Concepts inIsomorphisms of generic recursive polynomial types
Type theory
In mathematics, logic and computer science, type theory is any of several formal systems that can serve as alternatives to naive set theory, or the study of such formalisms in general. In programming language theory, a branch of computer science, type theory can refer to the design, analysis and study of type systems, although some computer scientists limit the term's meaning to the study of abstract formalisms such as typed ¿-calculi.
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Isomorphism
In abstract algebra, an isomorphism is a bijective homomorphism. Two mathematical structures are said to be isomorphic if there is an isomorphism between them. In category theory, an isomorphism is a morphism f: X ¿ Y in a category for which there exists an "inverse" f: Y ¿ X, with the property that both ff = idX and f f = idY.
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Recursion
Recursion is the process of repeating items in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other the nested images that occur are a form of infinite recursion. The term has a variety of meanings specific to a variety of disciplines ranging from linguistics to logic.
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Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x ¿ x/4 + 7 is a polynomial, but x ¿ 4/x + 7x is not, because its second term involves division by the variable x (4/x), and also because its third term contains an exponent that is not an integer (3/2).
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Recursive data type
In computer programming languages, a recursive data type (also known as a recursively-defined, inductively-defined or inductive data type) is a data type for values that may contain other values of the same type. Data of recursive types are usually viewed as directed graphs. An important application of recursion in computer science is in defining dynamic data structures such as Lists and Trees.
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Decidability (logic)
In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas, or, more precisely, an algorithm that can and will return a Boolean true or false value (instead of looping indefinitely). Logical systems such as propositional logic are decidable if membership in their set of logically valid formulas (or theorems) can be effectively determined.
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Computer algebra system
A computer algebra system (CAS) is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.
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Basis (linear algebra)
Basis vector redirects here. For basis vector in the context of crystals, see crystal structure. For a more general concept in physics, see frame of reference. In linear algebra, a basis is a set of linearly independent vectors that, in a linear combination, can represent every vector in a given vector space or free module, or, more simply put, which define a "coordinate system" (as long as the basis is given a definite order).
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