@@ -277,7 +301,7 @@
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).
@@ -294,51 +318,15 @@
|
-
-
- |
|
| 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 |
|
@@ -351,11 +339,8 @@
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_da_lpr snv_aaa snv_lsstas snv_lsstas_lpr snv_lpr snv_cpcs |
|
@@ -365,12 +350,9 @@
| equivalence |
- focalized equivalence |
- lfpcs ( â¦?⦠â¬* â¦?⦠) |
- lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs |
-
-
- |
+ decomposed extended equivalence |
+ cpes ( â¦?,?⦠⢠? â¢*â¬*[?,?] ? ) |
+ cpes_cpds |
|
@@ -382,14 +364,9 @@
|
-
-
- |
- fpcs ( â¦?,?⦠â¬* â¦?,?⦠) |
- fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs |
-
-
- |
+ context-sensitive equivalence |
+ cpcs ( â¦?,?⦠⢠? â¬* ? ) |
+ cpcs_aaa cpcs_cprs cpcs_cpcs |
|
@@ -398,98 +375,96 @@
-
-
- |
- local env. ref. for stratified static type assignment |
- lsubss ( ? â¢â[?] ? ) |
- lsubss_ldrop lsubss_ssta lsubss_cpcs |
-
-
- |
-
+ | conversion |
+ context-sensitive conversion |
+ cpc ( �,?⦠⢠? ⬠? ) |
+ cpc_cpc |
+
|
-
+ |
|
-
-
- |
- context-sensitive equivalence |
- cpcs ( ? ⢠? â¬* ? ) |
- cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs |
-
+ | computation |
+ evaluation for context-sensitive extended reduction |
+ cpxe ( â¦?,?⦠⢠â¡*[?,?] ðâ¦?⦠) |
+
|
-
+ |
|
-
+ |
|
- | conversion |
- focalized conversion |
- lfpc ( �⦠⬠�⦠) |
- lfpc_lfpc |
-
+ |
|
-
+ | evaluation for context-sensitive reduction |
+ cpre ( â¦?,?⦠⢠â¡* ðâ¦?⦠) |
+ cpre_cpre |
+
|
-
+ |
|
- |
+ |
|
-
+ | strongly normalizing "big tree" computation |
+ fsb ( �,?⦠⢠⦥[?,?] ? ) |
+ fsb_alt ( �,?⦠⢠⦥⦥[?,?] ? ) |
+ fsb_aaa fsb_csx |
+
|
- fpc ( �,?⦠⬠�,?⦠) |
- fpc_fpc |
-
+ |
+
+
|
-
+ | strongly normalizing extended computation |
+ lcosx ( ? ⢠⧤â¬*[?,?,?] ? ) |
+ lcosx_cpxs |
+
|
-
+ |
|
- |
+ |
|
- context-sensitive conversion |
- cpc ( ? ⢠? ⬠? ) |
- cpc_cpc |
-
+ |
|
-
+ | lsx ( ? ⢠ââ¬*[?,?,?,?] ? ) |
+ lsx_ldrop lsx_cpxs lsx_csx |
+
|
-
+ |
|
- | computation |
- focalized computation |
- lfprs ( â¦?⦠â¡* â¦?⦠) |
- lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs |
-
+ |
|
+
+
+ |
+ csx_vector ( â¦?,?⦠⢠â¬*[?,?] ? ) |
+ csx_tstc_vector csx_aaa |
|
@@ -504,11 +479,20 @@
|
- fprs ( â¦?,?⦠â¡* â¦?,?⦠) |
- fprs_aaa fprs_fprs |
-
+ | csx ( â¦?,?⦠⢠â¬*[?,?] ? ) |
+ csx_alt ( â¦?,?⦠⢠â¬â¬*[?,?] ? ) |
+ csx_lift csx_lpx csx_lpxs csx_fpbs |
+
|
+
+
+
+
+ |
+ "big tree" parallel computation |
+ fpbg ( â¦?,?,?⦠>â[?,?] â¦?,?,?⦠) |
+ fpbg_lift fpbg_fpns fpbg_fpbg |
|
@@ -520,12 +504,11 @@
|
- decomposed extended computation |
- dxprs ( â¦?,?⦠⢠? â¢*â¡*[?] ? ) |
- dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxprs_dxprs |
-
+ |
|
+ fpbc ( â¦?,?,?⦠â»â[?,?] â¦?,?,?⦠) |
+ fpbc_fpns fpbc_fpbs |
|
@@ -537,12 +520,11 @@
|
- weakly normalizing computation |
- cpe ( ? ⢠â¡* ðâ¦?⦠) |
- cpe_cpe |
-
+ |
|
+ fpbu ( â¦?,?,?⦠â»[?,?] â¦?,?,?⦠) |
+ fpbu_lift fpbu_fpns |
|
@@ -554,15 +536,12 @@
|
- strongly normalizing computation |
- csn_vector ( ? ⢠â¬* ? ) |
- csn_cpr_vector csn_tstc_vector csn_aaa |
-
-
- |
-
+ |
|
+ fpbs ( â¦?,?,?⦠â¥[?,?] â¦?,?,?⦠) |
+ fpbs_alt ( â¦?,?,?⦠â¥â¥[?,?] â¦?,?,?⦠) |
+ fpbs_lift fpbs_aaa fpbs_fpns fpbs_fpbs fpbs_ext |
|
@@ -571,12 +550,9 @@
|
-
-
- |
- csn ( ? ⢠â¬* ? ) |
- csn_alt ( ? ⢠â¬â¬* ? ) |
- csn_lift csn_cpr csn_lfpr |
+ parallel computation for "big tree" normal forms |
+ fpns ( â¦?,?,?⦠⢠ââ¡*[?,?] â¦?,?,?⦠) |
+ fpns_fpns |
|
@@ -588,15 +564,24 @@
|
- 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 |
+ decomposed extended computation |
+ cpds ( â¦?,?⦠⢠? â¢*â¡*[?,?] ? ) |
+ cpds_lift cpds_aaa cpds_cpds |
|
-
+ |
|
+
+
+
+
+ |
+ context-sensitive extended computation |
+ lpxs ( â¦?,?⦠⢠â¡*[?,?] ? ) |
+ lpxs_alt ( â¦?,?⦠⢠â¡â¡*[?,?] ? ) |
+ lpxs_ldrop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs |
|
@@ -605,10 +590,11 @@
|
- context-free computation |
- ltprs ( ? â¡* ? ) |
- ltprs_alt ( ? â¡â¡* ? ) |
- ltprs_ldrop ltprs_ltprs |
+
+
+ |
+ cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) |
+ cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs |
|
@@ -620,14 +606,23 @@
|
-
+ | context-sensitive computation |
+ lprs ( â¦?,?⦠⢠â¡* ? ) |
+ lprs_alt ( â¦?,?⦠⢠â¡â¡* ? ) |
+ lprs_ldrop lprs_cprs lprs_lprs |
+
|
- tprs ( ? â¡* ?) |
- tprs_lift tprs_tprs |
-
+ |
+
+
|
+
+
+ |
+ cprs ( â¦?,?⦠⢠? â¡* ?) |
+ cprs_lift cprs_cprs |
|
@@ -640,14 +635,11 @@
local env. ref. for abstract candidates of reducibility |
- lsubc ( ? â[?] ? ) |
+ lsubc ( ? ⢠? â[?] ? ) |
lsubc_ldrop lsubc_ldrops lsubc_lsuba |
|
-
-
- |
|
@@ -658,23 +650,17 @@
support for abstract computation properties |
acp |
- acp_cr ( â¦?,?⦠ϵ[?] ã?ã ) |
+ acp_cr ( â¦?,?,?⦠ϵ[?] ã?ã ) |
acp_aaa |
-
-
- |
|
- | reducibility |
- context-sensitive focalized reduction |
- cfpr ( ? ⢠�,?⦠⡠�,?⦠) |
- cnfpr_ltpss cfpr_aaa cfpr_cpr cfpr_cfpr |
-
-
- |
+ reduction |
+ "big tree" parallel reduction |
+ fpb ( â¦?,?,?⦠â½[?,?] â¦?,?,?⦠) |
+ fpb_lift fpb_aaa |
|
@@ -686,10 +672,9 @@
|
- context-free focalized reduction |
- lfpr ( �⦠⡠�⦠) |
- lfpr_alt ( â¦?⦠â¡â¡ â¦?⦠) |
- lfpr_aaa lfpr_cpr lfpr_fpr lfpr_lfpr |
+ normal forms for context-sensitive extended reduction |
+ cnx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) |
+ cnx_lift cnx_crx cnx_cix |
|
@@ -701,14 +686,9 @@
|
-
-
- |
- fpr ( �,?⦠⡠�,?⦠) |
- fpr_cpr fpr_fpr |
-
-
- |
+ context-sensitive extended reduction |
+ lpx ( â¦?,?⦠⢠â¡[?,?] ? ) |
+ lpx_ldrop lpx_lleq lpx_aaa |
|
@@ -720,12 +700,11 @@
|
- context-sensitive normal forms |
- cnf ( ? ⢠ðâ¦?⦠) |
- cnf_lift cnf_cif |
-
+ |
|
+ cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) |
+ cpx_leq cpx_lift cpx_lleq cpx_cix |
|
@@ -737,12 +716,9 @@
|
- revised context-sensitive reduction |
- lpr ( ? ⢠⡠? ) |
- lpr_ldrop lpr_cpr lpr_lpr |
-
-
- |
+ irreducible forms for context-sensitive extended reduction |
+ cix ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) |
+ cix_lift |
|
@@ -754,14 +730,9 @@
|
-
-
- |
- cpr ( ? ⢠? ⡠? ) |
- cpr_lift |
-
-
- |
+ reducible forms for context-sensitive extended reduction |
+ crx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) |
+ crx_lift |
|
@@ -773,12 +744,9 @@
|
- context-sensitive reduction |
- cpr ( ? ⢠? ⡠? ) |
- cpr_lift cpr_tpss cpr_ltpss_dx cpr_ltpss_sn cpr_delift cpr_aaa cpr_ltpr cpr_cpr |
-
-
- |
+ normal forms for context-sensitive reduction |
+ cnr ( â¦?,?⦠⢠⡠ðâ¦?⦠) |
+ cnr_lift cnr_crr cnr_cir |
|
@@ -790,11 +758,12 @@
|
- context-sensitive reducible forms |
- crf ( ? ⢠ðâ¦?⦠) |
- crf_append |
- cif ( ? ⢠ðâ¦?⦠) |
- cif_append |
+ context-sensitive reduction |
+ lpr ( �,?⦠⢠⡠? ) |
+ lpr_ldrop lpr_lpr |
+
+
+ |
|
@@ -803,14 +772,11 @@
|
- context-free normal forms |
- thnf ( ððâ¦?⦠) |
-
-
- |
-
+ |
|
+ cpr ( �,?⦠⢠? ⡠? ) |
+ cpr_lift cpr_cir |
|
@@ -822,12 +788,9 @@
|
- context-free reduction |
- ltpr ( ? â¡ ? ) |
- ltpr_ldrop ltpr_tps ltpr_tpss ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr |
-
-
- |
+ irreducible forms for context-sensitive reduction |
+ cir ( â¦?,?⦠⢠⡠ðâ¦?⦠) |
+ cir_lift |
|
@@ -839,14 +802,9 @@
|
-
-
- |
- tpr ( ? â¡ ? ) |
- tpr_lift tpr_delift tpr_tpr |
-
-
- |
+ reducible forms for context-sensitive reduction |
+ crr ( â¦?,?⦠⢠⡠ðâ¦?⦠) |
+ crr_lift |
|
@@ -856,9 +814,8 @@
| unfold |
- restricted parallel computation |
- lpqs ( ? ⢠â¤* ? ) |
- lpqs_ldrop lpqs_cpqs lpqs_lpqs |
+ unfold |
+ unfold ( �,?⦠⢠? ⧫* ? ) |
|
@@ -873,65 +830,47 @@
|
-
-
- |
- cpqs ( ? ⢠? â¤* ? ) |
- cpqs_lift |
-
-
- |
-
-
- |
+ iterated static type assignment |
+ lsstas ( â¦?,?⦠⢠? â¢*[?,?,?] ? ) |
+ lsstas_alt ( â¦?,?⦠⢠? â¢â¢*[?,?,?] ? ) |
+ lsstas_lift lsstas_aaa lsstas_lsstas |
|
-
-
- |
- unfold |
- unfold ( ? ⢠? ⧫* ? ) |
-
-
- |
-
-
- |
-
+ | 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_da aaa_ssta aaa_aaa |
+
|
-
+ |
|
- | static typing |
- stratified static type assignment |
- ssta ( â¦?,?⦠⢠? â¢[?,?] ? ) |
- ssta_lift ssta_lpss ssta_aaa ssta_ssta |
-
+ |
|
+ stratified static type assignment |
+ ssta ( â¦?,?⦠⢠? â¢[?,?] ? ) |
+ ssta_lift ssta_ssta |
|
@@ -943,12 +882,9 @@
|
- 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 |
|
@@ -960,12 +896,9 @@
|
- atomic arity assignment |
- aaa ( ? ⢠? â ? ) |
- aaa_lift aaa_lifts aaa_lpss aaa_aaa |
-
-
- |
+ degree assignment |
+ da ( â¦?,?⦠⢠? âª[?,?] ? ) |
+ da_lift da_da |
|
@@ -983,57 +916,29 @@
|
-
-
- |
|
- | substitution |
- parallel substitution |
- lpss ( ? ⢠â¶* ? ) |
- lpss_ldrop lpss_cpss lpss_lpss |
-
-
- |
-
-
- |
-
-
- |
-
-
-
-
- |
-
-
- |
- cpss ( ? ⢠? â¶* ? ) |
- cpss_lift |
-
+ |
|
-
+ | restricted local env. ref. |
+ lsubr ( ? â ? ) |
+ lsubr_lsubr |
+
|
-
+ |
|
-
-
- |
+ substitution |
iterated structural successor for closures |
- fsups ( â¦?,?⦠â* â¦?,?⦠) |
- fsups_fsups |
-
-
- |
+ fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) |
+ fqus_alt fqus_lleq fqus_fqus |
|
@@ -1048,11 +953,8 @@
|
- fsupp ( â¦?,?⦠â+ â¦?,?⦠) |
- fsupp_fsupp |
-
-
- |
+ fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) |
+ fqup_lleq fqup_fqup |
|
@@ -1064,15 +966,12 @@
|
- generic local env. slicing |
- ldrops ( â©*[?] ? â¡ ? ) |
+ iterated local env. slicing |
+ ldrops ( â©*[?,?] ? â¡ ? ) |
ldrops_ldrop ldrops_ldrops |
|
-
-
- |
|
@@ -1087,9 +986,6 @@
|
-
-
- |
|
@@ -1106,9 +1002,6 @@
|
-
-
- |
|
@@ -1121,21 +1014,27 @@
gr2 ( @�,?⦠⡠? ) |
gr2_plus ( ? + ? ) |
gr2_minus ( ? â ? â¡ ? ) |
- gr2_gr2 |
-
-
- |
+ gr2_gr2 |
| relocation |
structural successor for closures |
- fsup ( â¦?,?⦠â â¦?,?⦠) |
-
+ | fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) |
+ fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) |
+ fquq_lleq |
+
|
-
+ |
+
+
|
+
+
+ |
+ fqu ( â¦?,?,?⦠â â¦?,?,?⦠) |
+ fqu_lleq |
|
@@ -1153,9 +1052,6 @@
|
-
-
- |
|
@@ -1164,12 +1060,23 @@
|
- basic local env. slicing |
- ldrop ( â©[?,?] ? â¡ ? ) |
- ldrop_append ldrop_lpx ldrop_lpx_sn ldrop_lbotr ldrop_ldrop |
+ lazy equivalence for local environments |
+ lleq ( ? â[?,?] ? ) |
+ lleq_leq lleq_ldrop lleq_lleq |
|
+
+
+ |
+
+
+
+
+ |
+ lazy pointwise extension of a relation |
+ llpx_sn |
+ llpx_sn_leq llpx_sn_ldrop |
|
@@ -1181,10 +1088,9 @@
|
- local env. ref. for substitution |
- lsubr ( ? â[?,?] ? ) |
- (lsubr_lsubr) |
- lsubr_lbotr ( â[?,?] ? ) |
+ basic local env. slicing |
+ ldrop ( â©[?,?,?] ? â¡ ? ) |
+ ldrop_lpx_sn ldrop_leq ldrop_ldrop |
|
@@ -1202,9 +1108,6 @@
|
-
-
- |
|
@@ -1221,21 +1124,29 @@
|
-
-
- |
|
| grammar |
- same head term form |
- tshf ( ? â ? ) |
- (tshf_tshf) |
+ equivalence for local environments |
+ leq ( ? â[?,?] ? ) |
+ leq_leq |
|
+
+
+ |
+
+
+
+
+ |
+ pointwise extension of a relation |
+ lpx_sn |
+ lpx_sn_tc lpx_sn_lpx_sn |
|
@@ -1253,9 +1164,6 @@
|
-
-
- |
|
@@ -1265,11 +1173,8 @@
closures |
- cl_shift ( ? @@ ? ) |
- cl_weight ( â¯{?,?} ) |
-
-
- |
+ cl_weight ( â¯{?,?,?} ) |
+ cl_restricted_weight ( â¯{?,?} ) |
|
@@ -1289,9 +1194,6 @@
|
-
-
- |
|
@@ -1306,8 +1208,7 @@
lenv |
lenv_weight ( â¯{?} ) |
lenv_length ( |?| ) |
- lenv_append ( ? @@ ? ) |
- lenv_px lenv_px_sn lenv_px_bi |
+ lenv_append ( ? @@ ? ) |
|
@@ -1319,10 +1220,7 @@
| term |
term_weight ( â¯{?} ) |
term_simple ( ðâ¦?⦠) |
- term_vector |
-
-
- |
+ term_vector |
|
@@ -1338,9 +1236,6 @@
|
|
-
-
- |
|
@@ -1357,9 +1252,6 @@
|
-
-
- |
|
@@ -1398,6 +1290,6 @@
- Last update: Sat, 20 Apr 2013 21:34:40 +0200
+ Last update: Tue, 11 Mar 2014 19:37:30 +0100