@@ -262,7 +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).
@@ -279,34 +221,15 @@
|
-
-
- |
|
| 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_lsubd lsubsv_lsuba lsubsv_lsstas lsubsv_cpds lsubsv_cpcs lsubsv_snv |
|
@@ -318,12 +241,9 @@
|
- local env. ref. for stratified native validity |
- lsubsv ( ? ⢠? â©:â[?] ? ) |
- lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv |
-
-
- |
+ stratified native validity |
+ snv ( �,?⦠⢠? ¡[?,?] ) |
+ snv_lift snv_da_lpr snv_aaa snv_lsstas snv_lsstas_lpr snv_lpr snv_cpcs |
|
@@ -332,30 +252,24 @@
-
-
- |
- 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 |
-
-
- |
-
+ | equivalence |
+ decomposed extended equivalence |
+ cpes ( â¦?,?⦠⢠? â¢*â¬*[?,?] ? ) |
+ cpes_cpds |
+
|
-
+ |
|
- | equivalence |
- focalized equivalence |
- lfpcs ( â¦?⦠â¬* â¦?⦠) |
- lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs |
-
+ |
|
+ context-sensitive equivalence |
+ cpcs ( â¦?,?⦠⢠? â¬* ? ) |
+ cpcs_aaa cpcs_cprs cpcs_cpcs |
|
@@ -364,117 +278,122 @@
- |
+ | conversion |
+ context-sensitive conversion |
+ cpc ( �,?⦠⢠? ⬠? ) |
+ cpc_cpc |
+
|
-
+ |
|
- fpcs ( â¦?,?⦠â¬* â¦?,?⦠) |
- fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs |
-
+ |
+
+ | computation |
+ evaluation for context-sensitive extended reduction |
+ cpxe ( â¦?,?⦠⢠â¡*[?,?] ðâ¦?⦠) |
+
|
-
+ |
|
-
+ |
|
-
-
- |
- local env. ref. for context-sensitive equivalence |
- lsubse ( ? â¢â¢â[?] ? ) |
- lsubse_ldrop lsubse_ssta lsubse_cpcs |
-
+ |
|
-
+ | evaluation for context-sensitive reduction |
+ cpre ( â¦?,?⦠⢠â¡* ðâ¦?⦠) |
+ cpre_cpre |
+
|
-
+ |
|
- |
+ |
|
- context-sensitive equivalence |
- cpcs ( ? ⢠? â¬* ? ) |
- cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs |
-
+ | strongly normalizing "big tree" computation |
+ fsb ( �,?⦠⢠⦥[?,?] ? ) |
+ fsb_alt ( �,?⦠⢠⦥⦥[?,?] ? ) |
+ fsb_aaa fsb_csx |
+
|
-
+ |
+
+
|
-
+ | strongly normalizing extended computation |
+ lcosx ( ? ⢠~â¬*[?,?,?] ? ) |
+ lcosx_cpx |
+
+
+ |
+
|
- | conversion |
- focalized conversion |
- lfpc ( �⦠⬠�⦠) |
- lfpc_lfpc |
-
+ |
|
-
+ |
|
-
+ | lsx ( ? ⢠â¬*[?,?,?,?] ? ) |
+ lsx_alt ( ? ⢠â¬â¬*[?,?,?,?] ? ) |
+ lsx_ldrop lsx_lpx lsx_lpxs llsx_csx |
+
|
-
-
- |
-
+ |
|
- fpc ( �,?⦠⬠�,?⦠) |
- fpc_fpc |
-
+ |
|
-
+ | csx_vector ( â¦?,?⦠⢠â¬*[?,?] ? ) |
+ csx_tstc_vector csx_aaa |
+
|
-
+ |
|
-
-
- |
- context-sensitive conversion |
- cpc ( ? ⢠? ⬠? ) |
- cpc_cpc |
-
+ |
|
-
+ |
|
-
+ | csx ( â¦?,?⦠⢠â¬*[?,?] ? ) |
+ csx_alt ( â¦?,?⦠⢠â¬â¬*[?,?] ? ) |
+ csx_lift csx_lleq csx_lpx csx_lpxs csx_fpbs |
+
|
- | computation |
- focalized computation |
- lfprs ( â¦?⦠â¡* â¦?⦠) |
- lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs |
-
+ |
|
+ "big tree" parallel computation |
+ fpbg ( â¦?,?,?⦠>â[?,?] â¦?,?,?⦠) |
+ fpbg_lift fpbg_fleq fpbg_fpbg |
|
@@ -489,11 +408,8 @@
|
- fprs ( â¦?,?⦠â¡* â¦?,?⦠) |
- fprs_aaa fprs_fprs |
-
-
- |
+ fpbc ( â¦?,?,?⦠â»â[?,?] â¦?,?,?⦠) |
+ fpbc_fleq fpbc_fpbs |
|
@@ -505,15 +421,12 @@
|
- 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 |
|
@@ -522,15 +435,12 @@
|
- weakly normalizing computation |
- cpe ( ? ⢠â¡* ðâ¦?⦠) |
- cpe_cpe |
-
-
- |
-
+ |
|
+ fpbs ( â¦?,?,?⦠â¥[?,?] â¦?,?,?⦠) |
+ fpbs_alt ( â¦?,?,?⦠â¥â¥[?,?] â¦?,?,?⦠) |
+ fpbs_lift fpbs_fleq fpbs_aaa fpbs_fpbs fpbs_ext |
|
@@ -539,12 +449,9 @@
|
- strongly normalizing computation |
- csn_vector ( ? ⢠â¬* ? ) |
- csn_cpr_vector csn_tstc_vector csn_aaa |
-
-
- |
+ decomposed extended computation |
+ cpds ( â¦?,?⦠⢠? â¢*â¡*[?,?] ? ) |
+ cpds_lift cpds_aaa cpds_cpds |
|
@@ -556,12 +463,9 @@
|
-
-
- |
- csn ( ? ⢠â¬* ? ) |
- csn_alt ( ? ⢠â¬â¬* ? ) |
- csn_lift csn_cpr csn_lfpr |
+ context-sensitive extended computation |
+ lpxs ( â¦?,?⦠⢠â¡*[?,?] ? ) |
+ lpxs_ldrop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs |
|
@@ -573,12 +477,11 @@
|
- 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 |
-
+ |
|
+ cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) |
+ cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs |
|
@@ -590,10 +493,9 @@
|
- context-free computation |
- ltprs ( ? â¡* ? ) |
- ltprs_alt ( ? â¡â¡* ? ) |
- ltprs_ldrop ltprs_ltprs |
+ context-sensitive computation |
+ lprs ( â¦?,?⦠⢠â¡* ? ) |
+ lprs_ldrop lprs_cprs lprs_lprs |
|
@@ -608,11 +510,8 @@
|
- tprs ( ? â¡* ?) |
- tprs_lift tprs_tprs |
-
-
- |
+ cprs ( â¦?,?⦠⢠? â¡* ?) |
+ cprs_lift cprs_cprs |
|
@@ -625,14 +524,11 @@
local env. ref. for abstract candidates of reducibility |
- lsubc ( ? â[?] ? ) |
+ lsubc ( ? ⢠? â«[?] ? ) |
lsubc_ldrop lsubc_ldrops lsubc_lsuba |
|
-
-
- |
|
@@ -643,23 +539,17 @@
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 |
|
@@ -671,10 +561,9 @@
|
- 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 |
|
@@ -686,14 +575,9 @@
|
-
-
- |
- fpr ( �,?⦠⡠�,?⦠) |
- fpr_cpr fpr_fpr |
-
-
- |
+ context-sensitive extended reduction |
+ lpx ( â¦?,?⦠⢠â¡[?,?] ? ) |
+ lpx_ldrop lpx_lleq lpx_aaa |
|
@@ -705,12 +589,11 @@
|
- context-sensitive normal forms |
- cnf ( ? ⢠ðâ¦?⦠) |
- cnf_lift cnf_cif |
-
+ |
|
+ cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) |
+ cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix |
|
@@ -722,12 +605,9 @@
|
- context-sensitive reduction |
- cpr ( ? ⢠? ⡠? ) |
- cpr_lift cpr_tpss cpr_ltpss_dx cpr_ltpss_sn cpr_delift cpr_aaa cpr_ltpr cpr_cpr |
-
-
- |
+ irreducible forms for context-sensitive extended reduction |
+ cix ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) |
+ cix_lift |
|
@@ -739,11 +619,12 @@
|
- context-sensitive reducible forms |
- crf ( ? ⢠ðâ¦?⦠) |
- crf_append |
- cif ( ? ⢠ðâ¦?⦠) |
- cif_append |
+ reducible forms for context-sensitive extended reduction |
+ crx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) |
+ crx_lift |
+
+
+ |
|
@@ -752,14 +633,23 @@
|
- context-free normal forms |
- thnf ( ððâ¦?⦠) |
+ normal forms for context-sensitive reduction |
+ cnr ( â¦?,?⦠⢠⡠ðâ¦?⦠) |
+ cnr_lift cnr_crr cnr_cir |
|
-
+ |
+
+ |
+
+
+
|
+ context-sensitive reduction |
+ lpr ( �,?⦠⢠⡠? ) |
+ lpr_ldrop lpr_lpr |
|
@@ -771,12 +661,11 @@
|
- context-free reduction |
- ltpr ( ? â¡ ? ) |
- ltpr_ldrop ltpr_tps ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr |
-
+ |
|
+ cpr ( �,?⦠⢠? ⡠? ) |
+ cpr_lift cpr_llpx_sn cpr_cir |
|
@@ -788,14 +677,23 @@
|
-
+ | irreducible forms for context-sensitive reduction |
+ cir ( â¦?,?⦠⢠⡠ðâ¦?⦠) |
+ cir_lift |
+
|
- tpr ( ? â¡ ? ) |
- tpr_lift tpr_tps tpr_tpss tpr_delift tpr_tpr |
-
+ |
+
+ |
+
+
+
|
+ reducible forms for context-sensitive reduction |
+ crr ( â¦?,?⦠⢠⡠ðâ¦?⦠) |
+ crr_lift |
|
@@ -804,10 +702,9 @@
- | unwind |
- iterated stratified static type assignment |
- sstas ( â¦?,?⦠⢠? â¢*[?] ? ) |
- sstas_lift sstas_ltpss_dx sstas_ltpss_sn sstas_aaa sstas_sstas |
+ unfold |
+ unfold |
+ unfold ( �,?⦠⢠? ⧫* ? ) |
|
@@ -819,13 +716,22 @@
- | static typing |
- stratified static type assignment |
- ssta ( â¦?,?⦠⢠? â¢[?,?] ? ) |
- ssta_lift ssta_ltpss_dx ssta_ltpss_sn ssta_aaa ssta_ssta |
-
+ |
|
+ 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 |
|
@@ -837,12 +743,23 @@
|
- local env. ref. for atomic arity assignment |
- lsuba ( ? ââ ? ) |
- lsuba_ldrop lsuba_aaa lsuba_lsuba |
+ atomic arity assignment |
+ aaa ( â¦?,?⦠⢠? â ? ) |
+ aaa_lift aaa_lifts aaa_fqus aaa_lleq aaa_da aaa_ssta aaa_aaa |
|
+
+
+ |
+
+
+
+
+ |
+ stratified static type assignment |
+ ssta ( â¦?,?⦠⢠? â¢[?,?] ? ) |
+ ssta_lift ssta_lpx_sn ssta_ssta |
|
@@ -854,12 +771,23 @@
|
- atomic arity assignment |
- aaa ( ? ⢠? â ? ) |
- aaa_lift aaa_lifts aaa_ltpss_dx aaa_ltpss_sn aaa_aaa |
+ local env. ref. for degree assignment |
+ lsubd ( ? ⢠? âªâ« ? ) |
+ lsubd_da lsubd_lsubd |
|
+
+
+ |
+
+
+
+
+ |
+ degree assignment |
+ da ( â¦?,?⦠⢠? âª[?,?] ? ) |
+ da_lift da_da |
|
@@ -877,6 +805,17 @@
|
+
+
+ |
+
+
+
+
+ |
+ restricted local env. ref. |
+ lsubr ( ? â« ? ) |
+ lsubr_lsubr |
|
@@ -885,13 +824,10 @@
- | unfold |
- basic local env. thinning |
- thin ( ? â¼*[?,?] â¡ ? ) |
- thin_ldrop thin_delift |
-
-
- |
+ substitution |
+ lazy equivalence |
+ fleq ( â¦?,?,?⦠â[?] â¦?,?,?⦠) |
+ fleq_fleq |
|
@@ -903,10 +839,11 @@
|
- inverse basic term relocation |
- delift ( ? ⢠? â¼*[?,?] â¡ ? ) |
- delift_alt ( ? ⢠? â¼â¼*[?,?] â¡ ? ) |
- delift_lift delift_tpss delift_ltpss delift_delift |
+
+
+ |
+ lleq ( ? â[?,?] ? ) |
+ lleq_alt lleq_leq lleq_ldrop lleq_fqus lleq_lleq |
|
@@ -918,10 +855,9 @@
|
- partial unfold |
- ltpss_sn ( ? ⢠â¶*[?,?] ? ) |
- ltpss_sn_alt ( ? ⢠â¶â¶*[?,?] ? ) |
- ltpss_sn_ldrop ltpss_sn_tps ltpss_sn_tpss ltpss_sn_ltpss_sn |
+ 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 |
|
@@ -933,11 +869,8 @@
|
-
-
- |
- ltpss_dx ( ? â¶*[?,?] ? ) |
- ltpss_dx_ldrop ltpss_dx_tps ltpss_dx_tpss ltpss_dx_ltpss_dx |
+ pointwise union for local environments |
+ llor ( ? â©[?] ? â¡ ? ) |
|
@@ -952,13 +885,12 @@
|
-
+ | context-sensitive exclusion from free variables |
+ cofrees ( ? ⢠? ~ϵ ð
*[?]�⦠) |
+ cofrees_alt cofrees_lift |
+
|
- tpss ( ? ⢠? â¶*[?,?] ? ) |
- tpss_alt ( ? ⢠? â¶â¶*[?,?] ? ) |
- tpss_lift |
- tpss_tpss |
|
@@ -967,12 +899,21 @@
|
- generic local env. slicing |
- ldrops ( â©*[?] ? â¡ ? ) |
- ldrops_ldrop ldrops_ldrops |
-
+ | 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_alt fqus_fqus |
|
@@ -984,12 +925,11 @@
|
- iterated restricted structural predecessor for closures |
- frsups ( â¦?,?⦠â§* â¦?,?⦠) |
- frsups_frsups |
-
+ |
|
+ fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) |
+ fqup_fqup |
|
@@ -1001,14 +941,9 @@
|
-
-
- |
- frsupp ( â¦?,?⦠â§+ â¦?,?⦠) |
- frsupp_frsupp |
-
-
- |
+ iterated local env. slicing |
+ ldrops ( â©*[?,?] ? â¡ ? ) |
+ ldrops_ldrop ldrops_ldrops |
|
@@ -1026,9 +961,6 @@
|
-
-
- |
|
@@ -1045,9 +977,6 @@
|
-
-
- |
|
@@ -1060,19 +989,13 @@
gr2 ( @�,?⦠⡠? ) |
gr2_plus ( ? + ? ) |
gr2_minus ( ? â ? â¡ ? ) |
- gr2_gr2 |
-
-
- |
+ gr2_gr2 |
- | substitution |
- parallel substitution |
- tps ( ? ⢠? â¶[?,?] ? ) |
- tps_lift tps_tps |
-
-
- |
+ relocation |
+ structural successor for closures |
+ fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) |
+ fquq_alt ( â¦?,?,?⦠ââ⸮ â¦?,?,?⦠) |
|
@@ -1084,9 +1007,10 @@
|
- global env. slicing |
- gdrop ( â©[?] ? â¡ ? ) |
- gdrop_gdrop |
+
+
+ |
+ fqu ( â¦?,?,?⦠â â¦?,?,?⦠) |
|
@@ -1101,12 +1025,23 @@
|
- basic local env. slicing |
- ldrop ( â©[?,?] ? â¡ ? ) |
- ldrop_append ldrop_lpx ldrop_sfr ldrop_ldrop |
+ global env. slicing |
+ gget ( â©[?] ? â¡ ? ) |
+ gget_gget |
|
+
+
+ |
+
+
+
+
+ |
+ contxt-sensitive extended ordinary substitution |
+ cpy ( â¦?,?⦠⢠? â¶[?,?] ? ) |
+ cpy_lift cpy_nlift cpy_cpy |
|
@@ -1118,10 +1053,9 @@
|
- local env. ref. for substitution |
- lsubs ( ? â¼[?,?] ? ) |
- (lsubs_lsubs) |
- lsubs_sfr ( â½[?,?] ? ) |
+ local env. ref. for extended substitution |
+ lsuby ( ? âÃ[?,?] ? ) |
+ lsuby_lsuby |
|
@@ -1133,14 +1067,23 @@
|
- restricted structural predecessor for closures |
- frsup ( �,?⦠⧠�,?⦠) |
+ pointwise extension of a relation |
+ lpx_sn |
+ lpx_sn_alt lpx_sn_tc lpx_sn_ldrop lpx_sn_lpx_sn |
|
-
+ |
+
+ |
+
+
+
|
+ basic local env. slicing |
+ ldrop ( â©[?,?,?] ? â¡ ? ) |
+ ldrop_leq ldrop_ldrop |
|
@@ -1158,9 +1101,6 @@
|
-
-
- |
|
@@ -1173,10 +1113,7 @@
lift ( â§[?,?] ? â¡ ? ) |
- lift_lift |
-
-
- |
+ lift_neq lift_lift |
|
@@ -1186,12 +1123,9 @@
| grammar |
- same head term form |
- tshf ( ? â ? ) |
- (tshf_tshf) |
-
-
- |
+ equivalence for local environments |
+ leq ( ? â[?,?] ? ) |
+ leq_leq |
|
@@ -1209,9 +1143,6 @@
|
-
-
- |
|
@@ -1221,11 +1152,8 @@
closures |
- cl_shift ( ? @@ ? ) |
- cl_weight ( â¯{?,?} ) |
-
-
- |
+ cl_weight ( â¯{?,?,?} ) |
+ cl_restricted_weight ( â¯{?,?} ) |
|
@@ -1245,9 +1173,6 @@
|
-
-
- |
|
@@ -1262,8 +1187,7 @@
lenv |
lenv_weight ( â¯{?} ) |
lenv_length ( |?| ) |
- lenv_append ( ? @@ ? ) |
- lenv_px lenv_px_bi |
+ lenv_append ( ? @@ ? ) |
|
@@ -1275,10 +1199,7 @@
| term |
term_weight ( â¯{?} ) |
term_simple ( ðâ¦?⦠) |
- term_vector |
-
-
- |
+ term_vector |
|
@@ -1294,9 +1215,6 @@
|
|
-
-
- |
|
@@ -1313,9 +1231,6 @@
|
-
-
- |
|
@@ -1354,6 +1269,6 @@
- Last update: Fri, 15 Mar 2013 00:12:26 +0100
+ Last update: Fri, 23 May 2014 19:32:08 +0200
![[Spacer]](http://lambdadelta.info/images/rainbow.png "lambdadelta rainbow rule")