X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fwww%2Flambdadelta%2Fbasic_2.html;h=b0891996f5b4d39903a43e15d6654452a0ad9efc;hb=9b75ad80a3ee31314c02f113b255ad533a87d3d2;hp=3955a057459b0ef7f4c297e492f4c705c749a301;hpb=add1600e1ceef0f1c7e07a4d13c60edd7a3ea367;p=helm.git diff --git a/helm/www/lambdadelta/basic_2.html b/helm/www/lambdadelta/basic_2.html index 3955a0574..b0891996f 100644 --- a/helm/www/lambdadelta/basic_2.html +++ b/helm/www/lambdadelta/basic_2.html @@ -1,88 +1,1308 @@ - + - - - - - - lambdadelta version 2 - - - - + + + + + + \lambda\delta version 2 + + + + -
[lambdadelta home]
cic:/matita/lambdadelta/basic_2/ (λδ version 2)
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System's Syntax and Behavior
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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

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
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* In terms only. - ** In terms and local environments only. - *** In global environments only. - **** Sort level k in terms only. -
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Summary of the Specification
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Here is a numerical acount of the specification's contents + +
+ + [lambdadelta home] + +
+
cic:/matita/lambdadelta/basic_2/ (λδ version 2)
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+ [Spacer] +
+ + +
Summary of the Specification
+
Here is a numerical acount 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




sizesfiles252characters483454nodes1296744
propositionstheorems85lemmas1119total1204
conceptsdeclared46defined82total128
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Logical Structure of the Specification
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The source files are grouped in planes and components +
Logical Structure of the Specification
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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). + Notation files covering the whole specification are provided. + The notation for the relations or functions introduced in each file + is shown in parentheses (? are placeholders).
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componentplanefiles



dynamic typinglocal env. ref. for stratified native validitylsubsv ( ? ⊢ ? ⊩:⊑[?] ? )lsubsv_ldroplsubsv_snv


stratified native validitysnv ( ⦃?,?⦄ ⊩ ? :[?] )snv_lift snv_ltpss_dx snv_ltpss_sn snv_aaa snv_ssta snv_sstas snv_ssta_ltpr snv_ltpr snv_cpcs


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_dx cpcs_ltpss_sn cpcs_delift cpcs_aaa cpcs_ltpr cpcs_cprs cpcs_cpcs


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




fpc ( ⦃?,?⦄ ⬌ ⦃?,?⦄ )fpc_fpc



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


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




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



"big tree" parallel computationyprs ( ? ⊢ ⦃?,?⦄ ≥[g] ⦃?,?⦄ )yprs_yprsygt ( ? ⊢ ⦃?,?⦄ >[g] ⦃?,?⦄ )ygt_ygt

decomposed extended computationdxprs ( ⦃?,?⦄ ⊢ ? •*➡*[?] ? )dxprs_lift dxprs_ltpss_dx dxprs_ltpss_sn 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


context-sensitive computationcprs (? ⊢ ? ➡* ?)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-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



"big tree" parallel reductionypr ( ? ⊢ ⦃?,?⦄ ≽[g] ⦃?,?⦄ )ysc ( ? ⊢ ⦃?,?⦄ ≻[g] ⦃?,?⦄ )



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



context-sensitive reductioncpr ( ? ⊢ ? ➡ ? )cpr_lift cpr_tpss cpr_ltpss_dx cpr_ltpss_sn 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



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componentplanefiles +
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examplesterms with special featuresex_sta_ldec ex_cpr_omega ex_fpbg_refl +
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dynamic typinglocal env. ref. for stratified native validitylsubsv ( ? ⊢ ? ⫃¡[?,?] ? )lsubsv_lsuba lsubsv_lsubd lsubsv_lstas lsubsv_scpds lsubsv_cpcs lsubsv_snv +
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stratified native validityshnv ( ⦃?,?⦄ ⊢ ? ¡[?,?,?] ) +
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snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] )snv_lift snv_aaa snv_da_lpr snv_lstas snv_lstas_lpr snv_lpr snv_scpes snv_preserve +
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equivalencedecomposed rt-equivalencescpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?,?,?] ? )scpes_aaa scpes_cpcs scpes_scpes +
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context-sensitive equivalencecpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? )cpcs_aaa cpcs_cprs cpcs_cpcs +
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conversioncontext-sensitive conversioncpc ( ⦃?,?⦄ ⊢ ? ⬌ ? )cpc_cpc +
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computationevaluation for context-sensitive rt-reductioncpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ ) +
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evaluation for context-sensitive reductioncpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ )cpre_cpre +
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strongly normalizing qrst-computationfsb ( ⦃?,?⦄ ⊢ ⦥[?,?] ? )fsb_alt ( ⦃?,?⦄ ⊢ ⦥⦥[?,?] ? )fsb_aaa fsb_csx +
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strongly normalizing rt-computationlcosx ( ? ⊢ ~⬊*[?,?,?] ? )lcosx_cpx +
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lsx ( ? ⊢ ⬊*[?,?,?,?] ? )lsx_alt ( ? ⊢ ⬊⬊*[?,?,?,?] ? )lsx_drop lsx_lpx lsx_lpxs llsx_csx +
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csx_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )csx_tsts_vector csx_aaa +
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csx ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )csx_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )csx_lift csx_lleq csx_lpx csx_lpxs csx_fpbs +
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parallel qrst-computationfpbg ( ⦃?,?,?⦄ >≡[?,?] ⦃?,?,?⦄ )fpbg_lift fpbg_fleq fpbg_fpbs fpbg_fpbg +
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fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ )fpbs_lift fpbs_aaa fpbs_fpb fpbs_fpbs +
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decomposed rt-computationscpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?,?] ? )scpds_lift scpds_aaa scpds_scpds +
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context-sensitive rt-computationlpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? )lpxs_drop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs +
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cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? )cpxs_tsts cpxs_tsts_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs +
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context-sensitive computationlprs ( ⦃?,?⦄ ⊢ ➡* ? )lprs_drop lprs_cprs lprs_lprs +
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cprs ( ⦃?,?⦄ ⊢ ? ➡* ?)cprs_lift cprs_cprs +
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local env. ref. for generic reducibilitylsubc ( ? ⊢ ? ⫃[?] ? )lsubc_drop lsubc_drops lsubc_lsuba +
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support for generic computation propertiesgcpgcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 )gcp_aaa +
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reductionparallel qrst-reductionfpbq ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )fpbq_alt ( ⦃?,?,?⦄ ≽≽[?,?] ⦃?,?,?⦄ )fpbq_lift fpbq_aaa +
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fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )fpb_lift fpb_lleq fpb_fleq +
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normal forms for context-sensitive rt-reductioncnx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐍⦃?⦄ )cnx_lift cnx_crx cnx_cix +
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context-sensitive rt-reductionlpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? )lpx_drop lpx_frees lpx_lleq lpx_aaa +
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cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? )cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix +
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irreducible forms for context-sensitive rt-reductioncix ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐈⦃?⦄ )cix_lift +
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reducible forms for context-sensitive rt-reductioncrx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐑⦃?⦄ )crx_lift +
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normal forms for context-sensitive reductioncnr ( ⦃?,?⦄ ⊢ ➡ 𝐍⦃?⦄ )cnr_lift cnr_crr cnr_cir +
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context-sensitive reductionlpr ( ⦃?,?⦄ ⊢ ➡ ? )lpr_drop lpr_lpr +
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cpr ( ⦃?,?⦄ ⊢ ? ➡ ? )cpr_lift cpr_llpx_sn cpr_cir +
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irreducible forms for context-sensitive reductioncir ( ⦃?,?⦄ ⊢ ➡ 𝐈⦃?⦄ )cir_lift +
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reducible forms for context-sensitive reductioncrr ( ⦃?,?⦄ ⊢ ➡ 𝐑⦃?⦄ )crr_lift +
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unfoldunfoldunfold ( ⦃?,?⦄ ⊢ ? ⧫* ? ) +
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iterated static type assignmentlstas ( ⦃?,?⦄ ⊢ ? •*[?,?] ? )lstas_lift lstas_llpx_sn.ma lstas_aaa lstas_da lstas_lstas +
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static typinglocal env. ref. for degree assignmentlsubd ( ? ⊢ ? ⫃▪[?,?] ? )lsubd_da lsubd_lsubd +
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degree assignmentda ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? )da_lift da_aaa da_da +
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parametersshsd +
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local env. ref. for atomic arity assignmentlsuba ( ? ⊢ ? ⫃⁝ ? )lsuba_aaa lsuba_lsuba +
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atomic arity assignmentaaa ( ⦃?,?⦄ ⊢ ? ⁝ ? )aaa_lift aaa_lifts aaa_fqus aaa_lleq aaa_aaa +
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restricted local env. ref.lsubr ( ? ⫃ ? )lsubr_lsubr +
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multiple substitutionlazy equivalencefleq ( ⦃?,?,?⦄ ≡[?] ⦃?,?,?⦄ )fleq_fleq +
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lleq ( ? ≡[?,?] ? )lleq_alt lleq_alt_rec lleq_leq lleq_drop lleq_fqus lleq_llor lleq_lleq +
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lazy pointwise extension of a relationllpx_snllpx_sn_alt llpx_sn_alt_rec llpx_sn_tc llpx_sn_leq llpx_sn_drop llpx_sn_lpx_sn llpx_sn_frees llpx_sn_llor +
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pointwise union for local environmentsllor ( ? ⋓[?,?] ? ≡ ? )llor_alt llor_drop +
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context-sensitive exclusion from free variablesfrees ( ? ⊢ ? ϵ 𝐅*[?]⦃?⦄ )frees_append frees_leq frees_lift +
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contxt-sensitive multiple rt-substitutioncpys ( ⦃?,?⦄ ⊢ ? ▶*[?,?] ? )cpys_alt ( ⦃?,?⦄ ⊢ ? ▶▶*[?,?] ? )cpys_lift cpys_cpys +
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iterated structural successor for closuresfqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ )fqus_alt fqus_fqus +
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fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ )fqup_fqup +
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iterated local env. slicingdrops ( ⬇*[?,?] ? ≡ ? )drops_drop drops_drops +
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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 multiple relocationmr2 ( @⦃?,?⦄ ≡ ? )mr2_plus ( ? + ? )mr2_minus ( ? ▭ ? ≡ ? )mr2_mr2
substitutionstructural successor for closuresfquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ )fquq_alt ( ⦃?,?,?⦄ ⊐⊐⸮ ⦃?,?,?⦄ ) +
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fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ ) +
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global env. slicinggget ( ⬇[?] ? ≡ ? )gget_gget +
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contxt-sensitive ordinary rt-substitutioncpy ( ⦃?,?⦄ ⊢ ? ▶[?,?] ? )cpy_lift cpy_nlift cpy_cpy +
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local env. ref. for rt-substitutionlsuby ( ? ⊆[?,?] ? )lsuby_lsuby +
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pointwise extension of a relationlpx_snlpx_sn_alt lpx_sn_tc lpx_sn_drop lpx_sn_lpx_sn +
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basic local env. slicingdrop ( ⬇[?,?,?] ? ≡ ? )drop_append drop_leq drop_drop +
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basic term relocationlift_vector ( ⬆[?,?] ? ≡ ? )lift_lift_vector +
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lift ( ⬆[?,?] ? ≡ ? )lift_neq lift_lift +
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grammarequivalence for local environmentsleq ( ? ⩬[?,?] ? )leq_leq +
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same top term structuretsts ( ? ≂ ? )tsts_tsts tsts_vector +
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closurescl_weight ( ♯{?,?,?} )cl_restricted_weight ( ♯{?,?} ) +
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internal syntaxgenv +
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lenvlenv_weight ( ♯{?} )lenv_length ( |?| )lenv_append ( ? @@ ? )
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termterm_weight ( ♯{?} )term_simple ( 𝐒⦃?⦄ )term_vector ( Ⓐ?.? )
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item +
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external syntaxaarity +
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Physical Structure of the Specification
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The source files are grouped in directories, +
Physical Structure of the Specification
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The source files are grouped in directories, one for each component.
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Last update: 2013-03-09T23:27:52+01:00
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Last update: Sun, 05 Oct 2014 16:38:32 +0200