦?,?⦠⢠? â¡[?] ? ) |
- cpx_lift |
+ cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) |
+ cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix |
|
@@ -526,9 +605,9 @@
|
- context-sensitive normal forms |
- cnf ( ? ⢠ðâ¦?⦠) |
- cnf_liftt cnf_crf cnf_cif |
+ irreducible forms for context-sensitive extended reduction |
+ cix ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) |
+ cix_lift |
|
@@ -540,9 +619,9 @@
|
- context-sensitive reduction |
- lpr ( ? ⢠⡠? ) |
- lpr_ldrop lpr_lpss lpr_lpr |
+ reducible forms for context-sensitive extended reduction |
+ crx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) |
+ crx_lift |
|
@@ -554,11 +633,23 @@
|
-
+ | normal forms for context-sensitive reduction |
+ cnr ( â¦?,?⦠⢠⡠ðâ¦?⦠) |
+ cnr_lift cnr_crr cnr_cir |
+
+
+ |
+
+
+ |
+
+
+
|
- cpr ( ? ⢠? ⡠? ) |
- cpr_lift cpr_cif |
+ context-sensitive reduction |
+ lpr ( �,?⦠⢠⡠? ) |
+ lpr_ldrop lpr_lpr |
|
@@ -570,33 +661,53 @@
|
- context-sensitive reducible forms |
- crf ( ? ⢠ðâ¦?⦠) |
- crf_append |
- cif ( ? ⢠ðâ¦?⦠) |
- cif_append |
+
+
+ |
+ cpr ( �,?⦠⢠? ⡠? ) |
+ cpr_lift cpr_llpx_sn cpr_cir |
+
+
+ |
+
+
+ |
- | unfold |
- restricted parallel computation |
- lpqs ( ? ⢠â¤* ? ) |
- lpqs_ldrop lpqs_cpqs lpqs_lpqs |
-
+ |
|
-
+ | 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 ( �,?⦠⢠? ⧫* ? ) |
+
|
- cpqs ( ? ⢠? â¤* ? ) |
- cpqs_lift |
|
@@ -608,37 +719,47 @@
|
- unfold |
- unfold ( ? ⢠? ⧫* ? ) |
-
+ | iterated static type assignment |
+ lsstas ( â¦?,?⦠⢠? â¢*[?,?,?] ? ) |
+ lsstas_alt ( â¦?,?⦠⢠? â¢â¢*[?,?,?] ? ) |
+ lsstas_lift lsstas_aaa lsstas_lsstas |
+
|
-
+ |
+
+ | static typing |
+ local env. ref. for atomic arity assignment |
+ lsuba ( ? ⢠? ââ« ? ) |
+ lsuba_ldrop lsuba_aaa lsuba_lsuba |
+
|
-
+ |
|
- |
+ |
|
- iterated stratified static type assignment |
- sstas ( â¦?,?⦠⢠? â¢*[?] ? ) |
- sstas_lift sstas_lpss sstas_aaa sstas_sstas |
-
+ | atomic arity assignment |
+ aaa ( â¦?,?⦠⢠? â ? ) |
+ aaa_lift aaa_lifts aaa_fqus aaa_lleq aaa_da aaa_ssta aaa_aaa |
+
|
-
+ |
|
- | static typing |
+
+
+ |
stratified static type assignment |
ssta ( â¦?,?⦠⢠? â¢[?,?] ? ) |
- ssta_lift ssta_lpss ssta_aaa ssta_ssta |
+ ssta_lift ssta_lpx_sn ssta_ssta |
|
@@ -650,9 +771,9 @@
|
- 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 |
|
@@ -664,9 +785,9 @@
|
- atomic arity assignment |
- aaa ( ? ⢠? â ? ) |
- aaa_lift aaa_lifts aaa_lpss aaa_aaa |
+ degree assignment |
+ da ( â¦?,?⦠⢠? âª[?,?] ? ) |
+ da_lift da_da |
|
@@ -688,11 +809,25 @@
+
+
+
+ |
+ restricted local env. ref. |
+ lsubr ( ? â« ? ) |
+ lsubr_lsubr |
+
+
+ |
+
+
+ |
+
| substitution |
- parallel substitution |
- lpss ( ? ⢠â¶* ? ) |
- lpss_ldrop lpss_cpss lpss_lpss |
+ lazy equivalence |
+ fleq ( â¦?,?,?⦠â[?] â¦?,?,?⦠) |
+ fleq_fleq |
|
@@ -707,8 +842,8 @@
|
- cpss ( ? ⢠? â¶* ? ) |
- cpss_lift |
+ lleq ( ? â[?,?] ? ) |
+ lleq_alt lleq_leq lleq_ldrop lleq_fqus lleq_lleq |
|
@@ -720,9 +855,9 @@
|
- local env. ref. for substitution |
- lsubr ( ? â ? ) |
- lsubr_lsubr |
+ lazy pointwise extension of a relation |
+ llpx_sn |
+ llpx_sn_alt llpx_sn_alt2 llpx_sn_tc llpx_sn_leq llpx_sn_ldrop llpx_sn_lpx_sn |
|
@@ -730,13 +865,55 @@
+
+
+
+ |
+ pointwise union for local environments |
+ llor ( ? â©[?] ? â¡ ? ) |
+
+
+ |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ context-sensitive exclusion from free variables |
+ cofrees ( ? ⢠? ~ϵ ð
*[?]�⦠) |
+ cofrees_alt cofrees_lift |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ 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 |
|
@@ -751,8 +928,8 @@
|
- fsupp ( â¦?,?⦠â+ â¦?,?⦠) |
- fsupp_fsupp |
+ fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) |
+ fqup_fqup |
|
@@ -764,8 +941,8 @@
|
- generic local env. slicing |
- ldrops ( â©*[?] ? â¡ ? ) |
+ iterated local env. slicing |
+ ldrops ( â©*[?,?] ? â¡ ? ) |
ldrops_ldrop ldrops_ldrops |
@@ -817,8 +994,26 @@
|
| relocation |
structural successor for closures |
- fsup ( â¦?,?⦠â â¦?,?⦠) |
- fsupq ( â¦?,?⦠â⸮ â¦?,?⦠) |
+ fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) |
+ fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+
+
+ |
+ fqu ( â¦?,?,?⦠â â¦?,?,?⦠) |
+
+
+ |
|
@@ -831,8 +1026,50 @@
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 ( ? âÃ[?,?] ? ) |
+ lsuby_lsuby |
+
+
+ |
+
+
+ |
+
+
+
+
+ |
+ pointwise extension of a relation |
+ lpx_sn |
+ lpx_sn_alt lpx_sn_tc lpx_sn_ldrop lpx_sn_lpx_sn |
|
@@ -845,8 +1082,8 @@
basic local env. slicing |
- ldrop ( â©[?,?] ? â¡ ? ) |
- ldrop_append ldrop_lpx_sn ldrop_ldrop |
+ ldrop ( â©[?,?,?] ? â¡ ? ) |
+ ldrop_leq ldrop_ldrop |
|
@@ -876,7 +1113,7 @@
lift ( â§[?,?] ? â¡ ? ) |
- lift_lift |
+ lift_neq lift_lift |
|
@@ -886,9 +1123,9 @@
| grammar |
- pointwise extension of a relation |
- lpx_sn |
- lpx_sn_tc lpx_sn_lpx_sn |
+ equivalence for local environments |
+ leq ( ? â[?,?] ? ) |
+ leq_leq |
|
@@ -915,8 +1152,8 @@
closures |
- cl_shift ( ? @@ ? ) |
- cl_weight ( â¯{?,?} ) |
+ cl_weight ( â¯{?,?,?} ) |
+ cl_restricted_weight ( â¯{?,?} ) |
|
@@ -1032,6 +1269,6 @@
- Last update: Sat, 08 Jun 2013 22:22:33 +0200
+ Last update: Fri, 23 May 2014 19:32:08 +0200
![[Spacer]](http://lambdadelta.info/images/rainbow.png "lambdadelta rainbow rule")