We extend the framework of Pure Type Systems with sub-typing, as found in F !. This leads to a concise description of many existing systems with subtyping, and also to some new interesting systems.â€¦ (More)

In the FTA project in Nijmegen we have formalized a constructive proof of the Fundamental Theorem of Algebra. In the formalization, we have first defined the (constructive) algebraic hierarchy ofâ€¦ (More)

We describe a framework of algebraic structures in the proof assistant Coq. We have developed this framework as part of the FTA project in Nijmegen, in which a constructive proof of the Fundamentalâ€¦ (More)

We describe a framework for algebraic expressions for the proof assistant Coq. This framework has been developed as part of the FTA project in Nijmegen, in which a complete proof of the fundamentalâ€¦ (More)

This paper investigates the notion of dialgebra, which generalises the notions of algebra and coalgebra. We show that many (co)algebraic notions and results can be generalised to dialgebras, andâ€¦ (More)

We modify the reflection method to enable it to deal with partial functions like division. The idea behind reflection is to program a tactic for a theorem prover not in the implementation languageâ€¦ (More)

This paper addresses the crucial issue in the design of a proof development system of how to deal with partial functions and the related question of how to treat undefined terms. Often the problem isâ€¦ (More)

We deene an extension of a second-order type system with records, subtyping and record concatenation. This system can model the most important concepts of object-oriented languages. The novelty inâ€¦ (More)

We present an extension of type theory with a xed point combinator Y. We are particularly interested in using this Y for doing unbounded proof search in the proof system. Therefore we treat in someâ€¦ (More)