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cic:/matita/lambda_delta/basic_2/ (λδ version 2)
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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.
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.
Summary of the Specification
Here is a numerical acount of the specification's contents and its timeline.
categoryobjects




sizesfiles204bytes742579

propositionstheorems74lemmas889total963
conceptsdeclared40defined73total113
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).
componentplanefiles



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


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



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


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



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


computationextended computationxprs ( ⦃?,?⦄ ⊢ ? ➸*[?] ? )xprs_lift xprs_aaa xprs_cprs



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_cprs 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

reducibilityextended reductionxpr ( ⦃?,?⦄ ⊢ ? ➸[?] ? )xpr_lift xpr_aaa



context-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


unwind



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



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 ( ≽[?,?] ? )


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



Physical Structure of the Specification
The source files are grouped in directories, one for each component.
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Last update: 2012-10-18T16:59:43+02:00