X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fwww%2Flambdadelta%2Fbasic_2.html;h=5ae7da3063e1448a8bed8e391e332259463afc03;hb=f7d7f2459b3b0409be5f168822be3b836ccc929b;hp=6a7c568b1a67d5159a097a7174bf07fc6d1e82e5;hpb=816f8da9c917e86d4de69fe5ae9853ec427f2b57;p=helm.git diff --git a/helm/www/lambdadelta/basic_2.html b/helm/www/lambdadelta/basic_2.html index 6a7c568b1..5ae7da306 100644 --- a/helm/www/lambdadelta/basic_2.html +++ b/helm/www/lambdadelta/basic_2.html @@ -6,8 +6,8 @@ - - lambdadelta version 2 + + \lambda\delta home page @@ -19,1112 +19,649 @@ [lambdadelta home] -
cic:/matita/lambdadelta/basic_2/ (λδ version 2)
+
cic:/matita/lambdadelta/basic_2/ (core λδ version 2)
[Spacer]
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System's Syntax and Behavior
-
This is a summary of the "block structure" - of the System's syntactic items and reductions. -
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domainblockleaderapplicator (with →θ)*reduction→ζ *reference *
{X | Γ ⊢ X : W}local typed abstraction *Γ ⊢ +λWⓐV→βno#i
+ + home + + news + + specification +
local typed declaration **Γ ⊢ -λWⓐV→βno#i
+
global typed declaration ***Γ ⊢ pλWnonono$p
+ + documentation + + implementation +
native type annotation *Γ ⊢ ⓝWnonoyesno
{X | Γ ⊢ X = V}local abbreviation *Γ ⊢ +δVnolocal →δyes#i
+ + foreword + + milestones + + version 2 + (background - core - applications)
local definition **Γ ⊢ -δVnolocal →δno#i + version 2 + + library + (static LDDL directory)
+ + citations + + visibility + + version 1 + (background - core)(static HELM directory) + version 1 + + helena +
global definition ***Γ ⊢ pδVnoglobal →δno$p
nosort ****Γ ⊢ ⋆knononono
-
* In terms only. + +
Summary of the Specification [spacer] +
+
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].
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categoryobjects + categoryobjects
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sizesfiles268 characters402310nodes1205044sizesfiles102characters69295nodes245853
propositionstheorems82lemmas815total897propositionstheorems34lemmas256total290
conceptsdeclared44defined81total125conceptsdeclared21defined29total50
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    +
    Stage "B"
    +
    • - In progress. + Ongoing. Context-sensitive subject equivalence for native type assignment.
    -
      +
      Stage "A2": "Extending the Applicability Condition"
      +
        +
      • + 2015 October 9. + λδ version 2A2 is started. +
      • +
      +
      Stage "A1": "Extending the Applicability Condition"
      +
      • - In progress. - Closure of context-sensitive extended computation - for native validity. + 2015 August 27. + λδ version 2A1 appears too complex and is dismissed.
      -
        +
        • - 2013 August 7. + 2014 October 28. + λδ version 2A1 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. +
        • +
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          +
        • + 2014 June 9. + Strong qrst-normalization + for simply typed terms. +
        • +
        +
          +
        • + 2014 April 16. + Lazy equivalence on local environments + added as q-step to rst-computation on closures + (anniversary milestone). +
        • +
        +
          +
        • + 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. 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.
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              • - 2013 April 16. + 2013 April 16. Reaxiomatized substitution and reduction commute with respect to subclosure (anniversary milestone).
              -
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                • - 2013 March 16. + 2013 March 16. Mutual recursive preservation of stratified native validity - for hyper 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. - Term binders polarized to control ζ-reduction. + 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.
                        -
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                          • - 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.
                            -
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                              • - 2011 September 6. + 2011 September 6. Confluence for context-free parallel reduction on terms.
                              -
                                +
                                • - 2011 April 17. - Specification starts. + 2011 April 17. + λδ version 2 is started.
                                - -
                                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). +
                                Logical Structure of the Specification [spacer] +
                                +
                                This table reports the specification's components and their planes.
                                -
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                                - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + - - - - - - - - - - + + + + - - - - - - + + + - - - - - - + + + - - - - - - + + + - - + - - - - - - - - - - - - - - + + + + - - - - - - - - - - - - - - + + - - - - - - - - - - - + + + - - - - - - - - - - - - - + + - - - - - - + + + - - - - - - - - - - - - - - + + - - - + + + - - - - - - - - - + + + - - - - - - + + + + - - - - - - + + + - - - - - - + + + - - - - - - + + + - - - - - - + + - - - - - - - - - - - - - - - + + + - - - - - - + + + + - - - - - - + - - - - - - - - - - - - - - + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                                componentplanefiles -
                                -
                                -
                                -
                                -
                                -
                                dynamic typinglocal env. ref. for stratified native validitylsubsv ( ? ⊢ ? ¡⊑[?,?] ? )lsubsv_ldrop lsubsv_lsubd lsubsv_lsuba lsubsv_lsstas lsubsv_cpds lsubsv_cpcs lsubsv_snv -
                                -
                                -
                                -
                                -
                                -
                                stratified native validitysnv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )snv_lift snv_da_lpr snv_aaa snv_lsstas snv_lsstas_lpr snv_lpr snv_cpcs -
                                -
                                -
                                -
                                equivalencedecomposed extended equivalencecpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?] ? )cpes_cpds -
                                -
                                -
                                -
                                + componentplanefiles
                                context-sensitive equivalencecpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )cpcs_aaa cpcs_cprs cpcs_cpcs +
                                +
                                conversioncontext-sensitive conversioncpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )cpc_cpc + static typingparametersshsd
                                +
                                computationcontext-sensitive extended evaluationcpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ ) +
                                + restricted ref. for local env.lsubr ( ? ⫃ ? )lsubr_length lsubr_drops lsubr_lsubr
                                +
                                +
                                context-sensitive evaluationcpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )cpre_cpre + ranged equivalence for closuresfreq ( ⦃?,?,?⦄ ≡ ⦃?,?,?⦄ )freq_freq
                                +
                                +
                                strongly normalizing computationcsx_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )csx_tstc_vector csx_aaa + context-sensitive free variablesfrees ( ? ⊢ 𝐅*⦃?⦄ ≡ ? )frees_weight frees_lreq frees_frees
                                +
                                + s-computation +
                                +
                                csx ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )csx_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )csx_lift csx_lpx +
                                -
                                -
                                "big tree" parallel computationfpbg ( ⦃?,?,?⦄ >[?,?] ⦃?,?,?⦄ )fpbg_lift fpbg_fpbg -
                                -
                                +
                                + s-transitionstructural successor for closuresfquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )fquq_length fquq_weight
                                -
                                -
                                fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )fpbs_lift fpbs_fpbs +
                                -
                                -
                                decomposed extended computationcpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?] ? )cpds_lift cpds_aaa cpds_cpds +
                                +
                                + fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )fqu_length fqu_weight
                                context-sensitive extended computationlpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )lpxs_alt ( ⦃?,?⦄ ⊢ ➡➡*[?,?] ? )lpxs_ldrop lpxs_aaa lpxs_cpxs lpxs_lpxs +
                                -
                                -
                                -
                                -
                                cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )cpxs_tstc cpxs_tstc_vector cpxs_lift cpxs_aaa cpxs_cpxs -
                                -
                                + relocationgeneric slicing for local environmentsdrops_vector ( ⬇*[?,?] ? ≡ ? )
                                +
                                context-sensitive computationlprs ( ⦃?,?⦄ ⊢ ➡* ? )lprs_alt ( ⦃?,?⦄ ⊢ ➡➡* ? )lprs_ldrop lprs_cprs lprs_lprs +
                                +
                                +
                                cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)cprs_lift cprs_cprs + drops ( ⬇*[?,?] ? ≡ ? )drops_lstar drops_weight drops_length drops_ceq drops_lexs drops_lreq drops_drops
                                +
                                +
                                local env. ref. for abstract candidates of reducibilitylsubc ( ? ⊢ ? ⊑[?] ? )lsubc_ldrop lsubc_ldrops lsubc_lsuba + generic relocation for termslifts_vector ( ⬆*[?] ? ≡ ? )lifts_lifts_vector
                                +
                                +
                                support for abstract computation propertiesacpacp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )acp_aaa +
                                reduction"big tree" parallel reductionfpbc ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )fpbc_lift + lifts ( ⬆*[?] ? ≡ ? )lifts_simple lifts_weight lifts_lifts
                                +
                                +
                                + ranged equivalence for local environmentslreq ( ? ≡[?] ? )lreq_length lreq_lreq
                                fpb ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )fpb_lift -
                                -
                                +
                                +
                                context-sensitive extended normal formscnx ( ⦃?,?⦄ ⊢ 𝐍[?,?]⦃?⦄ )cnx_lift cnx_crx cnx_cix + generic entrywise extension of context-sensitive relations for termalexs ( ? ⦻*[?,?,?] ? )lexs_length lexs_lexs
                                +
                                -
                                -
                                context-sensitive extended reductionlpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )lpx_ldrop lpx_aaa + grammarappend for local environmentsappend ( ? @@ ? )append_length
                                +
                                -
                                -
                                +
                                cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )cpx_lift cpx_cix + context-sensitive equivalences for termsceqceq_ceq
                                +
                                +
                                context-sensitive extended irreducible formscix ( ⦃?,?⦄ ⊢ 𝐈[?,?]⦃?⦄ )cix_append cix_lift + same top term structuretsts ( ? ≂ ? )tsts_tsts tsts_vector
                                +
                                +
                                context-sensitive extended reducible formscrx ( ⦃?,?⦄ ⊢ 𝐑[?,?]⦃?⦄ )crx_append crx_lift + closurescl_weight ( ♯{?,?,?} )cl_restricted_weight ( ♯{?,?} )
                                +
                                +
                                context-sensitive normal formscnr ( ⦃?,?⦄ ⊢ 𝐍⦃?⦄ )cnr_lift cnr_crr cnr_cir + internal syntaxgenv
                                +
                                -
                                -
                                context-sensitive reductionlpr ( ⦃?,?⦄ ⊢ ➡ ? )lpr_ldrop lpr_lpr -
                                -
                                +
                                -
                                -
                                +
                                cpr ( ⦃?,?⦄ ⊢ ? ➡ ? )cpr_lift cpr_cir +
                                + lenvlenv_weight ( ♯{?} )lenv_length ( |?| )
                                -
                                -
                                context-sensitive irreducible formscir ( ⦃?,?⦄ ⊢ 𝐈⦃?⦄ )cir_append cir_lift +
                                +
                                termterm_weight ( ♯{?} )term_simple ( 𝐒⦃?⦄ )term_vector ( Ⓐ?.? )
                                +
                                context-sensitive reducible formscrr ( ⦃?,?⦄ ⊢ 𝐑⦃?⦄ )crr_append crr_lift +
                                + item
                                unfoldunfoldunfold ( ⦃?,?⦄ ⊢ ? ⧫* ? ) -
                                -
                                +
                                +
                                +
                                iterated static type assignmentlsstas ( ⦃?,?⦄ ⊢ ? •*[?,?,?] ? )lsstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?,?] ? )lsstas_lift lsstas_aaa lsstas_lsstas + external syntaxaarity
                                static typinglocal env. ref. for atomic arity assignmentlsuba ( ? ⊢ ? ⁝⊑ ? )lsuba_ldrop lsuba_aaa lsuba_lsuba +
                                -
                                -
                                -
                                -
                                atomic arity assignmentaaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )aaa_lift aaa_lifts aaa_da aaa_ssta aaa_aaa -
                                -
                                -
                                -
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                                stratified static type assignmentssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? )ssta_lift ssta_ssta -
                                -
                                -
                                -
                                -
                                -
                                local env. ref. for degree assignmentlsubd ( ? ⊢ ? ▪⊑ ? )lsubd_da lsubd_lsubd -
                                -
                                -
                                -
                                -
                                -
                                degree assignmentda ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )da_lift da_da -
                                -
                                -
                                -
                                -
                                -
                                parametersshsd -
                                -
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                                substitutionrestricted local env. ref.lsubr ( ? ⊑ ? )lsubr_lsubr -
                                -
                                -
                                -
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                                iterated structural successor for closuresfsups ( ⦃?,?,?⦄ ⊃* ⦃?,?,?⦄ )fsups_fsups -
                                -
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                                fsupp ( ⦃?,?,?⦄ ⊃+ ⦃?,?,?⦄ )fsupp_fsupp -
                                -
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                                generic local env. slicingldrops ( ⇩*[?] ? ≡ ? )ldrops_ldrop ldrops_ldrops -
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                                generic term relocationlifts_vector ( ⇧*[?] ? ≡ ? )lifts_lift_vector -
                                -
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                                lifts ( ⇧*[?] ? ≡ ? )lifts_lift lifts_lifts -
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                                -
                                support for generic relocationgr2 ( @⦃?,?⦄ ≡ ? )gr2_plus ( ? + ? )gr2_minus ( ? ▭ ? ≡ ? )gr2_gr2
                                relocationstructural successor for closuresfsup ( ⦃?,?,?⦄ ⊃ ⦃?,?,?⦄ )fsupq ( ⦃?,?,?⦄ ⊃⸮ ⦃?,?,?⦄ )fsupq_alt ( ⦃?,?,?⦄ ⊃⊃⸮ ⦃?,?,?⦄ ) -
                                -
                                -
                                -
                                global env. slicinggdrop ( ⇩[?] ? ≡ ? )gdrop_gdrop -
                                -
                                -
                                -
                                -
                                -
                                basic local env. slicingldrop ( ⇩[?,?] ? ≡ ? )ldrop_append ldrop_lpx_sn ldrop_ldrop -
                                -
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                                -
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                                basic term relocationlift_vector ( ⇧[?,?] ? ≡ ? )lift_lift_vector -
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                                lift ( ⇧[?,?] ? ≡ ? )lift_lift -
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                                grammarpointwise extension of a relationlpx_snlpx_sn_tc lpx_sn_lpx_sn -
                                -
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                                -
                                -
                                same top term constructortstc ( ? ≃ ? )tstc_tstc tstc_vector -
                                -
                                -
                                -
                                -
                                -
                                closurescl_shift ( ? @@ ? )cl_weight ( ♯{?,?,?} ) -
                                -
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                                -
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                                -
                                internal syntaxgenv -
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                                -
                                -
                                -
                                -
                                -
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                                lenvlenv_weight ( ♯{?} )lenv_length ( |?| )lenv_append ( ? @@ ? )
                                -
                                -
                                -
                                -
                                termterm_weight ( ♯{?} )term_simple ( 𝐒⦃?⦄ )term_vector
                                -
                                -
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                                -
                                item -
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                                -
                                -
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                                external syntaxaarity -
                                -
                                -
                                -
                                +
                                - -
                                Physical Structure of the Specification
                                -
                                The source files are grouped in directories, - one for each component. -
                                -
                                +
                                [Spacer]
                                @@ -1150,6 +687,6 @@

                                -
                                Last update: Sun, 06 Oct 2013 17:06:48 +0200
                                - +
                                Last update: Fri, 01 Apr 2016 23:30:53 +0200
                                +