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cic:/matita/lambdadelta/basic_2/ (λδ version 2)
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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 358 characters 430633 nodes 1858385
propositions theorems 130 lemmas 1283 total 1413
concepts declared 54 defined 89 total 143
Stage "B"
Stage "A": "Weakening the Applicability Condition"
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


examples terms with special features ex_sta_ldec ex_cpr_omega ex_fpbg_refl





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


stratified native validity shnv ( ⦃?,?⦄ ⊢ ? ¡[?,?,?] )




snv ( ⦃?,?⦄ ⊢ ? ¡[?,?] ) snv_lift snv_aaa snv_da_lpr snv_lstas snv_lstas_lpr snv_lpr snv_scpes snv_preserve

equivalence decomposed rt-equivalence scpes ( ⦃?,?⦄ ⊢ ? •*⬌*[?,?,?,?] ? ) scpes_aaa scpes_cpcs scpes_scpes


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

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

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



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


strongly normalizing qrst-computation fsb ( ⦃?,?⦄ ⊢ ⦥[?,?] ? ) fsb_alt ( ⦃?,?⦄ ⊢ ⦥⦥[?,?] ? ) fsb_aaa fsb_csx

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



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


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



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

parallel qrst-computation fpbg ( ⦃?,?,?⦄ >≡[?,?] ⦃?,?,?⦄ ) fpbg_lift fpbg_fleq fpbg_fpbs fpbg_fpbg



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

decomposed rt-computation scpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?,?] ? ) scpds_lift scpds_aaa scpds_scpds


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



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


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



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


local env. ref. for generic reducibility lsubc ( ? ⊢ ? ⫃[?] ? ) lsubc_drop lsubc_drops lsubc_lsuba


support for generic computation properties gcp gcp_cr ( ⦃?,?,?⦄ ϵ[?] 〚?〛 ) gcp_aaa
reduction parallel qrst-reduction fpbq ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ ) fpbq_alt ( ⦃?,?,?⦄ ≽≽[?,?] ⦃?,?,?⦄ ) fpbq_lift fpbq_aaa


fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ ) fpb_lift fpb_lleq fpb_fleq


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


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



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


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


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


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


context-sensitive reduction lpr ( ⦃?,?⦄ ⊢ ➡ ? ) lpr_drop 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 lstas ( ⦃?,?⦄ ⊢ ? •*[?,?] ? ) lstas_lift lstas_llpx_sn.ma lstas_aaa lstas_da lstas_lstas

static typing local env. ref. for degree assignment lsubd ( ? ⊢ ? ⫃▪[?,?] ? ) lsubd_da lsubd_lsubd


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


parameters sh sd


local env. ref. for atomic arity assignment lsuba ( ? ⊢ ? ⫃⁝ ? ) lsuba_aaa lsuba_lsuba


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


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

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



lleq ( ? ≡[?,?] ? ) lleq_alt lleq_alt_rec lleq_leq lleq_drop 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_drop llpx_sn_lpx_sn llpx_sn_frees llpx_sn_llor


pointwise union for local environments llor ( ? ⋓[?,?] ? ≡ ? ) llor_alt llor_drop


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


contxt-sensitive multiple rt-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 drops ( ⬇*[?,?] ? ≡ ? ) drops_drop drops_drops


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



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


support for multiple relocation mr2 ( @⦃?,?⦄ ≡ ? ) mr2_plus ( ? + ? ) mr2_minus ( ? ▭ ? ≡ ? ) mr2_mr2
substitution structural successor for closures fquq ( ⦃?,?,?⦄ ⊐⸮ ⦃?,?,?⦄ ) fquq_alt ( ⦃?,?,?⦄ ⊐⊐⸮ ⦃?,?,?⦄ )



fqu ( ⦃?,?,?⦄ ⊐ ⦃?,?,?⦄ )



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


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


local env. ref. for rt-substitution lsuby ( ? ⊆[?,?] ? ) lsuby_lsuby


pointwise extension of a relation lpx_sn lpx_sn_alt lpx_sn_tc lpx_sn_drop lpx_sn_lpx_sn


basic local env. slicing drop ( ⬇[?,?,?] ? ≡ ? ) drop_append drop_leq drop_drop


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



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

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


same top term structure tsts ( ? ≂ ? ) tsts_tsts tsts_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.
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Last update: Sun, 05 Oct 2014 16:38:32 +0200