Concepts in&lgr;-V-CS: an extended &lgr;-calculus for scheme
Π-calculus
In theoretical computer science, the π-calculus (or pi-calculus) is a process calculus originally developed by Robin Milner, Joachim Parrow and David Walker as a continuation of work on the process calculus CCS. The π-calculus allows channel names to be communicated along the channels themselves, and in this way it is able to describe concurrent computations whose network configuration may change during the computation. The π-calculus is elegantly simple yet very expressive.
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Functional programming
In computer science, functional programming is a programming paradigm that treats computation as the evaluation of mathematical functions and avoids state and mutable data. It emphasizes the application of functions, in contrast to the imperative programming style, which emphasizes changes in state. Functional programming has its roots in lambda calculus, a formal system developed in the 1930s to investigate function definition, function application, and recursion.
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Scheme (programming language)
Scheme is a functional programming language and one of the two main dialects of the programming language Lisp. Unlike Common Lisp, the other main dialect, Scheme follows a minimalist design philosophy specifying a small standard core with powerful tools for language extension. Its compactness and elegance have made it popular with educators, language designers, programmers, implementors, and hobbyists.
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Imperative programming
In computer science, imperative programming is a programming paradigm that describes computation in terms of statements that change a program state. In much the same way that imperative mood in natural languages expresses commands to take action, imperative programs define sequences of commands for the computer to perform.
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Calculus
Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus.
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Semantics
Semantics (from Greek: sēmantiká, neuter plural of sēmantikós) is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata. Linguistic semantics is the study of meaning that is used to understand human expression through language. Other forms of semantics include the semantics of programming languages, formal logics, and semiotics.
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Conservative extension
In mathematical logic, a logical theory is a conservative extension of a theory if the language of extends the language of ; every theorem of is a theorem of ; and any theorem of which is in the language of is already a theorem of . More generally, if Γ is a set of formulas in the common language of and, then is Γ-conservative over if every formula from Γ provable in is also provable in .
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Algebra
Algebra (from Arabic al-jebr meaning "reunion of broken parts") is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics.
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