Debian Science Logic packages

Agda is a dependently typed functional programming language: It has inductive families, which are like Haskell's GADTs, but they can be indexed by values and not just types. It also has parameterised modules, mixfix operators, Unicode characters, and an interactive Emacs interface (the type checker can assist in the development of your code).

Agda is also a proof assistant: It is an interactive system for writing and checking proofs. Agda is based on intuitionistic type theory, a foundational system for constructive mathematics developed by the Swedish logician Per Martin-Löf. It has many similarities with other proof assistants based on dependent types, such as Coq, Epigram and NuPRL.

This is a meta package which provides Agda's emacs mode, executable, standard library and its documentation.

Alt-Ergo is an automatic theorem prover geared towards application in program verification. It is based on CC(X), a congruence closure algorithm parameterized by an equational theory X. Alt-Ergo has built-in provers for propositional logic, linear arithmetic, uninterpreted function symbols, associative-commutative function symbols, polymorphic arrays, user-defined polymorphic record types and polymorphic enumeration types. It has restricted support for reasoning over arbitrary user-defined algebraic types, first-order quantifiers, and non-linear arithmetic.

This package contains the prover as a command-line executable.

Boolector is an efficient SMT solver for the quantifier-free theory of bit-vectors in combination with the quantifier-free extensional theory of arrays.

clasp is an answer set solver for (extended) normal logic programs. It combines the high-level modeling capacities of answer set programming (ASP) with state-of-the-art techniques from the area of Boolean constraint solving. The primary clasp algorithm relies on conflict-driven nogood learning, a technique that proved very successful for satisfiability checking (SAT). Unlike other learning ASP solvers, clasp does not rely on legacy software, such as a SAT solver or any other existing ASP solver. Rather, clasp has been genuinely developed for answer set solving based on conflict-driven nogood learning. clasp can be applied as an ASP solver (on LPARSE output format), as a SAT solver (on simplified DIMACS/CNF format), or as a PB solver (on OPB format).

Cbc (Coin-or branch and cut) is an open-source mixed integer programming solver written in C++. It can be used as a callable library or as a stand-alone executable.

This package contains cbc executable.

SYMPHONY is an open-source generic mixed-integer linear programs (MILP) solver, callable library, and extensible framework for implementing customized solvers SYMPHONY has a number of advanced capabilities, including the ability to solve multi-objective MILPs, the ability to warm start its solution procedure, and the ability to perform basic sensitivity analyses.

SYMPHONY is part of the larger COIN-OR initiative (Computational Infrastructure for Operations Research).

This package contains the symphony executable.

Coq is a proof assistant for higher-order logic, which allows the development of computer programs consistent with their formal specification. It is developed using Objective Caml and Camlp5.

This package provides coqtop, a command line interface to Coq.

A graphical interface for Coq is provided in the coqide package. Coq can also be used with ProofGeneral, which allows proofs to be edited using emacs and xemacs. This requires the proofgeneral package to be installed.

CVC4 is an efficient automatic theorem prover for satisfiability modulo theories (SMT) problems. It can be used to prove the validity (or, dually, the satisfiability) of first-order formulas in a large number of built-in logical theories and their combination.

CVC4 is intended to be an open and extensible SMT engine, and it can be used as a stand-alone tool or as a library. It is the fourth in the Cooperating Validity Checker family of tools (also including CVC, CVC Lite and CVC3). CVC4 has been designed to increase the performance and reduce the memory overhead of its predecessors.

This package contains binaries needed to use CVC4 as a stand-alone tool.

DepQBF is a search-based solver for quantified boolean formulae (QBF) in prenex conjunctive normal form. It is based on the DPLL algorithm for QBF, called QDPLL, with conflict-driven clause and solution-driven cube learning. By analyzing the syntactic structure of a formula, DepQBF tries to identify independent variables. In general, information on independent variables can be represented in the formal framework of dependency schemes. DepQBF computes the so-called "standard dependency scheme" of a given formula. In addition to other benefits, information on independent variables often increases the freedom for decision making and clause learning.

Current answer set solvers work on variable-free programs. Hence, a grounder is needed that, given an input program with first-order variables, computes an equivalent ground (variable-free) program.

This package contains the following tools:

• gringo: a grounder that, given an input program with first-order variables, computes an equivalent ground (variable-free) program in aspif format. Its output can be processed further with answer set solver clasp. Starting with gringo series 5, its output is no longer directly compatible with solvers like smodels or cmodels reading smodels format. Use lpconvert for translating aspif format to smodels format.
• clingo: combines both gringo and clasp into a monolithic system. This way it offers more control over the grounding and solving process than gringo and clasp can offer individually: multi-shot solving.
• lpconvert: converter between gringo's aspif and smodels format.
• reify: small utility that reifies logic programs given in aspif format. It produces a set of facts, which can be processed further with gringo.

HOL Light is an interactive theorem prover for Higher-Order Logic with a very simple logical core running in an OCaml toplevel. HOL Light is famous for the verification of floating-point arithmetic as well as for the Flyspeck project, which aimed at the formalization of Tom Hales' proof of the Kepler conjecture.

The HOL System is an environment for interactive theorem proving in a higher-order logic. Its most outstanding feature is its high degree of programmability through the meta-language ML. The system has a wide variety of uses from formalizing pure mathematics to verification of industrial hardware. Academic and industrial sites world-wide are using HOL.

This software converts a linear temporal logic (ltl) formula to a generalised Büchi automaton. The resulting automaton may be used, for instance, in model checking, where it represents a property to be verified from a model (e.g. a Petri net).

Maria is a powerful tool designed to aid engineers in modelling and solving concurrency related problems in parallel and distributed computing systems.

Maria finds deadlocks and violations against safety or liveness requirements by exploring all states that can be reached from the initial state of a system. The tool manages tens or hundreds of millions of reachable states and enabled actions.

The expressive power of Maria's formalism is close to high-level programming languages, thanks to its rich data type system and powerful algebraic operations.

Maude is a high-performance reflective language and system supporting both equational and rewriting logic specification and programming for a wide range of applications. Maude has been influenced in important ways by the OBJ3 language, which can be regarded as an equational logic sublanguage. Besides supporting equational specification and programming, Maude also supports rewriting logic computation.

Rewriting logic is a logic of concurrent change that can naturally deal with state and with concurrent computations. It has good properties as a general semantic framework for giving executable semantics to a wide range of languages and models of concurrency. In particular, it supports very well concurrent object-oriented computation. The same reasons making rewriting logic a good semantic framework make it also a good logical framework, that is, a metalogic in which many other logics can be naturally represented and executed.

Maude supports in a systematic and efficient way logical reflection. This makes Maude remarkably extensible and powerful, supports an extensible algebra of module composition operations, and allows many advanced metaprogramming and metalanguage applications. Indeed, some of the most interesting applications of Maude are metalanguage applications, in which Maude is used to create executable environments for different logics, theorem provers, languages, and models of computation.

Maude is of interest to the biomedical community for modeling and analysis of biological systems.

MinSat+ is a solver for Pseudo-Boolean Optimization (AKA 0-1 integer programming) that is based on the MiniSat SAT-solver. It supports optimizing a linear objective function, subject to a set of linear constraints. The variables of the objective function and constraints are boolean, i.e. required to be 0 or 1. Pseudo-Boolean optimization can be used to solve many kinds of combinatorial optimization problems. This version of Minisat+ is compiled with bignum support for constraint coefficients.

MONA is a tool that translates formulas in the logics WS1S or WS2S into finite-state automata represented by BDDs. The formulas may express search patterns, temporal properties of reactive systems, parse tree constraints, etc. MONA also analyses the automaton resulting from the compilation, and determines whether the formula is valid and, if the formula is not valid, generates a counter-example.

Documentation is available from the MONA website http://www.brics.dk/mona/.

Despite the NP completeness of the satisfiabilty problem of Boolean formulas (SAT), SAT solvers are often able to decide this problem in a reasonable time frame. As all other NP complete problems are reducible to SAT, the solvers have become a general purpose tool for this class of problems.

PicoSAT is a SAT solver that turned out to be faster on industrial instances than MiniSAT 2.0 and also can generate proofs and cores in memory.

Proof General is a major mode to turn Emacs into an interactive proof assistant to write formal mathematical proofs using a variety of theorem provers.

This package provides Proof General support for Coq. (There is no other proof assistant that one could sensibly support.)

This package provides the Prover9 resolution/paramodulation theorem prover and the Mace4 countermodel generator.

Prover9 is an automated theorem prover for first-order and equational logic. It is a successor of the Otter prover. Prover9 uses the inference techniques of ordered resolution and paramodulation with literal selection.

The program Mace4 searches for finite structures satisfying first-order and equational statements, the same kind of statement that Prover9 accepts. If the statement is the denial of some conjecture, any structures found by Mace4 are counterexamples to the conjecture.

Mace4 can be a valuable complement to Prover9, looking for counterexamples before (or at the same time as) using Prover9 to search for a proof. It can also be used to help debug input clauses and formulas for Prover9.

The aim of the SAT4J library is to provide an efficient library of SAT solvers in Java. Compared to the OpenSAT project, the SAT4J library targets first users of SAT "black boxes", willing to embed SAT technologies into their application without worrying about the details. The SAT4J project also tries to provide a basis of work for SAT researchers.

SPASS is a saturation-based automated theorem prover for first-order logic with equality. It is unique due to the combination of the superposition calculus with specific inference/reduction rules for sorts (types) and a splitting rule for case analysis motivated by the beta-rule of analytic tableaux and the case analysis employed in the Davis-Putnam procedure. Furthermore, SPASS provides a sophisticated clause normal form translation.

This package consists of the SPASS/FLOTTER binary, documentation, and a small example collection. The tools collections contain the proof checker pcs, the syntax translators dfg2otter and dfg2tptp, and the ASCII pretty printer dfg2ascii.

Toulbar2 is an exact discrete optimization tool for Graphical Models such as Cost Function Networks, Markov Random Fields, Weighted Constraint Satisfaction Problems and Bayesian Nets.

Why3 is a platform for deductive program verification. It provides a rich language for specification and programming, called WhyML, and relies on external theorem provers, both automated and interactive, to discharge verification conditions. Why3 comes with a standard library of logical theories (integer and real arithmetic, Boolean operations, sets and maps, etc.) and basic programming data structures (arrays, queues, hash tables, etc.). A user can write WhyML programs directly and get correct-by-construction OCaml programs through an automated extraction mechanism. WhyML is also used as an intermediate language for the verification of C, Java, or Ada programs.

Why3 is a complete reimplementation of the former Why platform. Among the new features are: numerous extensions to the input language, a new architecture for calling external provers, and a well-designed API, allowing to use Why3 as a software library. An important emphasis is put on modularity and genericity, giving the end user a possibility to easily reuse Why3 formalizations or to add support for a new external prover if wanted.

Z3 is a state-of-the-art theorem prover from Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories. Z3 offers a compelling match for software analysis and verification tools, since several common software constructs map directly into supported theories.

The Z3 input format is an extension of the one defined by the SMT-LIB 2.0 standard.

The Coin-MP optimizer is an open source solver, it is part of the COIN-OR project which is an initiative to spur the development of open-source software for the operations research community.

CoinMP is a C-API library that supports most of the functionality of CLP (Coin LP), CBC (Coin Branch-and-Cut), and CGL (Cut Generation Library) projects.

This package contains the files needed to build applications using libCoinMP.