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  • Developments and Contributions

    See the dependency graph of all the contributions in the NASA PVS Library NASA PVS Library 6.0.9 (11/10/14).

    Development Description Contributors
    ACCoRD (web) Framework for the analysis of air traffic conflict detection and resolution algorithms. AN, CM, GD, GH, JM, RB
    algebra Groups, monoids, rings, etc. DL, RB
    analysis Real analysis, limits, continuity, derivatives, integrals. AN, BD, RB
    Bernstein (web) Formalization of multivariate Bernstein polynomials. AN, CM
    complex Complex numbers.DL
    complex_alt Alternative formalization of complex numbers. DL
    complex_integration Complex integration.DL
    co_structures Sequences of countable length defined as coalgebra datatypes.JJ
    digraphs Directed graphs: circuits, maximal subtrees, paths, DAGs. AA, JS, KR, RB
    exact_real_arith Exact real arithmetic including trig functions.DL
    extended_nnreal Extended non-negative reals.DL
    fault_tolerance Fault tolerance protocols. AG, JM, LP, PM
    float Floating point numbers and arithmetic. PM, SB
    graphs Graph theory: connectedness, walks, trees, Menger's Theorem. RB, JS
    groups Group theory.ALG
    ints Integer division, gcd, mod, prime factorization, min, max. AG, BD, PM, RB
    interval_arith (web) Interval arithmetic and numerical approximations. Includes automated strategies numerical for computing numerical approximations and interval for checking satisfiability and validity of simply quantified real-valued formulas. This development includes a formalization of Allen interval temporal logic. AN, CM, DS
    lebesgue Lebesgue integral with connection to Riemann Integral.DL
    linear_algebra Linear algebra.HH, GP, SO
    lnexp Logarithm, exponential and hyperbolic functions. DL, RB
    lnexp_fnd Foundational definitions of logarithm, exponential and hyperbolic functions. AN, DL, RB
    measure_integration Sigma algebras, measures, Fubini-Tonelli Lemmas.DL
    metric_space Domains with a distance metric, continuity and uniform continuity.DL
    numbers Elementary number theory. AG, AN, RB
    orders Abstract orders, lattices, fix points. AG, BD, JJ
    power Generalized Power function (without ln/exp). DL
    probability Probability theory.DL
    reals Summations, sup, inf, sqrt over the reals, absolute value, etc. AN, BDV, CM, PM, RB
    scott Scott topology.DL
    series Power series, comparison test, ratio test, Taylor's theorem. AN, DL, RB
    sets_aux Powersets, orders, cardinality over infinite sets. Includes functional and relational facts based on Axiom of Choice and refinement relations based on equivalence relations. BD, DL, JJ, DS
    sigma_set Summations over countably infinite sets. DL
    structures Bounded arrays, finite sequences, bags, and several other structures. CM, DG, KR, LP, RB
    Sturm (web) Formalization of Sturm's theorem for univariate polynomials. Includes strategies sturm and mono-poly for automatically proving univariate polynomial relations over a real interval. AN, CM, AD
    Tarski (web) Formalization of Tarski's theorem for univariate polynomials. Includes strategy tarski for automatically proving systems of univaraite polynomial relations on the real line. AN, CM, AD
    topology Continuity, homeomorphisms, connected and compact spaces, Borel sets/functions.DL
    trig Trigonometry: definitions, identities, approximations. CM, BDV, DL, GD, HG, RB, VC
    trig_fnd Foundational development of trigonometry. AN, BDV, CM, DL, GD, HG, RB
    TRS Term rewrite systems and Robinson unification algorithm.AA, ALG, AR, MA
    TU_games Cooperative TU-games.EM
    vect_analysis Limits, continuity, and derivatives of vector functions. AN, CM, RB
    vectors 2-D, 3-D, 4-D, and n-dimensional vectors. AN, BDV, CM, HG, PM, RB
    while Semantics for the programming language "while".DL

    Major Theorems in the NASA PVS Library

    Theorem Theory PVS Name Author
    Cauchy-Schwarz Inequality vectors@vectorscauchy_schwartz RB
    Derivative of a Power Series series@power_series_derivpowerseries_deriv RB
    Fundamental Theorem of Arithmetic numbers@unique_factorization Fundamental_Theorem_Arithmetic RB
    Fundamental Theorem of Calculus analysis@fundamental_theorem fundamental RB
    Fundamental Theorem of Interval Arithmetic interval_arith@interval_expr Eval_fundamental CM, AN
    Inclusion Theorem of Interval Arithmetic interval_arith@interval_expr Eval_inclusion CM, AN
    Infinitude of Primes numbers@infinite_primesprimes_infinite RB
    Integral of a Power Series series@power_series_integintegral_powerseries RB
    Intermediate Value Theorem analysis@continuity_intervalintermeditate_value1 BD
    Law of Cosines trig_fnd@law_cosinesLaw_Cosines CM
    Mean Value Theorem analysis@derivative_propsmean_value BD
    Matel's Theorem graphs@mantelMantel AD
    Menger's Theorem graphs@mengerhard_menger JS
    Order of a Subgroup algebra@finite_grouplagrange DL
    Pythagorean Property - Sine and Cosine trig_fnd@trig_basicsin2_cos2 DL
    Ramsey's Theorem graphs@ramseyramseys_theorem NS
    Sum of a Geometric Series series@series geometric_sum RB
    Taylor's Theorem analysis@taylors Taylors RB
    Trig Identities: Sum and Diff of Two Angles trig_fnd@trig_basic sin_plus, ... DL
    Trig Identities: Double Angle Formulas trig_fnd@rig_basic sin2a, cos2s DL
    Schroeder-Berstein Theorem orders@set_antinsymmetric inj_inj_bij JJ
    Denumerability of the Rational Numbers sets_aux@countable_set countable_rat JJ
    Heine Theorem and Multiary Variants analysis@uniform_continuity Heine, multiary_Heine AN
    Fubini-Tonelli Lemmas measure_integration@fubini_tonelli fubini_tonelli_* DL
    Knuth-Bendix Critical Pair Theorem TRS@critical_pairsCP_Theorem ALG, MA
    Church-Rosser Theorem TRS@results_confluenceCR_iff_Confluent ALG, MA
    Newman Lemma TRS@newman_yokouchiNewman_lemma ALG, MA
    Yokouchi Lemma TRS@newman_yokouchiYokouchi_lemma ALG, MA
    Robinson Unification TRS@robinsonunificationcompleteness_robinson_unification_algorithm AA, MA
    Confluence of Orthogonal TRSs TRS@orthogonalityOrthogonal_implies_confluent AR, MA
    Sturm's Theorem Sturm@sturmsturm AN
    Tarski's Theorem Tarski@sturmtarskisturm_tarski_unbounded AN, AD

    Contributors

    AAAndreia Avelar Borges, University of Brasilia, Brazil
    Aaron Dutle, NASA, USA
    AGAlfons Geser, HTWK Leipzig, Germany
    ALGAndré Galdino, Federal University of Goiás, Brazil
    ANAnthony Narkawicz, NASA, USA
    ARAna Cristina Rocha Oliveira, University of Brasilia, Brazil
    BDBruno Dutertre[*], SRI, USA
    BDVBen Di Vito, NASA, USA
    CMCésar Muñoz, NASA, USA
    DGDavid Griffioen,CWI, The Netherlands
    DLDavid Lester[*], Manchester University, UK
    DSDragan Stosic, Ireland
    EMÉrik Martin-Dorel[*], U. Montpellier 2 & U. of Perpignan (formerly), France
    HHHeber Herencia-Zapana[*], NIA, USA
    JJJerry James, Utah State University (formerly), USA
    JMJeff Maddalon, NASA, USA
    JSJon Sjogren, Department of Defense, USA
    KRKristin Rozier, NASA, USA
    GDGilles Dowek[*], INRIA, France
    GHGeroge Hagen, NASA, USA
    GPGilberto Perez, University of La Coruña, Spain
    HGHanne Gottliebsen, NIA (formerly), USA
    LPLee Pike[*], Galois, USA
    MAMauricio Ayala-Rincón[*], University of Brasilia, Brazil
    NSNatarajan Shankar[*], SRI, USA
    PMPaul Miner, NASA, USA
    RBRicky Butler, NASA, USA
    SBSilvie Boldo[*], INRIA, France
    SOSam Owre[*], SRI, USA
    VCVíctor Carreño, NASA (formerly), USA

    If we have incorrectly attributed a PVS development, please let us know.

    The tag [*] identifies links that are outside the NASA domain