On Irrelevance and Algorithmic Equality in Predicative Type Theory

Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been put forward. We consider Pfenning's type theory with irre...

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Veröffentlicht in:Logical methods in computer science Jg. 8, Issue 1
Hauptverfasser: Abel, Andreas, Scherer, Gabriel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Logical Methods in Computer Science e.V 01.01.2012
Schlagworte:
computer science - logic in computer science
computer science - programming languages
f.4.1
ISSN:1860-5974, 1860-5974
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Abstract Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been put forward. We consider Pfenning's type theory with irrelevant quantification which is compatible with a type-based notion of equality that respects eta-laws. We extend Pfenning's theory to universes and large eliminations and develop its meta-theory. Subject reduction, normalization and consistency are obtained by a Kripke model over the typed equality judgement. Finally, a type-directed equality algorithm is described whose completeness is proven by a second Kripke model.
AbstractList Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To separate static and dynamic code, several static analyses and type systems have been put forward. We consider Pfenning's type theory with irrelevant quantification which is compatible with a type-based notion of equality that respects eta-laws. We extend Pfenning's theory to universes and large eliminations and develop its meta-theory. Subject reduction, normalization and consistency are obtained by a Kripke model over the typed equality judgement. Finally, a type-directed equality algorithm is described whose completeness is proven by a second Kripke model.
Author Abel, Andreas
Scherer, Gabriel
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Snippet Dependently typed programs contain an excessive amount of static terms which are necessary to please the type checker but irrelevant for computation. To...
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SubjectTerms computer science - logic in computer science
computer science - programming languages
f.4.1
Title On Irrelevance and Algorithmic Equality in Predicative Type Theory
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