Record types are an important tool for programming and are essential in objectoriented calculi. Dependent record types are proven to be very useful for program specification and verification. Unfortunately, all known embedding of the dependent record type in the type theory had some imperfections. In this paper we present a new type constructor, dependent intersection, i.e., the intersection of two types, where the second type may depend on elements of the first one (do not confuse it with the intersection of a family of types). This new type constructor allows us to define dependent records in a very simple way.

Abstract. In this paper we show how to extend a constructive type theory with a principle that captures the spirit of Markov’s principle from constructive recursive mathematics. Markov’s principle is especially useful for proving termination of specific computations. Allowing a limited form of classical reasoning we get more powerful resulting system which remains constructive and valid in the standard constructive semantics of a type theory. We also show that this principle can be formulated and used in a propositional fragment of a type theory.

MetaPRL is the latest system to come out of over twenty five years of research by the Cornell PRL group. While initially created at Cornell, MetaPRL is currently a collaborative project involving several universities in several countries. The MetaPRL system combines the properties of an interactive LCF-style tactic-based proof assistant, a logical framework, a logical programming environment, and a formal methods programming toolkit. MetaPRL is distributed under an open-source license and can be downloaded from http://metaprl.org/. This paper provides an overview of the system focusing on the features that did not exist in the previous generations of PRL systems.

In this thesis we explore the question of how to represent programming data structures in a constructive type theory. The basic data structures in programing languages are records and objects. Most known papers treat such data structure as primitive. That is, they add new primitive type constructors and supporting axioms for records and objects. This approach is not satisfactory. First of all it complicates a type theory a lot. Second, the validity of the new axioms is not easily established. As we will see the naive choice of axioms can lead to contradiction even in the simplest cases. We will show that records and objects can be defined in a powerful enough type theory. We will also show how to use these type constructors to define abstract data structure. BIOGRAPHICAL SKETCH Alexei Kopylov was born in Moscow State University on April 2, 1974. His parents were students in the Department of Mathematics and Mechanics there. First year of his life Alexei lived in a student dormitory in the main building of the Moscow State University. Then his parents moved to Chernogolovka, a cozy scientific town near Moscow. Alexei returned to Moscow State University as a student in 1991. Five years later he graduated from the Department of Mathematics and Mechanics and entered the graduate school of the same Department.

This document contains a listing of most of the MetaPRL logical theories. It is generated automatically on a daily basis. To get the latest version, go to

Abstract. General purpose theorem provers provide sophisticated proof methods, but lack some of the advanced structuring mechanisms found in specification languages. This paper builds on previous work extending the theorem prover Isabelle with such mechanisms. A way to build the quotient type over a given base type and an equivalence relation on it, and a generalised notion of folding over quotiented types is given as a formalised high-level step called a design tactic. The core of this paper are four axiomatic theories capturing the design tactic. The applicability is demonstrated by derivations of implementations for finite multisets and finite sets from lists in Isabelle. 1