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A Modular Type-Checking Algorithm for Type Theory with Singleton Types and
 

Summary: A Modular Type-Checking Algorithm for
Type Theory with Singleton Types and
Proof Irrelevance
Andreas Abel1
, Thierry Coquand2
, and Miguel Pagano3
1
Ludwig-Maximilians-Universit¨at M¨unchen, abel@informatik.uni-muenchen.de
2
G¨oteborg University, coquand@cs.chalmers.se
3
Universidad Nacional de C´ordoba, miguel.pagano@gmail.com
Abstract. We define a logical framework with singleton types and one
universe of small types. We give the semantics using a PER model; it is
used for constructing a normalisation-by-evaluation algorithm. We prove
completeness and soundness of the algorithm; and get as a corollary the
injectivity of type constructors. Then we give the definition of a correct
and complete type-checking algorithm for terms in normal form. We
extend the results to proof-irrelevant propositions.
1 Introduction and Related Work

  

Source: Abel, Andreas - Theoretische Informatik, Ludwig-Maximilians-Universität München

 

Collections: Computer Technologies and Information Sciences