Lua (programming language)Lua (ˈluːə ; from lua ˈlu(w)ɐ meaning moon) is a lightweight, high-level, multi-paradigm programming language designed primarily for embedded use in applications. Lua is cross-platform, since the interpreter of compiled bytecode is written in ANSI C, and Lua has a relatively simple C API to embed it into applications. Lua originated in 1993 as a language for extending software applications to meet the increasing demand for customization at the time.
"Hello, World!" programA "Hello, World!" program is generally a computer program that ignores any input, and outputs or displays a message similar to "Hello, World!". A small piece of code in most general-purpose programming languages, this program is used to illustrate a language's basic syntax. "Hello, World!" programs are often the first a student learns to write in a given language, and they can also be used as a sanity check to ensure computer software intended to compile or run source code is correctly installed, and that its operator understands how to use it.
Dependence logicDependence logic is a logical formalism, created by Jouko Väänänen, which adds dependence atoms to the language of first-order logic. A dependence atom is an expression of the form , where are terms, and corresponds to the statement that the value of is functionally dependent on the values of . Dependence logic is a logic of imperfect information, like branching quantifier logic or independence-friendly logic (IF logic): in other words, its game-theoretic semantics can be obtained from that of first-order logic by restricting the availability of information to the players, thus allowing for non-linearly ordered patterns of dependence and independence between variables.
RewritingIn mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. Such methods may be achieved by rewriting systems (also known as rewrite systems, rewrite engines, or reduction systems). In their most basic form, they consist of a set of objects, plus relations on how to transform those objects. Rewriting can be non-deterministic. One rule to rewrite a term could be applied in many different ways to that term, or more than one rule could be applicable.
Independence-friendly logicIndependence-friendly logic (IF logic; proposed by Jaakko Hintikka and Gabriel Sandu in 1989) is an extension of classical first-order logic (FOL) by means of slashed quantifiers of the form and , where is a finite set of variables. The intended reading of is "there is a which is functionally independent from the variables in ". IF logic allows one to express more general patterns of dependence between variables than those which are implicit in first-order logic.
Recursive definitionIn mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff). Some examples of recursively-definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set. A recursive definition of a function defines values of the function for some inputs in terms of the values of the same function for other (usually smaller) inputs.
Confluence (abstract rewriting)In computer science, confluence is a property of rewriting systems, describing which terms in such a system can be rewritten in more than one way, to yield the same result. This article describes the properties in the most abstract setting of an abstract rewriting system. The usual rules of elementary arithmetic form an abstract rewriting system. For example, the expression (11 + 9) × (2 + 4) can be evaluated starting either at the left or at the right parentheses; however, in both cases the same result is eventually obtained.
Theory (mathematical logic)In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first understood from context, after which an element of a deductively closed theory is then called a theorem of the theory. In many deductive systems there is usually a subset that is called "the set of axioms" of the theory , in which case the deductive system is also called an "axiomatic system". By definition, every axiom is automatically a theorem.
Abstract rewriting systemIn mathematical logic and theoretical computer science, an abstract rewriting system (also (abstract) reduction system or abstract rewrite system; abbreviated ARS) is a formalism that captures the quintessential notion and properties of rewriting systems. In its simplest form, an ARS is simply a set (of "objects") together with a binary relation, traditionally denoted with ; this definition can be further refined if we index (label) subsets of the binary relation.
Very high-level programming languageA very high-level programming language (VHLL) is a programming language with a very high level of abstraction, used primarily as a professional programmer productivity tool. VHLLs are usually domain-specific languages, limited to a very specific application, purpose, or type of task, and they are often scripting languages (especially extension languages), controlling a specific environment. For this reason, very high-level programming languages are often referred to as goal-oriented programming languages.
