NDLI: Logical relations for a logical framework

Content Provider	ACM Digital Library
Author	Rabe, Florian Sojakova, Kristina
Copyright Year	2013
Abstract	Logical relations are a central concept used to study various higher-order type theories and occur frequently in the proofs of a wide variety of meta-theorems. Besides extending the logical relation principle to more general languages, an important research question has been how to represent and thus verify logical relation arguments in logical frameworks. We formulate a theory of logical relations for Dependent Type Theory (DTT) with β η-equality which guarantees that any valid logical relation satisfies the Basic Lemma. Our definition is syntactic and reflective in the sense that a relation at a type is represented as a DTT type family but also permits expressing certain semantic definitions. We use the Edinburgh Logical Framework (LF) incarnation of DTT and implement our notion of logical relations in the type-checker Twelf. This enables us to formalize and mechanically decide the validity of logical relation arguments. Furthermore, our implementation includes a module system so that logical relations can be built modularly. We validate our approach by formalizing and verifying several syntactic and semantic meta-theorems in Twelf. Moreover, we show how object languages encoded in DTT can inherit a notion of logical relation from the logical framework.
Starting Page	1
Ending Page	34
Page Count	34
File Format	PDF
ISSN	15293785
e-ISSN	1557945X
DOI	10.1145/2536740.2536741
Volume Number	14
Issue Number	4
Journal	ACM Transactions on Computational Logic (TOCL)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2013-11-28
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	LF Logical relation Twelf Dependent type theory Logical framework Module system Parametricity
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Logic Computational Mathematics Computer Science

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