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Computer languages, often referred to as programming languages, are formal sets of instructions that can be used to communicate with and control computers. They consist of syntax (rules for structuring statements) and semantics (meaning behind the statements) that allow developers to write code that the computer can interpret and execute. There are several categories of computer languages: 1. **High-Level Languages**: These languages are closer to human language and abstract away much of the complexity of the computer's hardware.

Dependently typed languages are a category of programming languages that integrate a type system where types can depend on values. This means that types can be parameters that depend on specific values in the program, allowing for more expressive types that can capture more program properties within the type system itself. ### Key Features of Dependently Typed Languages: 1. **Types as First-Class Citizens**: In dependently typed languages, types can be treated as first-class entities.

Formal theories refer to systematic frameworks or systems of thought that use formal logic and mathematical structures to represent and analyze concepts, relationships, or processes. These theories are characterized by their reliance on precise definitions, axioms, rules of inference, and symbolic representations, which allow for rigorous reasoning and deduction.

Grammar frameworks are structured systems or models that define the rules and principles governing the syntax and semantics of a language. They provide a formal way to describe the grammatical properties of a language, enabling linguists and computer scientists to analyze, generate, and parse natural languages or programming languages systematically. Here are some notable types of grammar frameworks: 1. **Generative Grammar**: This is a theory of grammar that aims to describe the implicit knowledge that speakers of a language have about their language.

L-systems, or Lindenmayer systems, are a mathematical formalism introduced by the Hungarian botanist Aristid Lindenmayer in 1968 as a way to describe the growth processes of organisms, particularly plants. L-systems are particularly useful for modeling the branching structures of plants and other biological forms, as well as for generating fractal patterns and complex graphics.

Logic symbols are standardized symbols used to represent logical operations, relationships, and structures in formal logic, mathematics, computer science, and related fields. These symbols allow for a concise and unambiguous way of expressing logical expressions and propositions. Here are some common logic symbols and their meanings: 1. **Negation (¬)**: Represents logical negation (not). If \( p \) is a proposition, then \( \neg p \) means "not \( p \).

A metalanguage is a language or set of terms used for the description, analysis, or discussion of another language. It serves as a formal system to articulate the structure, syntax, semantics, and other aspects of the primary language it describes. Metalanguages are particularly common in fields like linguistics, computer science, and formal logic.

An Abstract Rewriting System (ARS) is a formal framework used in the field of computer science and mathematics to study the concept of rewriting, which is a fundamental operation in various areas such as term rewriting, functional programming, and automated theorem proving. In an ARS, we typically define a set of objects (often called terms or expressions) and a relation that describes how to transform these objects into one another through specific rewriting rules.

An Abstract Semantic Graph (ASG) is a conceptual representation used in various fields, particularly in natural language processing (NLP), knowledge representation, and artificial intelligence (AI). It is designed to model the meaning of sentences or texts in a structured format that captures the relationships and semantics of the components involved. Key features of Abstract Semantic Graphs include: 1. **Nodes and Edges**: An ASG is composed of nodes and edges. Nodes typically represent entities, concepts, or important terms.

An Abstract Syntax Tree (AST) is a data structure widely used in compilers and programming language interpreters to represent the structure of source code in a hierarchical tree format. The nodes of the tree represent constructs occurring in the source code, such as expressions, statements, variable declarations, control structures, and more, while the edges represent the relationships between these constructs.

Adaptive grammar is a concept that refers to a type of grammatical framework or model that can adjust and evolve its rules based on context, usage, or feedback.

Affix grammar is a concept in linguistic theory that focuses on the use of affixes in word formation. An affix is a morpheme—a meaningful unit of language—that is attached to a root or base word to modify its meaning or create a new word.

Agent Communication Language (ACL) refers to a set of protocols and languages designed to enable communication between intelligent agents in multi-agent systems. These systems consist of multiple agents that interact and collaborate to achieve specific goals, solve problems, or perform tasks. ACLs facilitate the exchange of information, negotiation, and cooperation among agents by providing a structured format for messages.

In formal languages, an **alphabet** is a finite set of symbols or characters used to construct strings and words. Each symbol in an alphabet is referred to as a "letter." For example: - The binary alphabet consists of two symbols: {0, 1}. - The alphabet for the English language can consist of 26 letters: {A, B, C, ..., Z}.

Ambiguous grammar refers to a type of formal grammar in which a single string (or sentence) can be generated by the grammar in multiple ways, producing more than one distinct parse tree or derivation. This ambiguity means that there may be multiple interpretations or meanings associated with that string, depending on the different parse trees. In the context of programming languages and compilers, ambiguous grammars can lead to confusion and difficulties in parsing, as they do not provide a clear association between syntax and semantics.

Arden's Rule is a principle in the field of mathematics and formal grammar, specifically concerning contexts in which one needs to solve systems of linear equations involving functions, particularly in Markov processes and stochastic systems.

Attribute grammar is a formalism used in the field of computer science, particularly in the design and implementation of programming languages and compilers. It extends context-free grammars by adding attributes to the grammar's symbols and defining rules for calculating these attributes. ### Key Components: 1. **Grammar**: Like a traditional context-free grammar (CFG), an attribute grammar defines a set of production rules that describe the syntactic structure of a language.

Augmented Backus–Naur Form (ABNF) is a notation used to express the syntax of languages, particularly programming languages and data formats. It is an extension of the original Backus–Naur Form (BNF), which was developed by John Backus and Peter Naur in the 1960s. ABNF incorporates several enhancements and features that make it more expressive and convenient compared to standard BNF.

Autocorrelation is a statistical concept that measures the relationship between a time series and a lagged version of itself over successive time intervals. In simpler terms, it assesses how a data set correlates with itself at different points in time. When analyzing a time series, autocorrelation helps to identify patterns, trends, or seasonal variations by determining whether past values influence future values.

Backus-Naur Form (BNF) is a formal notation used to specify the syntax of programming languages, data formats, and other formal grammars. It provides a way to express the rules and structure of a language in a concise and clear manner. BNF uses a set of derivation rules to define how symbols in the language can be combined to form valid strings.