Inductively defined types in the calculus of constructions

Inductively defined types in the calculus of constructions (1990)

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by Frank Pfenning , Christine Paulin-mohring

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Datum	Value	Source
TITLE	Inductively defined types in the calculus of constructions	INFERENCE
AUTHOR NAME	Frank Pfenning	SVM HeaderParse 0.2
AUTHOR AFFIL	School of Computer Science INRIA and LIENS, URA CNRS 1327; Carnegie Mellon University Ecole Normale Superiéure	SVM HeaderParse 0.2
AUTHOR ADDR	5000 Forbes Avenue 45 Rue d’Ulm; Pittsburgh, Pennsylvania 15213 75005 Paris, France	SVM HeaderParse 0.2
AUTHOR NAME	Christine Paulin-mohring	SVM HeaderParse 0.2
AUTHOR AFFIL	School of Computer Science INRIA and LIENS, URA CNRS 1327; Carnegie Mellon University Ecole Normale Superiéure	SVM HeaderParse 0.2
AUTHOR ADDR	5000 Forbes Avenue 45 Rue d’Ulm; Pittsburgh, Pennsylvania 15213 75005 Paris, France	SVM HeaderParse 0.2
ABSTRACT	We define the notion of an inductively defined type in the Calculus of Constructions and show how inductively defined types can be represented by closed types. We show that all primitive recursive functionals over these inductively defined types are also representable. This generalizes work by Böhm & Berarducci on synthesis of functions on term algebras in the second-order polymorphic λ-calculus (F2). We give several applications of this generalization, including a representation of F2-programs in F3, along with a definition of functions reify, reflect, and eval for F2 in F3. We also show how to define induction over inductively defined types and sketch some results that show that the extension of the Calculus of Construction by induction principles does not alter the set of functions in its computational fragment, Fω. This is because a proof by induction can be realized by primitive recursion, which is already definable in Fω. 1	SVM HeaderParse 0.2
YEAR	1990	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	209--228	INFERENCE
VOLUME	442	INFERENCE
CITATIONS	27 found	ParsCit 1.0