![[lambdadelta home]](http://lambdadelta.info/images/crux_32.png "lambdadelta home")
+
![[Spacer]](http://lambdadelta.info/images/rainbow.png "lambdadelta rainbow rule")
+
| domain | -block | -leader | -applicator (with âθ)* | -reduction | -âζ * | -reference * | -||||||||
| {X | Π⢠X : W} | -local typed abstraction * | -Π⢠+λW | -âV | -âβ | -no | -#i | -||||||||
|
- + | + home | -local typed declaration ** | -Π⢠-λW | -âV | -âβ | -no | -#i | -|||||||
| + | + news + | ++ specification + | +
|
- global typed declaration *** | -Π⢠pλW | -no | -no | -no | -$p | -|||||
| + |
|
- native type annotation * | -Π⢠âW | -no | -no | -yes | -no | -|||||||
| {X | Π⢠X = V} | -local abbreviation * | -Π⢠+δV | -no | -local âδ | -yes | -#i | -||||||||
| + | + documentation + | ++ implementation + | +
|
- local definition ** | -Π⢠-δV | -no | -local âδ | -no | -#i | |||||
| + | + foreword + | ++ milestones + | ++ version 2 + | +(background - core - applications) | +
|
- global definition *** | -Π⢠pδV | -no | -global âδ | -no | -$p | ++ version 2 + | ++ helena + | ++ Open Symbolic Notation (OSN) + |
| no | -sort **** | -Π⢠âk | -no | -no | -no | -no | ++ citations + | ++ visibility + | ++ version 1 + | +(background - core) | +(static HELM directory) | ++ version 1 + | ++ library + | +(static LDDL directory) |
![[butterfly]](http://lambdadelta.info/images/b4.png "\lambda\delta butterfly")
+ | category | -objects | -+ | category | +objects | +
|
- + |
|
- + |
|
- + |
|
- + |
|
| sizes | -files | -255 | -characters | -502802 | -nodes | -1365444 | +sizes | +files | +177 | +characters | +179834 | +nodes | +938855 |
| propositions | -theorems | -89 | -lemmas | -1126 | -total | -1215 | +propositions | +theorems | +49 | +lemmas | +618 | +total | +667 |
| concepts | -declared | -48 | -defined | -82 | -total | -130 | +concepts | +declared | +24 | +defined | +42 | +total | +66 |
+ | component | -plane | -files | -
- - |
-
- - |
-
- - |
-
- - |
- ||||||
| dynamic typing | -"big tree" parallel computation | -yprs ( ? ⢠â¦?,?⦠â¥[g] â¦?,?⦠) | -yprs_yprs | -ygt ( ? ⢠â¦?,?⦠>[g] â¦?,?⦠) | -ygt_ygt | -+ | component | +plane | +files | +
|
- ||
| + |
|
- "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 | -+ | rt-transition | +t-bound context-sensitive rt-transition | +lfpr ( â¦?,?⦠⢠â¡[?,?] ? ) | +lfpr_length lfpr_drops lfpr_fqup lfpr_frees lfpr_aaa lfpr_lfpx lfpr_lfpr | +
|
-
- - |
- + |
|
|
- - |
- 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 | -focalized equivalence | -lfpcs ( â¦?⦠â¬* â¦?⦠) | -lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs | -+ |
|
- + | cpr ( â¦?,?⦠⢠? â¡[?] ? ) | +cpr_drops | +
|
- + |
|
|
| + |
|
- + |
|
- fpcs ( â¦?,?⦠â¬* â¦?,?⦠) | -fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs | -+ | cpm ( â¦?,?⦠⢠? â¡[?,?] ? ) | +cpm_simple cpm_drops cpm_lsubr cpm_cpx | +
|
-
- - |
- + |
|
|
- - |
- local env. ref. for stratified static type assignment | -lsubss ( ? â¢â[?] ? ) | -lsubss_ldrop lsubss_ssta lsubss_cpcs | -+ |
|
- + | uncounted context-sensitive rt-transition | +lfpx ( â¦?,?⦠⢠â¬[?,?] ? ) | +lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_aaa | +
|
- + |
|
|
- - |
- context-sensitive equivalence | -cpcs ( ? ⢠? â¬* ? ) | -cpcs_ltpss_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs | -+ |
|
- + |
|
- + | cpx ( â¦?,?⦠⢠? â¬[?] ? ) | +cpx_simple cpx_drops cpx_lsubr | +
|
- |
| conversion | -focalized conversion | -lfpc ( �⦠⬠�⦠) | -lfpc_lfpc | -
- - |
-
- - |
- + |
|
|||||
| + |
|
- + | counted context-sensitive rt-transition | +cpg ( â¦?,?⦠⢠? â¬[?,?] ? ) | +cpg_simple cpg_drops cpg_lsubr | +
|
- fpc ( �,?⦠⬠�,?⦠) | -fpc_fpc | -
- - |
-
- - |
- + |
|
|
- - |
- context-sensitive conversion | -cpc ( ? ⢠? ⬠? ) | -cpc_cpc | -
- - |
- + | static typing | +parameters | +sh | +sd | +
|
- + |
|
| computation | -focalized computation | -lfprs ( â¦?⦠â¡* â¦?⦠) | -lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs | -+ |
|
- + | restricted ref. for atomic arity assignment | +lsuba ( ? ⢠? â«â ? ) | +lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba | +
|
- + |
|
|
- - |
- + |
|
- fprs ( â¦?,?⦠â¡* â¦?,?⦠) | -fprs_aaa fprs_fprs | -+ | atomic arity assignment | +aaa ( â¦?,?⦠⢠? â ? ) | +aaa_drops aaa_fqus aaa_lfeq aaa_aaa | +
|
-
- - |
- + |
|
|
- - |
- decomposed extended computation | -dxprs ( â¦?,?⦠⢠? â¢*â¡*[?] ? ) | -dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn dxprs_aaa dxprs_dxprs | -+ |
|
- + | equivalence for closures on referred entries | +ffeq ( �,?,?⦠⡠�,?,?⦠) | +ffeq_freq | +
|
- + |
|
| + |
|
- weakly normalizing computation | -cpe ( ? ⢠â¡* ðâ¦?⦠) | -cpe_cpe | -+ | equivalence for local environments on referred entries | +lfeq ( ? â¡[?] ? ) | +lfeq_length lfeq_lreq lfeq_fqup lfeq_lfeq | +
|
-
- - |
- + |
|
|
- - |
- strongly normalizing computation | -csn_vector ( ? ⢠â¬* ? ) | -csn_cpr_vector csn_tstc_vector csn_aaa | -+ |
|
- + | generic extension on referred entries | +lfxs ( ? ⦻*[?,?] ? ) | +lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs | +
|
- + |
|
|
- - |
- + |
|
- csn ( ? ⢠â¬* ? ) | -csn_alt ( ? ⢠â¬â¬* ? ) | -csn_lift csn_cpr csn_lfpr | -+ | restricted ref. for context-sensitive free variables | +lsubf ( â¦?,?⦠â«ð * â¦?,?⦠) | +lsubf_frees | +
|
- + |
|
| + |
|
- 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 | -+ | context-sensitive free variables | +frees ( ? ⢠ð *â¦?⦠⡠? ) | +frees_weight frees_lreq frees_drops frees_fqup frees_fqus frees_frees | +
|
-
- - |
- + |
|
| + |
|
- context-free computation | -ltprs ( ? â¡* ? ) | -ltprs_alt ( ? â¡â¡* ? ) | -ltprs_ldrop ltprs_ltprs | -+ | restricted ref. for local env. | +lsubr ( ? â« ? ) | +lsubr_length lsubr_drops lsubr_lsubr | +
|
- + |
|
|
- - |
- + | s-computation | +iterated structural successor for closures | +fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) | +fqus_weight fqus_drops fqus_fqup fqus_fqus | +
|
- tprs ( ? â¡* ?) | -tprs_lift tprs_tprs | -
- - |
-
- - |
- + |
|
| + |
|
- local env. ref. for abstract candidates of reducibility | -lsubc ( ? â[?] ? ) | -lsubc_ldrop lsubc_ldrops lsubc_lsuba | -+ |
|
- + | fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | +fqup_weight fqup_drops fqup_fqup | +
|
- + |
|
|
- - |
- support for abstract computation properties | -acp | -acp_cr ( â¦?,?⦠ϵ[?] ã?ã ) | -acp_aaa | -+ | s-transition | +structural successor for closures | +fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) | +fquq_length fquq_weight | +
|
- + |
|
| reducibility | -context-sensitive focalized reduction | -cfpr ( ? ⢠�,?⦠⡠�,?⦠) | -cnfpr_ltpss cfpr_aaa cfpr_cpr cfpr_cfpr | -
- - |
-
- - |
- + |
|
- |||||
| + |
|
- context-free focalized reduction | -lfpr ( â¦?⦠⡠â¦?⦠) | -lfpr_alt ( â¦?⦠â¡â¡ â¦?⦠) | -lfpr_aaa lfpr_cpr lfpr_fpr lfpr_lfpr | -+ | fqu ( â¦?,?,?⦠â â¦?,?,?⦠) | +fqu_length fqu_weight | +
|
- + |
|
|
|
- - |
-
- - |
- fpr ( â¦?,?⦠⡠â¦?,?⦠) | -fpr_cpr fpr_fpr | -+ | relocation | +generic slicing for local environments | +drops_vector ( â¬*[?,?] ? â¡ ? ) ( â¬*[?] ? â¡ ? ) | +
|
- + |
|
- + |
|
| + |
|
- context-sensitive normal forms | -cnf ( ? ⢠ðâ¦?⦠) | -cnf_lift cnf_cif | -+ |
|
- + | drops ( â¬*[?,?] ? â¡ ? ) ( â¬*[?] ? â¡ ? ) | +drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops | +
|
- + |
|
|
- - |
- context-sensitive reduction | -cpr ( ? ⢠? ⡠? ) | -cpr_lift cpr_tpss cpr_ltpss_dx cpr_ltpss_sn cpr_delift cpr_aaa cpr_ltpr cpr_cpr | -
- - |
-
- - |
- + |
|
- |||||
| + | generic relocation for terms | +lifts_vector ( â¬*[?] ? â¡ ? ) | +lifts_lifts_vector | +
|
- context-sensitive reducible forms | -crf ( ? ⢠ðâ¦?⦠) | -crf_append | -cif ( ? ⢠ðâ¦?⦠) | -cif_append | -+ |
|
|
|
- - |
- context-free normal forms | -thnf ( ððâ¦?⦠) | -+ |
|
- + |
|
- + | lifts ( â¬*[?] ? â¡ ? ) | +lifts_simple lifts_weight lifts_lifts | +
|
- + |
|
| + |
|
- context-free reduction | -ltpr ( ? â¡ ? ) | -ltpr_ldrop ltpr_tps ltpr_tpss ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr | -+ | ranged equivalence for local environments | +lreq ( ? â¡[?] ? ) | +lreq_length lreq_lreq | +
|
-
- - |
- + |
|
| + |
|
- + | generic entrywise extension | +lexs ( ? ⦻*[?,?,?] ? ) | +lexs_length lexs_lexs | +
|
- tpr ( ? â¡ ? ) | -tpr_lift tpr_delift tpr_tpr | -
- - |
-
- - |
- + |
|
| unwind | -iterated stratified static type assignment | -sstas ( â¦?,?⦠⢠? â¢*[?] ? ) | -sstas_lift sstas_ltpss_dx sstas_ltpss_sn sstas_aaa sstas_sstas | -+ | grammar | +append for local environments | +append ( ? @@ ? ) | +append_length | +
|
-
- - |
- + |
|
| static typing | -stratified static type assignment | -ssta ( â¦?,?⦠⢠? â¢[?,?] ? ) | -ssta_lift ssta_ltpss_dx ssta_ltpss_sn ssta_aaa ssta_ssta | -+ |
|
- + | context-sensitive equivalences for terms | +ceq | +ceq_ceq | +
|
- + |
|
|
- - |
- local env. ref. for atomic arity assignment | -lsuba ( ? ââ ? ) | -lsuba_ldrop lsuba_aaa lsuba_lsuba | -+ |
|
- + | same top term structure | +tsts ( ? â ? ) | +tsts_tsts tsts_vector | +
|
- + |
|
|
- - |
- atomic arity assignment | -aaa ( ? ⢠? â ? ) | -aaa_lift aaa_lifts aaa_ltpss_dx aaa_ltpss_sn aaa_aaa | -+ |
|
- + | closures | +cl_weight ( â¯{?,?,?} ) | +cl_restricted_weight ( â¯{?,?} ) | +
|
- + |
|
| + |
|
- parameters | -sh | -sd | -+ | internal syntax | +genv | +
|
- + |
|
- + |
|
| unfold | -basic local env. thinning | -thin ( ? â¼*[?,?] â¡ ? ) | -thin_ldrop thin_delift | -+ |
|
- + |
|
- + | lenv | +lenv_weight ( â¯{?} ) | +lenv_length ( |?| ) | +
|
|
- - |
- inverse basic term relocation | -delift ( ? ⢠? â¼*[?,?] â¡ ? ) | -delift_alt ( ? ⢠? â¼â¼*[?,?] â¡ ? ) | -delift_lift delift_tpss delift_ltpss delift_delift | -
- - |
-
- - |
- ||||||
|
- - |
- revised parallel substitution | -lcpss ( ? ⢠â¶* ? ) | -lcpss_ldrop lcpss_cpss lcpss_lcpss | -+ |
|
-
- - |
- + |
|
+ term | +term_weight ( â¯{?} ) | +term_simple ( ðâ¦?⦠) | +term_vector ( â¶?.? ) |
| + |
|
- + |
|
- cpss ( ? ⢠? â¶* ? ) | -cpss_lift | -+ | item | +
|
- + |
|
- + |
|
| + |
|
- partial unfold | -ltpss_sn ( ? ⢠â¶*[?,?] ? ) | -ltpss_sn_alt ( ? ⢠â¶â¶*[?,?] ? ) | -ltpss_sn_ldrop ltpss_sn_tps ltpss_sn_tpss ltpss_sn_ltpss_sn | -+ | external syntax | +aarity | +
|
- + |
|
- |
|
- - |
-
- - |
- ltpss_dx ( ? â¶*[?,?] ? ) | -ltpss_dx_ldrop ltpss_dx_tps ltpss_dx_tpss ltpss_dx_ltpss_dx | -
- - |
-
- - |
-
- - |
- ||||||
|
- - |
-
- - |
- tpss ( ? ⢠? â¶*[?,?] ? ) | -tpss_alt ( ? ⢠? â¶â¶*[?,?] ? ) | -tpss_lift | -tpss_tpss | -
- - |
- ||||||
|
- - |
- iterated structural successor for closures | -fsupp ( â¦?,?⦠â+ â¦?,?⦠) | -fsupp_fsupp | -
- - |
-
- - |
-
- - |
- ||||||
|
- - |
- generic local env. slicing | -ldrops ( â©*[?] ? â¡ ? ) | -ldrops_ldrop ldrops_ldrops | -
- - |
-
- - |
-
- - |
- ||||||
|
- - |
- generic term relocation | -lifts_vector ( â§*[?] ? â¡ ? ) | -lifts_lift_vector | -
- - |
-
- - |
-
- - |
- ||||||
|
- - |
-
- - |
- lifts ( â§*[?] ? â¡ ? ) | -lifts_lift lifts_lifts | -
- - |
-
- - |
-
- - |
- ||||||
|
- - |
- support for generic relocation | -gr2 ( @â¦?,?⦠⡠? ) | -gr2_plus ( ? + ? ) | -gr2_minus ( ? â ? â¡ ? ) | -gr2_gr2 | -
- - |
- ||||||
| substitution | -parallel substitution | -tps ( ? ⢠? â¶[?,?] ? ) | -tps_lift tps_tps | -
- - |
-
- - |
-
- - |
- ||||||
|
- - |
- structural successor for closures | -fsup ( â¦?,?⦠â â¦?,?⦠) | -
- - |
-
- - |
-
- - |
-
- - |
- ||||||
|
- - |
- global env. slicing | -gdrop ( â©[?] ? â¡ ? ) | -gdrop_gdrop | -
- - |
-
- - |
-
- - |
- ||||||
|
- - |
- basic local env. slicing | -ldrop ( â©[?,?] ? â¡ ? ) | -ldrop_append ldrop_lpx ldrop_lbotr ldrop_ldrop | -
- - |
-
- - |
-
- - |
- ||||||
|
- - |
- local env. ref. for substitution | -lsubr ( ? â[?,?] ? ) | -(lsubr_lsubr) | -lsubr_lbotr ( â[?,?] ? ) | -
- - |
-
- - |
- ||||||
|
- - |
- basic term relocation | -lift_vector ( â§[?,?] ? â¡ ? ) | -lift_lift_vector | -
- - |
-
- - |
-
- - |
- ||||||
|
- - |
-
- - |
- lift ( â§[?,?] ? â¡ ? ) | -lift_lift | -
- - |
-
- - |
-
- - |
- ||||||
| grammar | -same head term form | -tshf ( ? â ? ) | -(tshf_tshf) | -
- - |
-
- - |
-
- - |
- ||||||
|
- - |
- same top term constructor | -tstc ( ? â ? ) | -tstc_tstc tstc_vector | -
- - |
-
- - |
-
- - |
- ||||||
|
- - |
- closures | -cl_shift ( ? @@ ? ) | -cl_weight ( â¯{?,?} ) | -
- - |
-
- - |
-
- - |
- ||||||
|
- - |
- internal syntax | -genv | -
- - |
-
- - |
-
- - |
-
- - |
- ||||||
|
- - |
-
- - |
- lenv | -lenv_weight ( â¯{?} ) | -lenv_length ( |?| ) | -lenv_append ( ? @@ ? ) | -lenv_px lenv_px_bi | -||||||
|
- - |
-
- - |
- term | -term_weight ( â¯{?} ) | -term_simple ( ðâ¦?⦠) | -term_vector | -
- - |
- ||||||
|
- - |
-
- - |
- item | -
- - |
-
- - |
-
- - |
-
- - |
- ||||||
|
- - |
- external syntax | -aarity | -
- - |
-
- - |
-
- - |
- + |
|
+