Recursive Function Definition over Coinductive Types
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منابع مشابه
Wander types : A formalization of coinduction - recursion ∗
Wander types are a coinductive version of inductive-recursive definitions. They are defined by simultaneously specifying the constructors of the type and a function on the type itself. The types of the constructors can refer to the function component and the function itself is given by pattern matching on the constructors. Wander types are different from inductive-recursive types in two ways: t...
متن کاملWander Types A Formalization of Coinduction - Recursion ∗
Wander types are a coinductive version of inductive-recursive definitions. They are defined by simultaneously specifying the constructors of the type and a function on the type itself. The types of the constructors can refer to the function component and the function itself is given by pattern matching on the constructors. Wander types are different from inductive-recursive types in two ways: t...
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A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations, implementation of operational semantics, formalization of domain theory, and inductive definition of domain predicates. Here, a different solution is proposed: exploiti...
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We present guarded dependent type theory, gDTT, an extensional dependent type theory with a ‘later’ modality and clock quantifiers for programming and proving with guarded recursive and coinductive types. The later modality is used to ensure the productivity of recursive definitions in a modular, type based, way. Clock quantifiers are used for controlled elimination of the later modality and fo...
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We present a new model of Guarded Dependent Type Theory (GDTT), a type theory with guarded recursion and multiple clocks in which one can program with, and reason about coinductive types. Productivity of recursively defined coinductive programs and proofs is encoded in types using guarded recursion, and can therefore be checked modularly, unlike the syntactic checks implemented in modern proof ...
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تاریخ انتشار 1999