895 search results - page 1 / 179 » Type theory in type theory using quotient inductive types |
CIE
2007
Springer
13 years 10 months ago
2007
Springer
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...
TPHOL
2002
IEEE
13 years 9 months ago
2002
IEEE
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...
TPHOL
2005
IEEE
13 years 10 months ago
2005
IEEE
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...
TPHOL
1999
IEEE
13 years 8 months ago
1999
IEEE
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. ...
ENTCS
2006
13 years 4 months ago
2006
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...