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README.md

NASALib

NASALib is a continuing collaborative effort that has spanned over 3 decades, to aid in research related to theorem proving sponsored by NASA (https://shemesh.larc.nasa.gov/fm/pvs/). It consists of a collection of formal development (i.e., libraries) written in the Prototype Verification System (PVS), contributed by SRI, NASA,NIA, and the PVS community, and maintained by the NASA/NIA Formal Methods Team at LaRC.

Release

The current version of NASALib is 7.1.0 (11/05/20) and requires PVS 7.1.

Libraries

Currently, NASALib consists of 53 libraries and includes almost 30K lemmas.

Library Description
ACCoRD Framework for the analysis of air traffic conflict detection and resolution algorithms
affine_arith Formalization of affine arithmetic and strategy for evaluating polynomial functions with variables on interval domains.
algebra Groups, monoids, rings, etc.
analysis Real analysis, limits, continuity, derivatives, integrals.
ASP Denotational semantics of Answer Set Programming.
aviation Support definitions and properties for aviation-related formalizations.
Bernstein Formalization of multivariate Bernstein polynomials.
CCG Formalization of diverse termination criteria.
complex Complex numbers.
complex_alt Alternative formalization of complex numbers.
complex_integration Complex integration.
co_structures Sequences of countable length defined as co-algebraic datatypes.
digraphs Directed graphs: circuits, maximal subtrees, paths, DAGs.
exact_real_arith Exact real arithmetic including trig functions.
examples Examples of application of the functionality provided by NASALib.
extended_nnreal Extended non-negative reals.
fast_approx Approximations of standard numerical functions.
fault_tolerance Fault tolerance protocols.
float Floating point numbers and arithmetic.
graphs Graph theory.
groups Group theory.
interval_arith 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.
ints Integer division, gcd, mod, prime factorization, min, max.
lebesgue Lebesgue integral with connection to Riemann Integral.
linear_algebra Linear algebra.
lnexp Logarithm, exponential and hyperbolic functions. & Foundational definitions of logarithm, exponential and hyperbolic functions.
matrices Executable specification of MxN matrices. This library includes computation of inverse and basic matrix operations such as addition and multiplication.
measure_integration Sigma algebras, measures, Fubini-Tonelli Lemmas.
MetiTarski Integration of MetiTarski, an automated theorem prover for real-valued functions.
metric_space Domains with a distance metric, continuity and uniform continuity.
numbers Elementary number theory.
orders Abstract orders, lattices, fix points.
power Generalized Power function (without ln/exp).
probability Probability theory.
PVS0 Formalization of fundamental computability concepts.
PVSioChecker Animation of PVS specifications.
reals Summations, sup, inf, sqrt over the reals, absolute value, etc.
Riemann Riemann integral.
scott Scott topology.
series Power series, comparison test, ratio test, Taylor's theorem.
sets_aux Power sets, orders, cardinality over infinite sets. Includes functional and relational facts based on Axiom of Choice and refinement relations based on equivalence relations.
shapes 2D-Shapes: triangle, parallelogram, rectangle, circular segment
sigma_set Summations over countably infinite sets.
sorting Sorting algorithms.
structures Bounded arrays, finite sequences, bags, and several other structures.
Sturm Formalization of Sturm's theorem for univariate polynomials. Includes strategies sturm and mono-poly for automatically proving univariate polynomial relations over a real interval.
Tarski Formalization of Tarski's theorem for univariate polynomials. Includes strategy tarski for automatically proving systems of univariate polynomial relations on the real line.
topology Continuity, homeomorphisms, connected and compact spaces, Borel sets/functions.
trig Trigonometry: definitions, identities, approximations.
TRS Term rewrite systems and Robinson unification algorithm.
TU_games Cooperative TU-games.
vect_analysis Limits, continuity, and derivatives of vector functions.
vectors 2-D, 3-D, 4-D, and n-dimensional vectors.
while Semantics for the programming language While.

Dependencies

Check the NASALib dependency graph.

Scripts

NASALib also provides a collection of scripts that automates several tasks.

  • proveit (*) - Runs PVS in batch mode
  • provethem (*) - Runs proveit on several libraries
  • pvsio (*) - Command-line utility to run the PVSio ground evaluator.
  • prove-all - Runs proveit on each library in NASALib by wrapping provethem in order to provide a specific kind of run.
  • cleanbin-all - Clean .pvscontext and binary files from PVS libraries.
  • find-all - Searches strings matching a given regular expressions in PVS libraries.
  • dependencygraph - Generates a library dependency graph for libraries in the current directory.
  • dependency-all - Generates the dependency graphs for the PVS libraries in the current folder.

Click here for more details on these scripts.

(*) Already included in the PVS 7.1 distribution.

Getting NASALib

Via VSCode-PVS (recommended for new PVS users)

NASALib (v7.0.1) is fully compatible with VSCode-PVS, a modern graphical interface to PVS based on Visual Studio Code. The latest version of NASALib can be installed from VSCode-PVS.

Development Version

For PVS advanced users, the development version is available from GitHub. To clone the development version, type the following command inside directory where PVS 7.0 is installed. Henceforth, that directory will be referred to as <pvsdir>. In the following commands, the dollar sign represents the prompt of the operating system.

$ git clone http://github.com/nasa/pvslib nasalib 

The command above will put a copy of the library in the directory <pvsdir>/nasalib.

Major Recent Changes

  • The library trig_fnd is now deprecated. It's still provided for backward compatibility, but it should be replaced by trig. The new library trig, which used to be axiomatic, is now foundational. However, in contrast to trig_fnd, trigonometric definitions are based on infinite series, rather than integrals. This change considerably reduces the type-checking of theories involving trigonometric functions. The change from trig_fnd to trig should not have a major impact in your formal developments since names of definitions and lemmas are the same. However, theory importing may be slightly different.

  • The PVS developments TCASII, WellClear, and DAIDALUS are now available as part of the GitHub WellClear distribution. The PVS development PRECiSA is now available as part of the GitHub PRECiSA distribution. The PVS development PolyCARP is now available as part of the GitHub PolyCARP distribution.

Manual Installation

The following instructions assume that NASALib is located in the directory <pvsdir>/nasalib.

1) Add this directory to the environment variable PVS_LIBRARY_PATH

If it does not exists, creates such variable and with the path of this directory as only content. It is usually very useful to have your shell systems creating this variable at startup. To this end, and depending upon your shell, you may want to add one of the following lines in your startup script. For C shell (csh or tcsh), you may add this line in ~/.cshrc:

setenv PVS_LIBRARY_PATH "<pvsdir>/nasalib"

For Borne shell (bash or sh), add this line in either ~/.bashrc or ~/.profile:

export PVS_LIBRARY_PATH="<pvsdir>/nasalib"

2) Additional steps to protect previous NASALib configurations (optional)

If you had a previous installation of NASALib, either remove the file ~/.pvs.lisp or, if you have a special configuration in that file, remove the following line

(load "<pvsdir>/nasalib/pvs-patches.lisp") 

3) Install Scripts

Finally, go to the directory <pvsdir>/nasalib and run the following shell scripts (the dollar sign represents the prompt of the operating system).

The install-scripts command will update and install NASALib scripts as needed.

$ ./install-scripts

Older Versions

Older versions of NASALib are available from http://shemesh.larc.nasa.gov/fm/ftp/larc/PVS-library.

Contributors

NASALib has grown over the years thanks to the contribution of several people, among them:

  • Aaron Dutle, NASA, USA
  • Alfons Geser, HTWK Leipzig, Germany
  • Amer Tahat, Michigan Technological University, USA
  • Amy Isvik, Wartburg College, USA
  • Ana Cristina Rocha Oliveira, University of Brasilia, Brazil
  • André Galdino, Federal University of Goiás, Brazil
  • Andreia Avelar Borges, University of Brasilia, Brazil
  • Anthony Narkawicz, formerly at NASA, USA
  • Ariane Alves Almeida, University of Brasilia, Brazil
  • Bruno Dutertre, SRI, USA
  • Ben Di Vito, NASA (retired), USA
  • César Muñoz, NASA, USA
  • Concepción Vidal, University of La Coruña, Spain
  • David Griffioen,CWI, The Netherlands
  • David Lester, Manchester University, UK
  • Dragan Stosic, Ireland
  • Érik Martin-Dorel, U. Montpellier 2 & U. of Perpignan (formerly), France
  • Felicidad Aguado, University of La Coruña, Spain
  • Flavio L.C. de Moura, University of Brasilia, Brazil
  • Gilles Dowek, INRIA, France
  • George Hagen, NASA, USA
  • Gilberto Perez, University of La Coruña, Spain
  • Gregory Anderson, University of Texas at Austin, USA
  • Hanne Gottliebsen, formerly at NIA, USA
  • Heber Herencia-Zapana, formerly at NIA, USA
  • J. Tanner Slagel, NASA, USA
  • Jerry James, Utah State University, USA
  • Jeff Maddalon, NASA, USA
  • Jon Sjogren, Department of Defense, USA
  • John Siratt, formerly at University of Arkansas at Little Rock, USA
  • Katherine Cordwell, CMU, USA
  • Kristin Rozier, formerly at NASA, USA
  • Lee Pike, formerly at Galois, USA
  • Marco A. Feliú, NIA, USA
  • Mariano Moscato, NIA, USA
  • Mauricio Ayala-Rincón, University of Brasilia, Brazil
  • Natarajan Shankar, SRI, USA
  • Pablo Ascariz, formerly at University of La Coruña, Spain
  • Paul Miner, NASA, USA
  • Pedro Cabalar, University of La Coruña, Spain
  • Radu Siminiceanu, formerly at NIA, USA
  • Ricky Butler, NASA (retired), USA
  • Silvie Boldo, INRIA, France
  • Sam Owre, SRI, USA
  • Thaynara de Lima, Federal University of Goiás, Brazil
  • Thiago Mendonça Ferreira Ramos, University of Brasilia, Brazil
  • Thomas Norris
  • Víctor Carreño, NASA (retired), USA

If we have incorrectly attributed a PVS development or you have contributed to NASALib and your name is not included here, please let us know.

If you want to contribute please read this guide.

DISCLAIMER --< NASALib is a collection of formal specifications most of which have been in the public domain for several years. The Formal Methods Team at NASA LaRC still maintains these developments. For the developments originally made by the Formal Methods Team, these developments are considered fundamental research that do not constitute software. Contributions made by others may have particular licenses, which are listed in the file top.pvs in each respective directory. In case of doubt, please contact the developers of each contribution, which are also listed in that file.

PVS patches, which are included in the directory pvs-patches, are part of the PVS source code and they are covered by the PVS open source license.

Some proof strategies require third party research tools, e.g., MetiTarski and Z3. For convenience, they are included in this repository with permission from their authors. Licenses for these tools are also included as appropriate.

Enjoy it.

The NASA/NIA Formal Methods Team at LaRC

Contact: César A. Muñoz (NASA)

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