Abstract. We consider an extensional version, called qmTT, of the intensional Minimal Type Theory mTT, introduced in a previous paper with G. Sambin, enriched with proof-irrelevanc...
In this paper we introduce a new approach to axiomatizing quotient types in type theory. We suggest replacing the existing monolithic rule set by a modular set of rules for a speci...
The quotient operation is a standard feature of set theory, where a set is partitioned into subsets by an equivalence relation. We reinterpret this idea for higher order logic, whe...
We present a development of Universal Algebra inside Type Theory, formalized using the proof assistant Coq. We define the notion of a signature and of an algebra over a signature. ...
In this paper we introduce a new approach to formalizing certain type operations in type theory. Traditionally, many type constructors in type theory are independently axiomatized...