![[lambdadelta home]](http://lambdadelta.info/images/crux_32.png "lambdadelta home")
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| domain | -block | -leader | -applicator (with âθ)* | -reduction | -âζ * | -reference * | -||||||||
| {X | Π⢠X : W} | -local typed abstraction * | -Π⢠+λW | -âV | -âβ | -no | -#i | -||||||||
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- + | + home | -local typed declaration ** | -Π⢠-λW | -âV | -âβ | -no | -#i | -|||||||
| + | + news + | ++ specification + | +
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- global typed declaration *** | -Π⢠pλW | -no | -no | -no | -$p | -|||||
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- native type annotation * | -Π⢠âW | -no | -no | -yes | -no | -|||||||
| {X | Π⢠X = V} | -local abbreviation * | -Π⢠+δV | -no | -local âδ | -yes | -#i | -||||||||
| + | + documentation + | ++ implementation + | +
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- local definition ** | -Π⢠-δV | -no | -local âδ | -no | -#i | |||||
| + | + foreword + | ++ milestones + | ++ version 2 + | +(background - core - applications) | +
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- global definition *** | -Π⢠pδV | -no | -global âδ | -no | -$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 | +
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| sizes | -files | -176 | -characters | -373293 | -nodes | -1085467 | +sizes | +files | +177 | +characters | +179834 | +nodes | +938855 |
| propositions | -theorems | -76 | -lemmas | -780 | -total | -856 | +propositions | +theorems | +49 | +lemmas | +618 | +total | +667 |
| concepts | -declared | -43 | -defined | -71 | -total | -114 | +concepts | +declared | +24 | +defined | +42 | +total | +66 |
+ | component | -plane | -files | -+ | component | +plane | +files | +
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| dynamic typing | -"big tree" parallel computation | -yprs ( ? ⢠â¦?,?⦠â¥[g] â¦?,?⦠) | -yprs_yprs | -ygt ( ? ⢠â¦?,?⦠>[g] â¦?,?⦠) | -ygt_ygt | -||||||
| + | 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 | +
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- "big tree" parallel reduction | -ypr ( ? ⢠â¦?,?⦠â½[g] â¦?,?⦠) | -ysc ( ? ⢠â¦?,?⦠â»[g] â¦?,?⦠) | -
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- local env. ref. for stratified native validity | -lsubsv ( ? ⢠? ¡â[?] ? ) | -lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv | -+ |
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| + | cpr ( â¦?,?⦠⢠? â¡[?] ? ) | +cpr_drops | +
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- stratified native validity | -snv ( �,?⦠⢠? ¡[?] ) | -snv_lift snv_lpss snv_aaa snv_ssta snv_sstas snv_ssta_lpr snv_lpr snv_cpcs | -
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| equivalence | -local env. ref. for stratified static type assignment | -lsubss ( ? â¢â[?] ? ) | -lsubss_ldrop lsubss_ssta lsubss_cpcs | -
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- context-sensitive equivalence | -cpcs ( ? ⢠? â¬* ? ) | -cpcs_lpss cpcs_aaa cpcs_cprs cpcs_cpcs | -+ | cpm ( â¦?,?⦠⢠? â¡[?,?] ? ) | +cpm_simple cpm_drops cpm_lsubr cpm_cpx | +
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| conversion | -context-sensitive conversion | -cpc ( ? ⢠? ⬠? ) | -cpc_cpc | -
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| computation | -decomposed extended computation | -dxprs ( â¦?,?⦠⢠? â¢*â¡*[?] ? ) | -dxprs_lift dxprs_lpss dxprs_aaa dxprs_dxprs | -+ | uncounted context-sensitive rt-transition | +lfpx ( â¦?,?⦠⢠â¬[?,?] ? ) | +lfpx_length lfpx_drops lfpx_fqup lfpx_frees lfpx_aaa | +
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- context-sensitive extended computation | -cpxs ( â¦?,?⦠⢠? â¡*[?] ? ) | -cpxs_lift | -+ |
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- + | cpx ( â¦?,?⦠⢠? â¬[?] ? ) | +cpx_simple cpx_drops cpx_lsubr | +
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- weakly normalizing computation | -cpe ( ? ⢠â¡* ðâ¦?⦠) | -cpe_cpe | -
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- strongly normalizing computation | -csn_vector ( ? ⢠â¬* ? ) | -csn_tstc_vector csn_aaa | -+ | counted context-sensitive rt-transition | +cpg ( â¦?,?⦠⢠? â¬[?,?] ? ) | +cpg_simple cpg_drops cpg_lsubr | +
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| + | static typing | +parameters | +sh | +sd | +
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- csn ( ? ⢠â¬* ? ) | -csn_alt ( ? ⢠â¬â¬* ? ) | -csn_lift csn_lpr | -+ |
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- context-sensitive computation | -lprs ( ? ⢠â¡* ? ) | -lprs_alt ( ? ⢠â¡â¡* ? ) | -lprs_ldrop lprs_lpss lprs_aaa lprs_cprs lprs_lprs | -
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- cprs ( ? ⢠? â¡* ?) | -cprs_tstc cprs_tstc_vector cprs_lift cprs_lpss cprs_aaa cprs_cprs | -+ | restricted ref. for atomic arity assignment | +lsuba ( ? ⢠? â«â ? ) | +lsuba_drops lsuba_lsubr lsuba_aaa lsuba_lsuba | +
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- local env. ref. for abstract candidates of reducibility | -lsubc ( ? â[?] ? ) | -lsubc_ldrop lsubc_ldrops lsubc_lsuba | -+ | atomic arity assignment | +aaa ( â¦?,?⦠⢠? â ? ) | +aaa_drops aaa_fqus aaa_lfeq aaa_aaa | +
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- support for abstract computation properties | -acp | -acp_cr ( â¦?,?⦠ϵ[?] ã?ã ) | -acp_aaa | -+ | equivalence for closures on referred entries | +ffeq ( â¦?,?,?⦠⡠â¦?,?,?⦠) | +ffeq_freq | +
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| reduction | -context-sensitive extended reduction | -lpx ( â¦?,?⦠⢠â¡[?] ? ) | -lpx_ldrop lpx_aaa | -
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- cpx ( â¦?,?⦠⢠? â¡[?] ? ) | -cpx_lift | -+ | equivalence for local environments on referred entries | +lfeq ( ? â¡[?] ? ) | +lfeq_length lfeq_lreq lfeq_fqup lfeq_lfeq | +
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- context-sensitive normal forms | -cnf ( ? ⢠ðâ¦?⦠) | -cnf_liftt cnf_crf cnf_cif | -+ | generic extension on referred entries | +lfxs ( ? ⦻*[?,?] ? ) | +lfxs_length lfxs_drops lfxs_fqup lfxs_lfxs | +
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- context-sensitive reduction | -lpr ( ? ⢠⡠? ) | -lpr_ldrop lpr_lpss lpr_lpr | -+ | restricted ref. for context-sensitive free variables | +lsubf ( â¦?,?⦠â«ð * â¦?,?⦠) | +lsubf_frees | +
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- + | context-sensitive free variables | +frees ( ? ⢠ð *â¦?⦠⡠? ) | +frees_weight frees_lreq frees_drops frees_fqup frees_fqus frees_frees | +
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- cpr ( ? ⢠? ⡠? ) | -cpr_lift cpr_cif | -
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- context-sensitive reducible forms | -crf ( ? ⢠ðâ¦?⦠) | -crf_append | -cif ( ? ⢠ðâ¦?⦠) | -cif_append | -|||||
| unfold | -restricted parallel computation | -lpqs ( ? ⢠â¤* ? ) | -lpqs_ldrop lpqs_cpqs lpqs_lpqs | -+ | restricted ref. for local env. | +lsubr ( ? â« ? ) | +lsubr_length lsubr_drops lsubr_lsubr | +
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- + | s-computation | +iterated structural successor for closures | +fqus ( â¦?,?,?⦠â* â¦?,?,?⦠) | +fqus_weight fqus_drops fqus_fqup fqus_fqus | +
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- cpqs ( ? ⢠? â¤* ? ) | -cpqs_lift | -
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- unfold | -unfold ( ? ⢠? ⧫* ? ) | -+ |
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- + | fqup ( â¦?,?,?⦠â+ â¦?,?,?⦠) | +fqup_weight fqup_drops fqup_fqup | +
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- iterated stratified static type assignment | -sstas ( â¦?,?⦠⢠? â¢*[?] ? ) | -sstas_lift sstas_lpss sstas_aaa sstas_sstas | -+ | s-transition | +structural successor for closures | +fquq ( â¦?,?,?⦠â⸮ â¦?,?,?⦠) | +fquq_length fquq_weight | +
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| static typing | -stratified static type assignment | -ssta ( â¦?,?⦠⢠? â¢[?,?] ? ) | -ssta_lift ssta_lpss ssta_aaa ssta_ssta | -+ |
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| + | fqu ( â¦?,?,?⦠â â¦?,?,?⦠) | +fqu_length fqu_weight | +
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- local env. ref. for atomic arity assignment | -lsuba ( ? ââ ? ) | -lsuba_ldrop lsuba_aaa lsuba_lsuba | -
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| + | relocation | +generic slicing for local environments | +drops_vector ( â¬*[?,?] ? â¡ ? ) ( â¬*[?] ? â¡ ? ) | +
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- atomic arity assignment | -aaa ( ? ⢠? â ? ) | -aaa_lift aaa_lifts aaa_lpss aaa_aaa | -+ |
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- parameters | -sh | -sd | -+ |
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| substitution | -parallel substitution | -lpss ( ? ⢠â¶* ? ) | -lpss_ldrop lpss_cpss lpss_lpss | -+ | drops ( â¬*[?,?] ? â¡ ? ) ( â¬*[?] ? â¡ ? ) | +drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops | +
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- + | generic relocation for terms | +lifts_vector ( â¬*[?] ? â¡ ? ) | +lifts_lifts_vector | +
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- cpss ( ? ⢠? â¶* ? ) | -cpss_lift | -
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- local env. ref. for substitution | -lsubr ( ? â ? ) | -lsubr_lsubr | -+ |
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- iterated structural successor for closures | -fsups ( â¦?,?⦠â* â¦?,?⦠) | -fsups_fsups | -+ | lifts ( â¬*[?] ? â¡ ? ) | +lifts_simple lifts_weight lifts_lifts | +
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- fsupp ( â¦?,?⦠â+ â¦?,?⦠) | -fsupp_fsupp | -+ | ranged equivalence for local environments | +lreq ( ? â¡[?] ? ) | +lreq_length lreq_lreq | +
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- generic local env. slicing | -ldrops ( â©*[?] ? â¡ ? ) | -ldrops_ldrop ldrops_ldrops | -+ | generic entrywise extension | +lexs ( ? ⦻*[?,?,?] ? ) | +lexs_length lexs_lexs | +
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| + | grammar | +append for local environments | +append ( ? @@ ? ) | +append_length | +
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- generic term relocation | -lifts_vector ( â§*[?] ? â¡ ? ) | -lifts_lift_vector | -
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- + | context-sensitive equivalences for terms | +ceq | +ceq_ceq | +
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- lifts ( â§*[?] ? â¡ ? ) | -lifts_lift lifts_lifts | -
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- support for generic relocation | -gr2 ( @â¦?,?⦠⡠? ) | -gr2_plus ( ? + ? ) | -gr2_minus ( ? â ? â¡ ? ) | -gr2_gr2 | -|||||
| relocation | -structural successor for closures | -fsup ( â¦?,?⦠â â¦?,?⦠) | -fsupq ( â¦?,?⦠â⸮ â¦?,?⦠) | -fsupq_alt | -
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| + | same top term structure | +tsts ( ? â ? ) | +tsts_tsts tsts_vector | +
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- global env. slicing | -gdrop ( â©[?] ? â¡ ? ) | -gdrop_gdrop | -
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- basic local env. slicing | -ldrop ( â©[?,?] ? â¡ ? ) | -ldrop_append ldrop_lpx_sn ldrop_ldrop | -+ | closures | +cl_weight ( â¯{?,?,?} ) | +cl_restricted_weight ( â¯{?,?} ) | +
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- basic term relocation | -lift_vector ( â§[?,?] ? â¡ ? ) | -lift_lift_vector | -+ |
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- + | internal syntax | +genv | +
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- lift ( â§[?,?] ? â¡ ? ) | -lift_lift | -
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| grammar | -pointwise extension of a relation | -lpx_sn | -lpx_sn_tc lpx_sn_lpx_sn | -
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- same top term constructor | -tstc ( ? â ? ) | -tstc_tstc tstc_vector | -+ |
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- + | lenv | +lenv_weight ( â¯{?} ) | +lenv_length ( |?| ) | +
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- closures | -cl_shift ( ? @@ ? ) | -cl_weight ( â¯{?,?} ) | -+ |
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+ term | +term_weight ( â¯{?} ) | +term_simple ( ðâ¦?⦠) | +term_vector ( â¶?.? ) |
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- internal syntax | -genv | -+ |
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- + | item | +
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- lenv | -lenv_weight ( â¯{?} ) | -lenv_length ( |?| ) | -lenv_append ( ? @@ ? ) | -||||||
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- term | -term_weight ( â¯{?} ) | -term_simple ( ðâ¦?⦠) | -term_vector | -||||||
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- item | -
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- external syntax | -aarity | -+ | external syntax | +aarity | +
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