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Alt-Ergo
Alt-Ergo is an automatic solver for mathematical formulas, specifically designed for program verification. It is based on satisfiability modulo theories (SMT) and distributed under an open-source license (CeCILL-C). Its original authors were Sylvain Conchon and Evelyne Contejean, aLRI but it is now developed and maintained aOCamlPro Technologies Design choices Contrary to most SMT solvers, Alt-Ergo uses a specific input language with prenex polymorphism. This helps reducing the number of quantified axioms and the complexity of problems. It also partially supports SMT-LIB 2 language, but performs less efficiently on SMT files. Main components The core of Alt-Ergo is made of three parts: a DFS-based SAT solver, a quantifiers instantiation engine based on E-Matching, and a combination of decision procedures for a set of built-in theories. Built-in theories Alt-Ergo implements (semi-)decision procedures for the following theories: * empty theory * linear integer arithmet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Satisfiability Modulo Theories
In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable. It generalizes the Boolean satisfiability problem (SAT) to more complex formulas involving real numbers, integers, and/or various data structures such as lists, arrays, bit vectors, and strings. The name is derived from the fact that these expressions are interpreted within ("modulo") a certain formal theory in first-order logic with equality (often disallowing quantifiers). SMT solvers are tools which aim to solve the SMT problem for a practical subset of inputs. SMT solvers such as Z3 and cvc5 have been used as a building block for a wide range of applications across computer science, including in automated theorem proving, program analysis, program verification, and software testing. Since Boolean satisfiability is already NP-complete, the SMT problem is typically NP-hard, and for many theories it is undecidable. Resea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frama-C
Frama-C stands for ''Framework for Modular Analysis of C programs''. Frama-C is a set of interoperable program analyzers for C programs. Frama-C has been developed by the French Commissariat à l'Énergie Atomique et aux Énergies Alternatives ( CEA-List) and Inria. It has also received funding from the Core Infrastructure Initiative. Frama-C, as a static analyzer, inspects programs without executing them. Despite its name, the software is not related to the French project Framasoft. Architecture Frama-C has a modular plugin architecture comparable to that of Eclipse (software) or GIMP. Frama-C relies on CIL ( C Intermediate Language) to generate an abstract syntax tree. The abstract syntax tree supports annotations written in ANSI/ISO C Specification Language (ACSL). Several modules can manipulate the abstract syntax tree to add ANSI/ISO C Specification Language (ACSL) annotations. Among frequently used plugins are: * ''Value analysis'' computes a value or a set of po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SPARK (programming Language)
SPARK is a formally defined computer programming language based on the Ada programming language, intended for the development of high integrity software used in systems where predictable and highly reliable operation is essential. It facilitates the development of applications that demand safety, security, or business integrity. Originally, there were three versions of the SPARK language (SPARK83, SPARK95, SPARK2005) based on Ada 83, Ada 95 and Ada 2005 respectively. A fourth version of the SPARK language, SPARK 2014, based on Ada 2012, was released on April 30, 2014. SPARK 2014 is a complete re-design of the language and supporting verification tools. The SPARK language consists of a well-defined subset of the Ada language that uses contracts to describe the specification of components in a form that is suitable for both static and dynamic verification. In SPARK83/95/2005, the contracts are encoded in Ada comments and so are ignored by any standard Ada compiler, but are p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Z3 Theorem Prover
Z3, also known as the Z3 Theorem Prover, is a cross-platform satisfiability modulo theories (SMT) solver by Microsoft. Overview Z3 was developed in the ''Research in Software Engineering'' (RiSE) group at Microsoft Research and is targeted at solving problems that arise in software verification and program analysis. Z3 supports arithmetic, fixed-size bit-vectors, extensional arrays, datatypes, uninterpreted functions, and quantifiers. Its main applications are extended static checking, test case generation, and predicate abstraction. In 2015, it received the ''Programming Languages Software Award'' from ACM SIGPLAN. In 2018, Z3 received the ''Test of Time Award'' from the European Joint Conferences on Theory and Practice of Software (ETAPS). Microsoft researchers Nikolaj Bjørner and Leonardo de Moura received the 2019 Herbrand Award for Distinguished Contributions to Automated Reasoning in recognition of their work in advancing theorem proving with Z3. Z3 was open sourced in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Polymorphism
In programming languages and type theory, parametric polymorphism allows a single piece of code to be given a "generic" type, using variables in place of actual types, and then instantiated with particular types as needed. Parametrically polymorphic functions and data types are sometimes called generic functions and generic datatypes, respectively, and they form the basis of generic programming. Parametric polymorphism may be contrasted with ad hoc polymorphism. Parametrically polymorphic definitions are ''uniform'': they behave identically regardless of the type they are instantiated at. In contrast, ad hoc polymorphic definitions are given a distinct definition for each type. Thus, ad hoc polymorphism can generally only support a limited number of such distinct types, since a separate implementation has to be provided for each type. Basic definition It is possible to write functions that do not depend on the types of their arguments. For example, the identity function \math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SAT Solver
The SAT ( ) is a standardized test widely used for college admissions in the United States. Since its debut in 1926, its name and scoring have changed several times; originally called the Scholastic Aptitude Test, it was later called the Scholastic Assessment Test, then the SAT I: Reasoning Test, then the SAT Reasoning Test, then simply the SAT. The SAT is wholly owned, developed, and published by the College Board, a private, not-for-profit organization in the United States. It is administered on behalf of the College Board by the Educational Testing Service, which until recently developed the SAT as well. The test is intended to assess students' readiness for college. The SAT was originally designed not to be aligned with high school curricula, but several adjustments were made for the version of the SAT introduced in 2016, and College Board president David Coleman has said that he also wanted to make the test reflect more closely what students learn in high school with the ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Empty Theory
In mathematical logic, an uninterpreted function or function symbol is one that has no other property than its name and ''n-ary'' form. Function symbols are used, together with constants and variables, to form terms. The theory of uninterpreted functions is also sometimes called the free theory, because it is freely generated, and thus a free object, or the empty theory, being the theory having an empty set of sentences (in analogy to an initial algebra). Theories with a non-empty set of equations are known as equational theories. The satisfiability problem for free theories is solved by syntactic unification; algorithms for the latter are used by interpreters for various computer languages, such as Prolog. Syntactic unification is also used in algorithms for the satisfiability problem for certain other equational theories, see Unification (computer science). Example As an example of uninterpreted functions for SMT-LIB, if this input is given to an SMT solver: (declare-fun f (In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating Point Arithmetic
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be represented as a base-ten floating-point number: 12.345 = \underbrace_\text \times \underbrace_\text\!\!\!\!\!\!^ In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common. The term ''floating point'' refers to the fact that the number's radix point can "float" anywhere to the left, right, or between the significant digits of the number. This position is indicated by the exponent, so floating point can be considered a form of scientific notation. A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enumerated Type
In computer programming, an enumerated type (also called enumeration, enum, or factor in the R programming language, and a categorical variable in statistics) is a data type consisting of a set of named values called ''elements'', ''members'', ''enumeral'', or ''enumerators'' of the type. The enumerator names are usually identifiers that behave as constants in the language. An enumerated type can be seen as a degenerate tagged union of unit type. A variable that has been declared as having an enumerated type can be assigned any of the enumerators as a value. In other words, an enumerated type has values that are different from each other, and that can be compared and assigned, but are not specified by the programmer as having any particular concrete representation in the computer's memory; compilers and interpreters can represent them arbitrarily. For example, the four suits in a deck of playing cards may be four enumerators named ''Club'', ''Diamond'', ''Heart'', and ''Spade'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Record (computer Science)
In computer science, a record (also called a structure, struct, or compound data) is a basic data structure. Records in a database or spreadsheet are usually called "rows". A record is a collection of ''fields'', possibly of different data types, typically in a fixed number and sequence. The fields of a record may also be called ''members'', particularly in object-oriented programming; fields may also be called ''elements'', though this risks confusion with the elements of a collection. For example, a date could be stored as a record containing a numeric year field, a month field represented as a string, and a numeric day-of-month field. A personnel record might contain a name, a salary, and a rank. A Circle record might contain a center and a radius—in this instance, the center itself might be represented as a point record containing x and y coordinates. Records are distinguished from arrays by the fact that their number of fields is determined in the definition of the rec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
B-Method
The B method is a method of software development based on B, a tool-supported formal method based on an abstract machine notation, used in the development of computer software. Overview B was originally developed in the 1980s by Jean-Raymond Abrial in France and the UK. B is related to the Z notation (also originated by Abrial) and supports development of programming language code from specifications. B has been used in major safety-critical system applications in Europe (such as the automatic Paris Métro lines 14 and 1 and the Ariane 5 rocket). It has robust, commercially available tool support for specification, design, proof and code generation. Compared to Z, B is slightly more low-level and more focused on refinement to code rather than just formal specification — hence it is easier to correctly implement a specification written in B than one in Z. In particular, there is good tool support for this. The same language is used in specification, design and programming. Mec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rodin Tool
The Rodin tool is a tool for formal modelling in Event-B. Event-B is a notation and method developed from the B-Method and is intended to be used with an incremental style of modelling. The idea of incremental modelling has been taken from programming: modern programming languages come with integrated development environment that make it easy to modify and improve programs. The Rodin tool provides such an environment for Event-B. The two main characteristics of the Rodin tool are its ease of use and its extensibility. The tool focuses on modelling. It is easy to modify models and try out variations of a model. The tool can also be extended easily. This makes it possible to adapt the tool to specific needs, so the tool can be adapted to fit into existing development processes instead of demanding the opposite. The Event-wikiis a useful user and developer resource. Rodin (Rigorous Open Development Environment for Complex Systems) is an extension of Eclipse IDE (Java based). Rodin E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
