X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=helm%2Fwww%2Flambdadelta%2Fbasic_2.html;h=09ff142bf7dc510b68bf194cc9faedd44e4ebd42;hb=68a413ec8a20ef0d73fcd5810be7db659abe6f92;hp=42f31ada768a54699881823b1b28dea7856d8ae8;hpb=9c5e448d33057cb8ce6a02eba2d81a5e043cac24;p=helm.git diff --git a/helm/www/lambdadelta/basic_2.html b/helm/www/lambdadelta/basic_2.html index 42f31ada7..09ff142bf 100644 --- a/helm/www/lambdadelta/basic_2.html +++ b/helm/www/lambdadelta/basic_2.html @@ -1,88 +1,1037 @@ - + - - - - - + + + + + lambdadelta version 2 - - - - + + + + -
[lambdadelta home]
cic:/matita/lambdadelta/basic_2/ (λδ version 2)
[Spacer]
-
System's Syntax and Behavior
-
This is a summary of the "block structure" + +
+ + [lambdadelta home] + +
+
cic:/matita/lambdadelta/basic_2/ (λδ version 2)
+
+ [Spacer] +
+
System's Syntax and Behavior
+
This is a summary of the "block structure" of the System's syntactic items and reductions.
-
domainblockleaderapplicator (with →θ)*reduction→ζ *reference *
{X | Γ ⊢ X : W}local typed abstraction *Γ ⊢ +λWⓐV→βno#i

local typed declaration **Γ ⊢ -λWⓐV→βno#i

global typed declaration ***Γ ⊢ pλWnonono$p

native type annotation *Γ ⊢ ⓝWnonoyesno
{X | Γ ⊢ X = V}local abbreviation *Γ ⊢ +δVnolocal →δyes#i

local definition **Γ ⊢ -δVnolocal →δno#i

global definition ***Γ ⊢ pδVnoglobal →δno$p
nosort ****Γ ⊢ ⋆knononono
-
* In terms only. - ** In terms and local environments only. +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
domainblockleaderapplicator (with →θ)*reduction→ζ *reference *
{X | Γ ⊢ X : W}local typed abstraction *Γ ⊢ +λWⓐV→βno#i
+
+ 		local typed declaration **Γ ⊢ -λWⓐV→βno#i
+
+ 		global typed declaration ***Γ ⊢ pλWnonono$p
+
+ 		native type annotation *Γ ⊢ ⓝWnonoyesno
{X | Γ ⊢ X = V}local abbreviation *Γ ⊢ +δVnolocal →δyes#i
+
+ 		local definition **Γ ⊢ -δVnolocal →δno#i
+
+ 		global definition ***Γ ⊢ pδVnoglobal →δno$p
nosort ****Γ ⊢ ⋆knononono
+
+
* In terms only. + ** In terms and local environments only. *** In global environments only. - **** Sort level k in terms only. + **** Sort level k in terms only.
- -
Summary of the Specification
-
Here is a numerical acount of the specification's contents + +
Summary of the Specification
+
Here is a numerical acount of the specification's contents and its timeline.
-
categoryobjects




sizesfiles232characters451402nodes1252094
propositionstheorems83lemmas1045total1128
conceptsdeclared42defined78total120
-
  • In progress. +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    categoryobjects +
    +     		+
    +     		+
    +     		+
    +     		+
    +
    sizesfiles173 characters363812nodes1057233
    propositionstheorems75lemmas750total825
    conceptsdeclared43defined68total111
    +
    +
      +
    • + In progress. Context-sensitive subject equivalence - for native type assignment. -
    -
    • In progress. + for native type assignment. +
      • +
    +
      +
    • + In progress. Closure of extended context-sensitive computation - for native validity. -
    -
    • In progress. + for native validity. +
      • +
    +
      +
    • + In progress. Extended context-sensitive strong normalization - for simply typed terms. -
    -
    • 2012 October 16. + for simply typed terms. +
      • +
    +
      +
    • + 2013 April 16. + Reaxiomatized substitution and reduction + commute with respect to subclosure + (anniversary milestone). +
      • +
    +
      +
    • + 2013 March 16. + Mutual recursive preservation of stratified native validity + for hyper computation on closures. +
      • +
    +
      +
    • + 2012 October 16. Confluence for context-free parallel reduction on closures. -
    -
    • 2012 July 26. +
      • +
    +
      +
    • + 2012 July 26. Term binders polarized to control ζ reduction. -
    -
    • 2012 April 16. +
      • +
    +
      +
    • + 2012 April 16. Context-sensitive subject equivalence - for atomic arity assignment - (anniversary milestone). -
    -
    • 2012 March 15. + for atomic arity assignment + (anniversary milestone). +
      • +
    +
      +
    • + 2012 March 15. Context-sensitive strong normalization - for simply typed terms. -
    -
    • 2012 January 27. + for simply typed terms. +
      • +
    +
      +
    • + 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. -
    +
    • +
-
Logical Structure of the Specification
-
The source files are grouped in planes and components +
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. - The notation for the relations or functions introduced in each file - is shown in parentheses (? are placeholders). + The notation for the relations or functions introduced in each file + is shown in parentheses (? are placeholders).
-
componentplanefiles



dynamic typingstratified native validitysnv ( ⦃?,?⦄ ⊩ ? :[?] )snv_lift snv_aaa snv_ssta snv_ltpr


equivalencefocalized equivalencelfpcs ( ⦃?⦄ ⬌* ⦃?⦄ )lfpcs_aaa lfpcs_fpcs lfpcs_lfprs lfpcs_lfpcs




fpcs ( ⦃?,?⦄ ⬌* ⦃?,?⦄ )fpcs_aaa fpcs_cpcs fpcs_fprs fpcs_fpcs



local env. ref. for context-sensitive equivalencelsubse ( ? ⊢•⊑[?] ? )lsubse_ldrop lsubse_ssta lsubse_cpcs



context-sensitive equivalencecpcs ( ? ⊢ ? ⬌* ? )cpcs_ltpss cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs


conversionfocalized conversionlfpc ( ⦃?⦄ ⬌ ⦃?⦄ )lfpc_lfpc




fpc ( ⦃?,?⦄ ⬌ ⦃?,?⦄ )fpc_fpc



context-sensitive conversioncpc ( ? ⊢ ? ⬌ ? )cpc_cpc


computationdecomposed extended computationdxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )dxprs_lift dxprs_aaa dxpr_lsubss dxprs_dxprs



weakly normalizing computationcpe ( ? ⊢ ➡* 𝐍⦃?⦄ )cpe_cpe



strongly normalizing computationcsn_vector ( ? ⊢ ⬊* ? )csn_cpr_vector csn_tstc_vector csn_aaa




csn ( ? ⊢ ⬊* ? )csn_alt ( ? ⊢ ⬊⬊* ? )csn_lift csn_cpr csn_lfpr


focalized computationlfprs ( ⦃?⦄ ➡* ⦃?⦄ )lfprs_aaa lfprs_ltprs lfprs_cprs lfprs_fprs lfprs_lfprs




fprs ( ⦃?,?⦄ ➡* ⦃?,?⦄ )fprs_aaa fprs_fprs



context-sensitive computationcprs (? ⊢ ? ➡* ?)cprs_lift cprs_delift cprs_aaa cprs_ltpr cprs_lfpr cprs_cprs cprs_lfprs cprs_tstc cprs_tstc_vector



context-free computationltprs ( ? ➡* ? )ltprs_alt ( ? ➡➡* ? )ltprs_ldrop ltprs_ltprs



tprs ( ? ➡* ?)tprs_lift tprs_tprs



local env. ref. for abstract candidates of reducibilitylsubc ( ? ⊑[?] ? )lsubc_ldrop lsubc_ldrops lsubc_lsuba



support for abstract computation propertiesacpacp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )acp_aaa

reducibilitycontext-sensitive focalized reductioncfpr ( ? ⊢ ⦃?,?⦄ ➡ ⦃?,?⦄ )cnfpr_ltpss cfpr_aaa cfpr_cpr cfpr_cfpr



context-free focalized reductionlfpr ( ⦃?⦄ ➡ ⦃?⦄ )lfpr_alt ( ⦃?⦄ ➡➡ ⦃?⦄ )lfpr_aaa lfpr_cpr lfpr_fpr lfpr_lfpr



fpr ( ⦃?,?⦄ ➡ ⦃?,?⦄ )fpr_cpr fpr_fpr



context-sensitive normal formscnf ( ? ⊢ 𝐍⦃?⦄ )cnf_lift cnf_cif



context-sensitive reductioncpr ( ? ⊢ ? ➡ ? )cpr_lift cpr_tpss cpr_ltpss cpr_delift cpr_aaa cpr_ltpr cpr_cpr



context-sensitive reducible formscrf ( ? ⊢ 𝐑⦃?⦄ )crf_appendcif ( ? ⊢ 𝐈⦃?⦄ )cif_append

context-free normal formsthnf ( 𝐇𝐍⦃?⦄ )




context-free reductionltpr ( ? ➡ ? )ltpr_ldrop ltpr_tps ltpr_ltpss_dx ltpr_ltpss_sn ltpr_aaa ltpr_ltpr




tpr ( ? ➡ ? )tpr_lift tpr_tps tpr_tpss tpr_delift tpr_tpr


unwinditerated stratified static type assignmentsstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )sstas_lift sstas_ltpss_dx sstas_ltpss_sn sstas_aaa sstas_lsubss sstas_sstas


static typinglocal env. ref. for stratified static type assignmentlsubss ( ? •⊑[?] ? )lsubss_ldrop lsubss_ssta lsubss_lsubss



stratified static type assignmentssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )ssta_lift ssta_ltpss_dx ssta_ltpss_sn ssta_aaa ssta_ssta



local env. ref. for atomic arity assignmentlsuba ( ? ⁝⊑ ? )lsuba_ldrop lsuba_aaa lsuba_lsuba



atomic arity assignmentaaa ( ? ⊢ ? ⁝ ? )aaa_lift aaa_lifts aaa_ltpss_dx aaa_ltpss_sn aaa_aaa



parametersshsd


unfoldbasic local env. thinningthin ( ? ▼*[?,?] ≡ ? )thin_ldrop thin_delift



inverse basic term relocationdelift ( ? ⊢ ? ▼*[?,?] ≡ ? )delift_alt ( ? ⊢ ? ▼▼*[?,?] ≡ ? )delift_lift delift_tpss delift_ltpss delift_delift


partial unfoldltpss_sn ( ? ⊢ ▶*[?,?] ? )ltpss_sn_alt ( ? ⊢ ▶▶*[?,?] ? )ltpss_sn_ldrop ltpss_sn_tps ltpss_sn_tpss ltpss_sn_ltpss_sn



ltpss_dx ( ? ▶*[?,?] ? )ltpss_dx_ldrop ltpss_dx_tps ltpss_dx_tpss ltpss_dx_ltpss_dx




tpss ( ? ⊢ ? ▶*[?,?] ? )tpss_alt ( ? ⊢ ? ▶▶*[?,?] ? )tpss_lifttpss_tpss

generic local env. slicingldrops ( ⇩*[?] ? ≡ ? )ldrops_ldrop ldrops_ldrops



iterated restricted structural predecessor for closuresfrsups ( ⦃?,?⦄ ⧁* ⦃?,?⦄ )frsups_frsups




frsupp ( ⦃?,?⦄ ⧁+ ⦃?,?⦄ )frsupp_frsupp



generic term relocationlifts_vector ( ⇧*[?] ? ≡ ? )lifts_lift_vector




lifts ( ⇧*[?] ? ≡ ? )lifts_lift lifts_lifts



support for generic relocationgr2 ( @⦃?,?⦄ ≡ ? )gr2_plus ( ? + ? )gr2_minus ( ? ▭ ? ≡ ? )gr2_gr2
substitutionparallel substitutiontps ( ? ⊢ ? ▶[?,?] ? )tps_lift tps_tps



global env. slicinggdrop ( ⇩[?] ? ≡ ? )gdrop_gdrop



basic local env. slicingldrop ( ⇩[?,?] ? ≡ ? )ldrop_append ldrop_lpx ldrop_sfr ldrop_ldrop



local env. ref. for substitutionlsubs ( ? ≼[?,?] ? )(lsubs_lsubs)lsubs_sfr ( ≽[?,?] ? )


restricted structural predecessor for closuresfrsup ( ⦃?,?⦄ ⧁ ⦃?,?⦄ )




basic term relocationlift_vector ( ⇧[?,?] ? ≡ ? )lift_lift_vector




lift ( ⇧[?,?] ? ≡ ? )lift_lift


grammarsame head term formtshf ( ? ≈ ? )(tshf_tshf)



same top term constructortstc ( ? ≃ ? )tstc_tstc tstc_vector



closurescl_shift ( ? @@ ? )cl_weight ( ♯{?,?} )



internal syntaxgenv





lenvlenv_weight ( ♯{?} )lenv_length ( |?| )lenv_append ( ? @@ ? )lenv_px lenv_px_bi


termterm_weight ( ♯{?} )term_simple ( 𝐒⦃?⦄ )term_vector


item




external syntaxaarity



+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
componentplanefiles +
+ 		+
+ 		+
+
dynamic typing"big tree" parallel computationyprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )yprs_yprsygt ( ? ⊢ ⦃?,?⦄ >[g] ⦃?,?⦄ )ygt_ygt
+
+ 		"big tree" parallel reductionypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ ) +
+ 		+
+
+
+ 		local env. ref. for stratified native validitylsubsv ( ? ⊢ ? ¡⊑[?] ? )lsubsv_ldrop lsubsv_lsuba lsubsv_ssta lsubsv_dxprs lsubsv_cpcs lsubsv_snv +
+ 		+
+
+
+ 		stratified native validitysnv ( ⦃?,?⦄ ⊢ ? ¡[?] )snv_lift snv_lpss snv_aaa snv_ssta snv_sstas snv_ssta_lpr snv_lpr snv_cpcs +
+ 		+
+
equivalencelocal env. ref. for stratified static type assignmentlsubss ( ? •⊑[?] ? )lsubss_ldrop lsubss_ssta lsubss_cpcs +
+ 		+
+
+
+ 		context-sensitive equivalencecpcs ( ? ⊢ ? ⬌* ? )cpcs_lpss cpcs_aaa cpcs_cprs cpcs_cpcs +
+ 		+
+
conversioncontext-sensitive conversioncpc ( ? ⊢ ? ⬌ ? )cpc_cpc +
+ 		+
+
computationdecomposed extended computationdxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )dxprs_lift dxprs_lpss dxprs_aaa dxprs_dxprs +
+ 		+
+
+
+ 		weakly normalizing computationcpe ( ? ⊢ ➡* 𝐍⦃?⦄ )cpe_cpe +
+ 		+
+
+
+ 		strongly normalizing computationcsn_vector ( ? ⊢ ⬊* ? )csn_tstc_vector csn_aaa +
+ 		+
+
+
+ 		+
+ 		csn ( ? ⊢ ⬊* ? )csn_alt ( ? ⊢ ⬊⬊* ? )csn_lift csn_lpr +
+
+
+ 		context-sensitive computationlprs ( ? ⊢ ➡* ? )lprs_alt ( ? ⊢ ➡➡* ? )lprs_ldrop lprs_lpss lprs_aaa lprs_cprs lprs_lprs +
+
+
+ 		+
+ 		cprs ( ? ⊢ ? ➡* ?)cprs_tstc cprs_tstc_vector cprs_lift cprs_lpss cprs_aaa cprs_cprs +
+ 		+
+
+
+ 		local env. ref. for abstract candidates of reducibilitylsubc ( ? ⊑[?] ? )lsubc_ldrop lsubc_ldrops lsubc_lsuba +
+ 		+
+
+
+ 		support for abstract computation propertiesacpacp_cr ( ⦃?,?⦄ ϵ[?] 〚?〛 )acp_aaa +
+
reductioncontext-sensitive extended reductionlpx ( ⦃?,?⦄ ⊢ ➡[?] ? )lpx_ldrop lpx_aaa +
+ 		+
+
+
+ 		+
+ 		cpx ( ⦃?,?⦄ ⊢ ? ➡[?] ? )cpx_lift +
+ 		+
+
+
+ 		context-sensitive normal formscnf ( ? ⊢ 𝐍⦃?⦄ )cnf_liftt cnf_crf cnf_cif +
+ 		+
+
+
+ 		context-sensitive reductionlpr ( ? ⊢ ➡ ? )lpr_ldrop lpr_lpss lpr_lpr +
+ 		+
+
+
+ 		+
+ 		cpr ( ? ⊢ ? ➡ ? )cpr_lift cpr_cif +
+ 		+
+
+
+ 		context-sensitive reducible formscrf ( ? ⊢ 𝐑⦃?⦄ )crf_appendcif ( ? ⊢ 𝐈⦃?⦄ )cif_append
unfoldrestricted parallel computationlpqs ( ? ⊢ ➤* ? )lpqs_ldrop lpqs_cpqs lpqs_lpqs +
+ 		+
+
+
+ 		+
+ 		cpqs ( ? ⊢ ? ➤* ? )cpqs_lift +
+ 		+
+
+
+ 		unfoldunfold ( ? ⊢ ? ⧫* ? ) +
+ 		+
+ 		+
+
+
+ 		iterated stratified static type assignmentsstas ( ⦃?,?⦄ ⊢ ? •*[?] ? )sstas_lift sstas_lpss sstas_aaa sstas_sstas +
+ 		+
+
static typingstratified static type assignmentssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )ssta_lift ssta_lpss ssta_aaa ssta_ssta +
+ 		+
+
+
+ 		local env. ref. for atomic arity assignmentlsuba ( ? ⁝⊑ ? )lsuba_ldrop lsuba_aaa lsuba_lsuba +
+ 		+
+
+
+ 		atomic arity assignmentaaa ( ? ⊢ ? ⁝ ? )aaa_lift aaa_lifts aaa_lpss aaa_aaa +
+ 		+
+
+
+ 		parametersshsd +
+ 		+
+
substitutionparallel substitutionlpss ( ? ⊢ ▶* ? )lpss_ldrop lpss_cpss lpss_lpss +
+ 		+
+
+
+ 		+
+ 		cpss ( ? ⊢ ? ▶* ? )cpss_lift +
+ 		+
+
+
+ 		local env. ref. for substitutionlsubr ( ? ⊑ ? )lsubr_lsubr +
+ 		+
+
+
+ 		iterated structural successor for closuresfsups ( ⦃?,?⦄ ⊃* ⦃?,?⦄ )fsups_fsups +
+ 		+
+
+
+ 		+
+ 		fsupp ( ⦃?,?⦄ ⊃+ ⦃?,?⦄ )fsupp_fsupp +
+ 		+
+
+
+ 		generic local env. slicingldrops ( ⇩*[?] ? ≡ ? )ldrops_ldrop ldrops_ldrops +
+ 		+
+
+
+ 		generic term relocationlifts_vector ( ⇧*[?] ? ≡ ? )lifts_lift_vector +
+ 		+
+
+
+ 		+
+ 		lifts ( ⇧*[?] ? ≡ ? )lifts_lift lifts_lifts +
+ 		+
+
+
+ 		support for generic relocationgr2 ( @⦃?,?⦄ ≡ ? )gr2_plus ( ? + ? )gr2_minus ( ? ▭ ? ≡ ? )gr2_gr2
relocationstructural successor for closuresfsup ( ⦃?,?⦄ ⊃ ⦃?,?⦄ )fsupq ( ⦃?,?⦄ ⊃⸮ ⦃?,?⦄ ) +
+ 		+
+
+
+ 		global env. slicinggdrop ( ⇩[?] ? ≡ ? )gdrop_gdrop +
+ 		+
+
+
+ 		basic local env. slicingldrop ( ⇩[?,?] ? ≡ ? )ldrop_append ldrop_lpx_sn ldrop_ldrop +
+ 		+
+
+
+ 		basic term relocationlift_vector ( ⇧[?,?] ? ≡ ? )lift_lift_vector +
+ 		+
+
+
+ 		+
+ 		lift ( ⇧[?,?] ? ≡ ? )lift_lift +
+ 		+
+
grammarpointwise extension of a relationlpx_snlpx_sn_tc lpx_sn_lpx_sn +
+ 		+
+
+
+ 		same top term constructortstc ( ? ≃ ? )tstc_tstc tstc_vector +
+ 		+
+
+
+ 		closurescl_shift ( ? @@ ? )cl_weight ( ♯{?,?} ) +
+ 		+
+
+
+ 		internal syntaxgenv +
+ 		+
+ 		+
+
+
+ 		+
+ 		lenvlenv_weight ( ♯{?} )lenv_length ( |?| )lenv_append ( ? @@ ? )
+
+ 		+
+ 		termterm_weight ( ♯{?} )term_simple ( 𝐒⦃?⦄ )term_vector
+
+ 		+
+ 		item +
+ 		+
+ 		+
+
+
+ 		external syntaxaarity +
+ 		+
+ 		+
+
+
-
Physical Structure of the Specification
-
The source files are grouped in directories, +
Physical Structure of the Specification
+
The source files are grouped in directories, one for each component.
-
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+
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Last update: Sat, 08 Jun 2013 22:22:33 +0200