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Conservativity of embeddings in the lambda-Pi calculus modulo rewriting (long version)

Abstract

The lambda-Pi calculus can be extended with rewrite rules to embed any other functional pure type system. The normalization and conserva-tivity properties of the embedding is an open problem. In this paper, we show that the embedding is conservative. We define an inverse translation into a pure type system completion and show that the completion is con-servative using the reducibility method. This result further justifies the use of the lambda-Pi calculus modulo rewriting as a logical framework.
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Dates and versions

hal-01084165 , version 1 (18-11-2014)
hal-01084165 , version 2 (20-04-2015)
hal-01084165 , version 3 (20-04-2015)

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Ali Assaf. Conservativity of embeddings in the lambda-Pi calculus modulo rewriting (long version). 2015. ⟨hal-01084165v3⟩

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