CythonCython (ˈsaɪθɒn) is a superset of the programming language Python, which allows developers to write Python code (with optional, C-inspired syntax extensions) that yields performance comparable to that of C. Cython is a compiled language that is typically used to generate CPython extension modules. Annotated Python-like code is compiled to C (also usable from e.g. C++) and then automatically wrapped in interface code, producing extension modules that can be loaded and used by regular Python code using the import statement, but with significantly less computational overhead at run time.
File systemIn computing, a file system or filesystem (often abbreviated to fs) is a method and data structure that the operating system uses to control how data is stored and retrieved. Without a file system, data placed in a storage medium would be one large body of data with no way to tell where one piece of data stopped and the next began, or where any piece of data was located when it was time to retrieve it. By separating the data into pieces and giving each piece a name, the data are easily isolated and identified.
R (programming language)R is a programming language for statistical computing and graphics supported by the R Core Team and the R Foundation for Statistical Computing. Created by statisticians Ross Ihaka and Robert Gentleman, R is used among data miners, bioinformaticians and statisticians for data analysis and developing statistical software. The core R language is augmented by a large number of extension packages containing reusable code and documentation. According to user surveys and studies of scholarly literature databases, R is one of the most commonly used programming languages in data mining.
ApplyIn mathematics and computer science, apply is a function that applies a function to arguments. It is central to programming languages derived from lambda calculus, such as LISP and Scheme, and also in functional languages. It has a role in the study of the denotational semantics of computer programs, because it is a continuous function on complete partial orders. Apply is also a continuous function in homotopy theory, and, indeed underpins the entire theory: it allows a homotopy deformation to be viewed as a continuous path in the space of functions.
File formatA file format is a standard way that information is encoded for storage in a . It specifies how bits are used to encode information in a digital storage medium. File formats may be either proprietary or free. Some file formats are designed for very particular types of data: PNG files, for example, store bitmapped using lossless data compression. Other file formats, however, are designed for storage of several different types of data: the Ogg format can act as a container for different types of multimedia including any combination of audio and video, with or without text (such as subtitles), and metadata.
MatitaMatita is an experimental proof assistant under development at the Computer Science Department of the University of Bologna. It is a tool aiding the development of formal proofs by man-machine collaboration, providing a programming environment where formal specifications, executable algorithms and automatically verifiable correctness certificates naturally coexist. Matita is based on a dependent type system known as the Calculus of (Co)Inductive Constructions (a derivative of Calculus of Constructions), and is compatible, to some extent, with Coq.
Proof by contradictionIn logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally valid. More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved.
Agda (programming language)Agda is a dependently typed functional programming language originally developed by Ulf Norell at Chalmers University of Technology with implementation described in his PhD thesis. The original Agda system was developed at Chalmers by Catarina Coquand in 1999. The current version, originally known as Agda 2, is a full rewrite, which should be considered a new language that shares a name and tradition. Agda is also a proof assistant based on the propositions-as-types paradigm, but unlike Coq, has no separate tactics language, and proofs are written in a functional programming style.
Mathematical proofA mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation".
Literate programmingLiterate programming is a programming paradigm introduced in 1984 by Donald Knuth in which a computer program is given as an explanation of how it works in a natural language, such as English, interspersed (embedded) with snippets of macros and traditional source code, from which compilable source code can be generated. The approach is used in scientific computing and in data science routinely for reproducible research and open access purposes. Literate programming tools are used by millions of programmers today.
PrologProlog is a logic programming language associated with artificial intelligence and computational linguistics. Prolog has its roots in first-order logic, a formal logic, and unlike many other programming languages, Prolog is intended primarily as a declarative programming language: the program logic is expressed in terms of relations, represented as facts and rules. A computation is initiated by running a query over these relations.
Logic programmingLogic programming is a programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. Major logic programming language families include Prolog, answer set programming (ASP) and Datalog. In all of these languages, rules are written in the form of clauses: H :- B1, ..., Bn. and are read declaratively as logical implications: H if B1 and ... and Bn. H is called the head of the rule and B1, .
