Combining generic judgments with recursive definitions

Combining generic judgments with recursive definitions

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by Andrew Gacek , Dale Miller , Gopalan Nadathur

Venue:	in "23th Symp. on Logic in Computer Science", F. PFENNING (editor), IEEE Computer Society Press, 2008, p. 33–44, http://www.lix.polytechnique.fr/Labo/Dale.Miller/papers/lics08a.pdf US
Citations:	11 - 2 self

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Datum	Value	Source
TITLE	Combining generic judgments with recursive definitions	SVM HeaderParse 0.2
AUTHOR NAME	Andrew Gacek	SVM HeaderParse 0.2
AUTHOR AFFIL	Department of CS&E; University of Minnesota	SVM HeaderParse 0.2
AUTHOR NAME	Dale Miller	SVM HeaderParse 0.2
AUTHOR AFFIL	INRIA Saclay- Île-de-France; & LIX/École polytechnique	SVM HeaderParse 0.2
AUTHOR NAME	Gopalan Nadathur	SVM HeaderParse 0.2
AUTHOR AFFIL	Department of CS&E; University of Minnesota	SVM HeaderParse 0.2
ABSTRACT	Many semantical aspects of programming languages are specified through calculi for constructing proofs: consider, for example, the specification of structured operational semantics, labeled transition systems, and typing systems. Recent proof theory research has identified two features that allow direct, logic-based reasoning about such descriptions: the treatment of atomic judgments as fixed points (recursive definitions) and an encoding of binding constructs via generic judgments. However, the logics encompassing these two features have thus far treated them orthogonally. In particular, they have not contained the ability to form definitions of object-logic properties that themselves depend on an intrinsic treatment of binding. We propose a new and simple integration of these features within an intuitionistic logic enhanced with induction over natural numbers and we show that the resulting logic is consistent. The pivotal part of the integration allows recursive definitions to define generic judgments in general and not just the simpler atomic judgments that are traditionally allowed. The usefulness of this logic is illustrated by showing how it can provide elegant treatments of object-logic contexts that appear in proofs involving typing calculi and arbitrarily cascading substitutions in reducibility arguments.	SVM HeaderParse 0.2
VENUE	in "23th Symp. on Logic in Computer Science", F. PFENNING (editor), IEEE Computer Society Press, 2008, p. 33–44, http://www.lix.polytechnique.fr/Labo/Dale.Miller/papers/lics08a.pdf US	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
CITATIONS	23 found	ParsCit 1.0