Recursive data type in the context of Proof-theoretic


Recursive data type in the context of Proof-theoretic

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⭐ Core Definition: Recursive data type

In computer programming, a recursive data type is a data type whose definition contains values of the same type. It is also known as a recursively defined, inductively defined or inductive data 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. Recursive data structures can dynamically grow to an arbitrarily large size in response to runtime requirements; in contrast, a static array's size requirements must be set at compile time.

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Recursive data type in the context of Proof theory

Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.

Some of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, proof-theoretic semantics, reverse mathematics, proof mining, automated theorem proving, and proof complexity. Much research also focuses on applications in computer science, linguistics, and philosophy.

View the full Wikipedia page for Proof theory
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