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| + foreword + | ++ milestones + | ++ version 2 + | +(background - core - applications) | +
+ + |
+ + version 2 + | ++ library + | +(static LDDL directory) | +
| + citations + | ++ visibility + | ++ version 1 + | +(background - core) | +(static HELM directory) | ++ version 1 + | ++ helena + | +
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+
Summary of the Specification ![[spacer]](http://lambdadelta.info/images/b4.png "lambdadelta butterfly")
+
+
+ Here is a numerical account of the specification's contents
and its timeline.
- Nodes are counted according to the "intrinsinc complexity measure"
- [F. Guidi: "Procedural Representation of CIC Proof Terms"
- Journal of Automated Reasoning 44(1-2), Springer (February 2010),
- pp. 53-78].
-
+
-
| sizes | files | -367 | +360 | characters | -431848 | +437272 | nodes | -1830463 | +1935835 |
| propositions | theorems | -128 | +130 | lemmas | 1303 | total | -1431 | +1433 | |
| concepts | declared | -55 | +54 | defined | -84 | +89 | total | -139 | +143 |
-
+
- - In progress. + Ongoing. Context-sensitive subject equivalence for native type assignment.
- - 2014 June 18. + 2014 October 28. + λδ version 2A is released. + +
- + 2014 September 9. + Iterated static type assignment defined (more elegantly) + as a primitive notion. + +
- + 2014 June 18. Preservation of stratified native validity for context-sensitive computation on terms.
- - 2014 June 9. - "Big tree" strong normalization + 2014 June 9. + Strong qrst-normalization for simply typed terms.
- - 2014 April 16. - lazy equivalence on local environments - serves as irrelevant step in "big tree" computation on closures + 2014 April 16. + Lazy equivalence on local environments + added as q-step to rst-computation on closures (anniversary milestone).
- - 2014 January 20. - Parametrized slicing for local environments + 2014 January 20. + Parametrized slicing of local environments comprises both versions of this operation (one from basic_1, the other used in basic_2 till now).
- - 2013 August 7. + 2013 August 7. Passive support for global environments.
- - 2013 July 27. - Reaxiomatized β-reductum as in extended β-reduction + 2013 July 27. + Reaxiomatized β-reductum as in rt-reduction.
- - 2013 July 20. - Context-sensitive extended strong normalization + 2013 July 20. + Context-sensitive strong rt-normalization for simply typed terms.
- - 2013 April 16. + 2013 April 16. Reaxiomatized substitution and reduction commute with respect to subclosure (anniversary milestone).
- - 2013 March 16. + 2013 March 16. Mutual recursive preservation of stratified native validity - for "big tree" computation on closures. + for rst-computation on closures.
- - 2012 October 16. + 2012 October 16. Confluence for context-free parallel reduction on closures.
- - 2012 July 26. + 2012 July 26. Term binders polarized to control ζ-reduction (not released).
- - 2012 April 16. + 2012 April 16. Context-sensitive subject equivalence for atomic arity assignment (anniversary milestone).
- - 2012 March 15. + 2012 March 15. Context-sensitive strong normalization for simply typed terms.
- - 2012 January 27. + 2012 January 27. Support for abstract candidates of reducibility.
- - 2011 September 21. + 2011 September 21. Confluence for context-sensitive parallel reduction on terms.
- - 2011 September 6. + 2011 September 6. Confluence for context-free parallel reduction on terms.
- - 2011 April 17. + 2011 April 17. Specification starts.
Stage "B"
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Stage "A": "Extending the Applicability Condition"
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Logical Structure of the Specification
- The source files are grouped in planes and components
- according to the following table.
- 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).
+
Logical Structure of the Specification
+
+
+ This table reports the specification's components and their planes.
-
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-
| examples | terms with special features | -ex_cpr_omega | +ex_sta_ldec ex_cpr_omega ex_fpbg_refl ex_snv_eta |
|
@@ -278,7 +375,9 @@
stratified native validity | shnv ( �,?⦠⢠? ¡[?,?,?] ) | -shnv_aaa | +
+ + |
|
@@ -294,7 +393,7 @@
snv ( �,?⦠⢠? ¡[?,?] ) | -snv_lift snv_aaa snv_da_lpr snv_lstas snv_lstas_lpr snv_lpr snv_scpes snv_preserve | +snv_lift snv_aaa snv_da_lpr snv_lstas snv_lstas_lpr snv_lpr snv_fsb snv_scpes snv_preserve |
|
@@ -304,7 +403,7 @@
|||||||||||||||||||||||||||||||||||||||||||
| equivalence | -decomposed extended equivalence | +decomposed rt-equivalence | scpes ( â¦?,?⦠⢠? â¢*â¬*[?,?,?,?] ? ) | scpes_aaa scpes_cpcs scpes_scpes | @@ -342,7 +441,7 @@ | |||||||||||||||||||||||||||||||||||||||||||||||||||
| computation | -evaluation for context-sensitive extended reduction | +evaluation for context-sensitive rt-reduction | cpxe ( â¦?,?⦠⢠â¡*[?,?] ðâ¦?⦠) |
@@ -372,9 +471,9 @@ |
|
- strongly normalizing "big tree" computation | -fsb ( �,?⦠⢠⦥[?,?] ? ) | -fsb_alt ( �,?⦠⢠⦥⦥[?,?] ? ) | +strongly normalizing qrst-computation | +fsb ( ⦥[?,?] �,?,?⦠) | +fsb_alt ( ⦥⦥[?,?] �,?,?⦠) | fsb_aaa fsb_csx |
@@ -384,7 +483,7 @@ |
|
- strongly normalizing extended computation | +strongly normalizing rt-computation | lcosx ( ? ⢠~â¬*[?,?,?] ? ) | lcosx_cpx |
@@ -416,7 +515,7 @@
|
csx_vector ( â¦?,?⦠⢠â¬*[?,?] ? ) | -csx_tstc_vector csx_aaa | +csx_tsts_vector csx_aaa |
|
@@ -442,41 +541,9 @@
|
- "big tree" parallel computation | +parallel qrst-computation | fpbg ( â¦?,?,?⦠>â¡[?,?] â¦?,?,?⦠) | -fpbg_lift fpbg_fleq fpbg_fpbg | -
- - |
-
- - |
- ||||||||||||||||||||||||||
|
- - |
-
- - |
- fpbc ( â¦?,?,?⦠â»â¡[?,?] â¦?,?,?⦠) | -fpbc_fleq fpbc_fpbs | -
- - |
-
- - |
- |||||||||||||||||||||||||||||||||||||||||||||||||||
|
- - |
-
- - |
- fpbu ( â¦?,?,?⦠â»[?,?] â¦?,?,?⦠) | -fpbu_lift fpbu_lleq fpbu_fleq | +fpbg_lift fpbg_fleq fpbg_fpbs fpbg_fpbg |
|
@@ -493,7 +560,7 @@
fpbs ( â¦?,?,?⦠â¥[?,?] â¦?,?,?⦠) | fpbs_alt ( â¦?,?,?⦠â¥â¥[?,?] â¦?,?,?⦠) | -fpbs_lift fpbs_fleq fpbs_aaa fpbs_fpbs fpbs_ext | +fpbs_lift fpbs_aaa fpbs_fpb fpbs_fpbs |
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@@ -502,7 +569,7 @@
|
- decomposed extended computation | +decomposed rt-computation | scpds ( â¦?,?⦠⢠? â¢*â¡*[?,?,?] ? ) | scpds_lift scpds_aaa scpds_scpds | @@ -516,7 +583,7 @@ |
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- context-sensitive extended computation | +context-sensitive rt-computation | lpxs ( â¦?,?⦠⢠â¡*[?,?] ? ) | lpxs_drop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs |
@@ -534,7 +601,7 @@
|
cpxs ( â¦?,?⦠⢠? â¡*[?,?] ? ) | -cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs | +cpxs_tsts cpxs_tsts_vector cpxs_lreq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs |
|
@@ -576,7 +643,7 @@
|
- local env. ref. for abstract candidates of reducibility | +local env. ref. for generic reducibility | lsubc ( ? ⢠? â«[?] ? ) | lsubc_drop lsubc_drops lsubc_lsuba | @@ -590,19 +657,33 @@ |
|
- support for abstract computation properties | -acp | -acp_cr ( â¦?,?,?⦠ϵ[?] ã?ã ) | -acp_aaa | +support for generic computation properties | +gcp | +gcp_cr ( â¦?,?,?⦠ϵ[?] ã?ã ) | +gcp_aaa |
|
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| reduction | -"big tree" parallel reduction | -fpb ( â¦?,?,?⦠â½[?,?] â¦?,?,?⦠) | -fpb_lift fpb_aaa | +parallel qrst-reduction | +fpbq ( â¦?,?,?⦠â½[?,?] â¦?,?,?⦠) | +fpbq_alt ( â¦?,?,?⦠â½â½[?,?] â¦?,?,?⦠) | +fpbq_lift fpbq_aaa | +
+ + |
+ ||||||||||||||||||||||||||||||||||||||||||||||||
|
+ + |
+
+ + |
+ fpb ( â¦?,?,?⦠â»[?,?] â¦?,?,?⦠) | +fpb_lift fpb_lleq fpb_fleq |
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@@ -614,7 +695,7 @@
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- normal forms for context-sensitive extended reduction | +normal forms for context-sensitive rt-reduction | cnx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | cnx_lift cnx_crx cnx_cix | @@ -628,7 +709,7 @@ |
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- context-sensitive extended reduction | +context-sensitive rt-reduction | lpx ( â¦?,?⦠⢠â¡[?,?] ? ) | lpx_drop lpx_frees lpx_lleq lpx_aaa |
@@ -646,7 +727,7 @@
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cpx ( â¦?,?⦠⢠? â¡[?,?] ? ) | -cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix | +cpx_lreq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix |
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@@ -658,7 +739,7 @@
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- irreducible forms for context-sensitive extended reduction | +irreducible forms for context-sensitive rt-reduction | cix ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | cix_lift | @@ -672,7 +753,7 @@ |
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- reducible forms for context-sensitive extended reduction | +reducible forms for context-sensitive rt-reduction | crx ( â¦?,?⦠⢠â¡[?,?] ðâ¦?⦠) | crx_lift | @@ -774,8 +855,10 @@ | iterated static type assignment | lstas ( â¦?,?⦠⢠? â¢*[?,?] ? ) | -lstas_alt ( â¦?,?⦠⢠? â¢â¢*[?,?] ? ) | -lstas_lift lstas_aaa lstas_da lstas_lstas | +lstas_lift lstas_llpx_sn.ma lstas_aaa lstas_da lstas_lstas | +
+ + |
|
@@ -798,21 +881,7 @@
degree assignment | da ( â¦?,?⦠⢠? âª[?,?] ? ) | -da_lift da_aaa da_sta da_da | -
- - |
-
- - |
- ||||||||||||
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- - |
- static type assignment | -sta ( â¦?,?⦠⢠? â¢[?] ? ) | -sta_lift sta_lpx_sn sta_aaa sta_sta | +da_lift da_aaa da_da |
|
@@ -896,7 +965,7 @@
lleq ( ? â¡[?,?] ? ) | -lleq_alt lleq_alt_rec lleq_leq lleq_drop lleq_fqus lleq_llor lleq_lleq | +lleq_alt lleq_alt_rec lleq_lreq lleq_drop lleq_fqus lleq_llor lleq_lleq |
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@@ -910,7 +979,7 @@
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 | +llpx_sn_alt llpx_sn_alt_rec llpx_sn_tc llpx_sn_lreq llpx_sn_drop llpx_sn_lpx_sn llpx_sn_frees llpx_sn_llor |
|
@@ -923,7 +992,7 @@
pointwise union for local environments | -llor ( ? â©[?,?] ? â¡ ? ) | +llor ( ? â[?,?] ? â¡ ? ) | llor_alt llor_drop |
@@ -938,7 +1007,7 @@ |
context-sensitive exclusion from free variables | frees ( ? ⢠? ϵ ð *[?]â¦?⦠) | -frees_append frees_leq frees_lift | +frees_append frees_lreq frees_lift |
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@@ -950,7 +1019,7 @@
|
- contxt-sensitive extended multiple substitution | +context-sensitive multiple rt-substitution | cpys ( â¦?,?⦠⢠? â¶*[?,?] ? ) | cpys_alt ( â¦?,?⦠⢠? â¶â¶*[?,?] ? ) | cpys_lift cpys_cpys | @@ -993,7 +1062,7 @@iterated local env. slicing | -drops ( â©*[?,?] ? â¡ ? ) | +drops ( â¬*[?,?] ? â¡ ? ) | drops_drop drops_drops |
@@ -1007,7 +1076,7 @@ |
generic term relocation | -lifts_vector ( â§*[?] ? â¡ ? ) | +lifts_vector ( â¬*[?] ? â¡ ? ) | lifts_lift_vector |
@@ -1023,7 +1092,7 @@ |
|
- lifts ( â§*[?] ? â¡ ? ) | +lifts ( â¬*[?] ? â¡ ? ) | lifts_lift lifts_lifts |
@@ -1036,11 +1105,11 @@ |
|
- support for generic relocation | -gr2 ( @â¦?,?⦠⡠? ) | -gr2_plus ( ? + ? ) | -gr2_minus ( ? â ? â¡ ? ) | -gr2_gr2 | +support for multiple relocation | +mr2 ( @â¦?,?⦠⡠? ) | +mr2_plus ( ? + ? ) | +mr2_minus ( ? â ? â¡ ? ) | +mr2_mr2 |
| substitution | @@ -1077,7 +1146,7 @@global env. slicing | -gget ( â©[?] ? â¡ ? ) | +gget ( â¬[?] ? â¡ ? ) | gget_gget |
@@ -1090,7 +1159,7 @@ |
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- contxt-sensitive extended ordinary substitution | +context-sensitive ordinary rt-substitution | cpy ( â¦?,?⦠⢠? â¶[?,?] ? ) | cpy_lift cpy_nlift cpy_cpy | @@ -1104,7 +1173,7 @@ |
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- local env. ref. for extended substitution | +local env. ref. for rt-substitution | lsuby ( ? â[?,?] ? ) | lsuby_lsuby |
@@ -1133,8 +1202,8 @@
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basic local env. slicing | -drop ( â©[?,?,?] ? â¡ ? ) | -drop_append drop_leq drop_drop | +drop ( â¬[?,?,?] ? â¡ ? ) | +drop_append drop_lreq drop_drop |
|
@@ -1147,7 +1216,7 @@
basic term relocation | -lift_vector ( â§[?,?] ? â¡ ? ) | +lift_vector ( â¬[?,?] ? â¡ ? ) | lift_lift_vector |
@@ -1163,7 +1232,7 @@ |
|
- lift ( â§[?,?] ? â¡ ? ) | +lift ( â¬[?,?] ? â¡ ? ) | lift_neq lift_lift |
@@ -1175,8 +1244,8 @@ | |||||||||||||||||||||||
| grammar | equivalence for local environments | -leq ( ? ⩬[?,?] ? ) | -leq_leq | +lreq ( ? ⩬[?,?] ? ) | +lreq_lreq |
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@@ -1188,9 +1257,9 @@
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- same top term constructor | -tstc ( ? â ? ) | -tstc_tstc tstc_vector | +same top term structure | +tsts ( ? â ? ) | +tsts_tsts tsts_vector |
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@@ -1289,12 +1358,7 @@
Physical Structure of the Specification
- The source files are grouped in directories,
- one for each component.
-
-
+
![[Spacer]](http://lambdadelta.info/images/rainbow.png "lambdadelta rainbow rule")
@@ -1320,6 +1384,6 @@
-
Last update: Thu, 07 Aug 2014 19:13:43 +0200
-