Debian Science Logic packages

Agda は依存型付けされた関数プログラミング言語です (Haskell の GADTs のよう な、帰納的定義型の種別を持ちますが、その型は型だけではなく値にインデックス されうる型です)。パラメータ付きモジュール、mixfix 演算子、Unicode 文字およ び Emacs 用対話的インターフェースを含みます (型検査器が、あなたのコードの開発を 補助します)。

Agda は定理証明支援系でもあります (証明を待ち、検査する対話的システムです)。 Agda は直観主義的な型理論に基づいています (スイスの論理学者 Per Martin-Löf によって開拓された構成的な数学の基礎理論です)。Coq, Epigram および NuPRL といった、依存型に基づいている他の定理証明支援系とも多くの類似点があります。

Agda の emacs mode、実行形式、標準ライブラリおよびそのドキュメントを提供する メタパッケージです。

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 はビットベクトルの量化子フリー理論と配列の量化子フリー拡張理論を 組み合わせた効率的な SMT ソルバーです。

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) は、C++ で書かれたオープンソースの混合整数 プログラミグソルバです。呼び出し可能なライブラリとしても、スタンドアローン の実行可能ファイルとしても使えます。

本パッケージには cbc 実行可能ファイルが含まれます。

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 は高階論理の証明アシスタントで、コンピュータプログラムを形式的な仕様との 整合性を保ちながら開発できます。Objective Caml と Camlp5 を用いて 開発されています。

本パッケージは Coq へのコマンドラインインターフェース coqtop を提供します。

Coq のグラフィカルインターフェースは coqide パッケージが提供します。 Coq は ProofGeneral とも併用でき、証明を emacs や xemacs で 編集できるようになります。これには proofgeneral パッケージのインストールが 必要です。

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.

現在の解集合ソルバは、変数のないプログラムを取り扱います。 したがって、与えられた一階変数を持つ入力プログラムと等価なグラウンド (変数のない) プログラムを計算するグラウンダが必要です。

このパッケージには次のツールが含まれています:

• gringo: 一階変数を伴う入力プログラムから等価なグラウンド (変数フリー) を aspif フォーマットで計算します。この出力をさらに解集合ソルバ clasp で処理することができます。gringo シリーズ 5 からは、出力は smodels や cmodels などの smodels フォーマットと直接互換では なくなりました。lpconvert を使って aspif フォーマットから smodels フォーマットに変換してください。
• clingo: gringo と clasp を組み合わせてモノリシックなシステムにします。 この方法により、gringo と clasp がそれぞれ提供するよりもより詳細に グラウンディングおよびソルビングプロセスを制御することができます。 マルチショット・ソルビング
• lpconvert: gringo の aspif と smodels フォーマット間の変換器
• reify: aspif フォーマットで与えられる論理プログラムを具体化する 小さなユーティリティ。gringo でさらに処理できる一連のファクトが生成 されます。

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.

このソフトウェアは、線形時相論理 (ltl) 論理式を 汎用の Büchi オートマトンに変換します。出力されるオートマトンは、 例えば、モデルの検査に利用できるかもしれません。そのモデル検査では、 オートマトンはモデル (例: ペトリネット) から検証されるプロパティ を表します。

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 は、WS1S や WS2S 論理の式を BDD で表現された有限状態のオートマトンに変 換するツールです。式は検索パターン、反応システムの時間的特性、解析木の制約 などを表すことができます。MONA はまた、コンパイルの結果得られたオートマトン を解析してその式が妥当かどうかを判定し、妥当でなければ反例を生成します。

ドキュメンテーションは MONA のウェブサイト http://www.brics.dk/mona/ から入 手できます。

論理式の充足可能性問題 (SAT) は NP 完全ですが、SAT ソルバはしばしばこの問題 を適度な時間で決定することができます。他のすべての NP 完全な問題は SAT に還 元することができるので、SAT ソルバはこのクラスの問題のための汎用的なツール となっています。

PicoSAT は、産業的な事例において MiniSAT 2.0 より高速であると判明した SAT ソルバです。メモリ上で proof と core を生成することもできます。

Proof General は、Emacs を対話型証明アシスタントにするメジャーモードで、 様々な定理証明系を用いて形式的数学証明を記述することができます。

このパッケージは、Coq に対する Proof General のサポートを提供します。 (他にまともにサポートできる証明アシスタントが存在していません。)

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.

SAT4J ライブラリの狙いは、Java 上に効率的な SAT ソルバーライブラリを提供 することです。OpenSAT プロジェクトと比較して、SAT4J ライブラリは SAT を「ブラックボックス」として使い、詳細を気にせずにアプリケーションに SAT テクノロジを組み込みたい初心者をターゲットにしています。SAT4J プロジェクトは SAT 研究者に仕事の基礎を提供することも目指しています。

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.