[lambdadelta home]
cic:/matita/lambdadelta/basic_2/ (λδ version 2)
[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].
category objects




sizes files 360 characters 646465 nodes 1812003
propositions theorems 117 lemmas 1283 total 1400
concepts declared 54 defined 81 total 135
Logical Structure of the Specification
The source files are grouped in planes and components according to the following table. 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).
component plane files


dynamic typing local env. ref. for stratified native validity lsubsv ( ? ⊢ ? ¡⫃[?,?] ? ) lsubsv_ldrop lsubsv_lsubd lsubsv_lsuba lsubsv_lsstas lsubsv_cpds lsubsv_cpcs lsubsv_snv


stratified native validity snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] ) snv_lift snv_da_lpr snv_aaa snv_lsstas snv_lsstas_lpr snv_lpr snv_cpcs

equivalence decomposed extended equivalence cpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?] ? ) cpes_cpds


context-sensitive equivalence cpcs ( ⦃?,?⦄ ⊢ ? ⬌* ? ) cpcs_aaa cpcs_cprs cpcs_cpcs

conversion context-sensitive conversion cpc ( ⦃?,?⦄ ⊢ ? ⬌ ? ) cpc_cpc

computation evaluation for context-sensitive extended reduction cpxe ( ⦃?,?⦄ ⊢ ➡*[?,?] 𝐍⦃?⦄ )



evaluation for context-sensitive reduction cpre ( ⦃?,?⦄ ⊢ ➡* 𝐍⦃?⦄ ) cpre_cpre


strongly normalizing "big tree" computation fsb ( ⦃?,?⦄ ⊢ ⦥[?,?] ? ) fsb_alt ( ⦃?,?⦄ ⊢ ⦥⦥[?,?] ? ) fsb_aaa fsb_csx

strongly normalizing extended computation lcosx ( ? ⊢ ~⬊*[?,?,?] ? ) lcosx_cpx



lsx ( ? ⊢ ⬊*[?,?,?,?] ? ) lsx_alt ( ? ⊢ ⬊⬊*[?,?,?,?] ? ) lsx_ldrop lsx_lpx lsx_lpxs llsx_csx


csx_vector ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? ) csx_tstc_vector csx_aaa



csx ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? ) csx_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? ) csx_lift csx_lleq csx_lpx csx_lpxs csx_fpbs

"big tree" parallel computation fpbg ( ⦃?,?,?⦄ >⋕[?,?] ⦃?,?,?⦄ ) fpbg_lift fpbg_fleq fpbg_fpbg



fpbc ( ⦃?,?,?⦄ ≻⋕[?,?] ⦃?,?,?⦄ ) fpbc_fleq fpbc_fpbs



fpbu ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ ) fpbu_lift fpbu_lleq fpbu_fleq


fpbs ( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ ) fpbs_alt ( ⦃?,?,?⦄ ≥≥[?,?] ⦃?,?,?⦄ ) fpbs_lift fpbs_fleq fpbs_aaa fpbs_fpbs fpbs_ext

decomposed extended computation cpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?] ? ) cpds_lift cpds_aaa cpds_cpds


context-sensitive extended computation lpxs ( ⦃?,?⦄ ⊢ ➡*[?,?] ? ) lpxs_ldrop lpxs_lleq lpxs_aaa lpxs_cpxs lpxs_lpxs



cpxs ( ⦃?,?⦄ ⊢ ? ➡*[?,?] ? ) cpxs_tstc cpxs_tstc_vector cpxs_leq cpxs_lift cpxs_lleq cpxs_aaa cpxs_cpxs


context-sensitive computation lprs ( ⦃?,?⦄ ⊢ ➡* ? ) lprs_ldrop lprs_cprs lprs_lprs



cprs ( ⦃?,?⦄ ⊢ ? ➡* ?) cprs_lift cprs_cprs


local env. ref. for abstract candidates of reducibility lsubc ( ? ⊢ ? ⫃[?] ? ) lsubc_ldrop lsubc_ldrops lsubc_lsuba


support for abstract computation properties acp acp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 ) acp_aaa
reduction "big tree" parallel reduction fpb ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ ) fpb_lift fpb_aaa


normal forms for context-sensitive extended reduction cnx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐍⦃?⦄ ) cnx_lift cnx_crx cnx_cix


context-sensitive extended reduction lpx ( ⦃?,?⦄ ⊢ ➡[?,?] ? ) lpx_ldrop lpx_frees lpx_lleq lpx_aaa


cpx ( ⦃?,?⦄ ⊢ ? ➡[?,?] ? ) cpx_leq cpx_lift cpx_llpx_sn cpx_lleq cpx_cix


irreducible forms for context-sensitive extended reduction cix ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐈⦃?⦄ ) cix_lift


reducible forms for context-sensitive extended reduction crx ( ⦃?,?⦄ ⊢ ➡[?,?] 𝐑⦃?⦄ ) crx_lift


normal forms for context-sensitive reduction cnr ( ⦃?,?⦄ ⊢ ➡ 𝐍⦃?⦄ ) cnr_lift cnr_crr cnr_cir


context-sensitive reduction lpr ( ⦃?,?⦄ ⊢ ➡ ? ) lpr_ldrop lpr_lpr



cpr ( ⦃?,?⦄ ⊢ ? ➡ ? ) cpr_lift cpr_llpx_sn cpr_cir


irreducible forms for context-sensitive reduction cir ( ⦃?,?⦄ ⊢ ➡ 𝐈⦃?⦄ ) cir_lift


reducible forms for context-sensitive reduction crr ( ⦃?,?⦄ ⊢ ➡ 𝐑⦃?⦄ ) crr_lift

unfold unfold unfold ( ⦃?,?⦄ ⊢ ? ⧫* ? )



iterated static type assignment lsstas ( ⦃?,?⦄ ⊢ ? •*[?,?,?] ? ) lsstas_alt ( ⦃?,?⦄ ⊢ ? ••*[?,?,?] ? ) lsstas_lift lsstas_aaa lsstas_lsstas
static typing local env. ref. for atomic arity assignment lsuba ( ? ⊢ ? ⁝⫃ ? ) lsuba_ldrop lsuba_aaa lsuba_lsuba


atomic arity assignment aaa ( ⦃?,?⦄ ⊢ ? ⁝ ? ) aaa_lift aaa_lifts aaa_fqus aaa_lleq aaa_da aaa_ssta aaa_aaa


stratified static type assignment ssta ( ⦃?,?⦄ ⊢ ? •[?,?] ? ) ssta_lift ssta_lpx_sn ssta_ssta


local env. ref. for degree assignment lsubd ( ? ⊢ ? ▪⫃ ? ) lsubd_da lsubd_lsubd


degree assignment da ( ⦃?,?⦄ ⊢ ? ▪[?,?] ? ) da_lift da_da


parameters sh sd


restricted local env. ref. lsubr ( ? ⫃ ? ) lsubr_lsubr

multiple substitution lazy equivalence fleq ( ⦃?,?,?⦄ ⋕[?] ⦃?,?,?⦄ ) fleq_fleq



lleq ( ? ⋕[?,?] ? ) lleq_alt lleq_alt_rec lleq_leq lleq_ldrop lleq_fqus lleq_llor lleq_lleq


lazy pointwise extension of a relation llpx_sn llpx_sn_alt llpx_sn_alt_rec llpx_sn_tc llpx_sn_leq llpx_sn_ldrop llpx_sn_lpx_sn llpx_sn_frees llpx_sn_llor


pointwise union for local environments llor ( ? ⩖[?,?] ? ≡ ? ) llor_alt llor_ldrop


context-sensitive exclusion from free variables frees ( ? ⊢ ? ϵ 𝐅*[?]⦃?⦄ ) frees_append frees_leq frees_lift


contxt-sensitive extended multiple substitution cpys ( ⦃?,?⦄ ⊢ ? ▶*[?,?] ? ) cpys_alt ( ⦃?,?⦄ ⊢ ? ▶▶*[?,?] ? ) cpys_lift cpys_cpys

iterated structural successor for closures fqus ( ⦃?,?,?⦄ ⊐* ⦃?,?,?⦄ ) fqus_alt fqus_fqus



fqup ( ⦃?,?,?⦄ ⊐+ ⦃?,?,?⦄ ) fqup_fqup


iterated local env. slicing ldrops ( ⇩*[?,?] ? ≡ ? ) ldrops_ldrop ldrops_ldrops


generic term relocation lifts_vector ( ⇧*[?] ? ≡ ? ) lifts_lift_vector



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


support for generic relocation gr2 ( @⦃?,?⦄ ≡ ? ) gr2_plus ( ? + ? ) gr2_minus ( ? ▭ ? ≡ ? ) gr2_gr2
substitution structural successor for closures fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ ) fquq_alt ( ⦃?,?,?⦄ ⊐⊐⸮ ⦃?,?,?⦄ )



fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )



global env. slicing gget ( ⇩[?] ? ≡ ? ) gget_gget


contxt-sensitive extended ordinary substitution cpy ( ⦃?,?⦄ ⊢ ? ▶[?,?] ? ) cpy_lift cpy_nlift cpy_cpy


local env. ref. for extended substitution lsuby ( ? ⊑×[?,?] ? ) lsuby_lsuby


pointwise extension of a relation lpx_sn lpx_sn_alt lpx_sn_tc lpx_sn_ldrop lpx_sn_lpx_sn


basic local env. slicing ldrop ( ⇩[?,?,?] ? ≡ ? ) ldrop_append ldrop_leq ldrop_ldrop


basic term relocation lift_vector ( ⇧[?,?] ? ≡ ? ) lift_lift_vector



lift ( ⇧[?,?] ? ≡ ? ) lift_neq lift_lift

grammar equivalence for local environments leq ( ? ≃[?,?] ? ) leq_leq


same top term constructor tstc ( ? ≃ ? ) tstc_tstc tstc_vector


closures cl_weight ( ♯{?,?,?} ) cl_restricted_weight ( ♯{?,?} )


internal syntax genv




lenv lenv_weight ( ♯{?} ) lenv_length ( |?| ) lenv_append ( ? @@ ? )


term term_weight ( ♯{?} ) term_simple ( 𝐒⦃?⦄ ) term_vector


item



external syntax aarity


Physical Structure of the Specification
The source files are grouped in directories, one for each component.
[Spacer]

[Valid XHTML 1.1] [Valid CSS level 2] [Generated from XML via XSL] [PNG used here] [Viewable with any browser]

Last update: Mon, 09 Jun 2014 22:16:19 +0200