Type theory in type theory using quotient inductive typesTools Altenkirch, Thorsten and Kaposi, Ambrus (2016) Type theory in type theory using quotient inductive types. In: POPL '16 The 43rd Annual ACM SIGPLANSIGACT Symposium on Principles of Programming Languages, 2022 January 2016, St Petersburg, Florida, United States of America.
Official URL: http://dl.acm.org/citation.cfm?doid=2837614.2837638
AbstractWe present an internal formalisation of a type heory with dependent types in Type Theory using a special case of higher inductive types from Homotopy Type Theory which we call quotient inductive types (QITs). Our formalisation of type theory avoids referring to preterms or a typability relation but defines directly well typed objects by an inductive definition. We use the elimination principle to define the settheoretic and logical predicate interpretation. The work has been formalized using the Agda system extended with QITs using postulates.
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