This paper is dedicated to my longtime friend and colleague Roel de Vrijer on the occasion of his sixtieth birthday. With its subject I have tried to go a little in his direction by taking a very syntactic subject. The work is part of a project in progress in cooperation with Rosalie Iemhoff and Nick Vaporis. It concerns the disjunction property in… (More)
Dedicated to Roel de Vrijer on occasion of his 60th birthday.
This is the manual of the ProofWeb system that was implemented at the Radboud University Nijmegen and the Free University Amsterdam in the SURF education innovation project Web deduction for education in formal thinking.
Proof terms in term rewriting are a representation means for reduction sequences, and more in general for contraction activity, allowing to distinguish e.g. simultaneous from sequential reduction. Proof terms for finitary, first-order, left-linear term rewriting are described in , ch. 8. In a previous work  we defined an extension of the finitary… (More)
One of the main foundations for this work is the theory of countable ordinals; (citation needed) and (citation needed) are good references on this subject. We want to point out some definitions and results which are critical in order to prove some of the basic properties of infinitary proof terms. In order to deal with infinitary composition, we will need… (More)
Barendregt's Lemma in its original form is a statement on Combinatory Logic that holds also for the lambda calculus and gives important insight into the syntactic interplay between substitution and reduction. Its origin lies in undefinablity proofs, but there are other applications as well. It is connected to the so-called Square Brackets Lemma, introduced… (More)
The calculus c serves as a general framework for representing contexts. Essential features are control over variable capturing and the freedom to manipulate contexts before or after hole lling, by a mechanism of delayed substitution. The context calculus c is given in the form of an extension of the lambda calculus. Many notions of context can be… (More)
1 To all my parents 2 Acknowledgements This is the part I'm writing as the last one of this survey and it is the only part about which I'm really sure of. The work you are holding in the hands is the result of the eeort that Roel de Vrijer and Jan Willem Klop did, while supervising me in doing my thesis. Roel de Vrijer and Jan Willem Klop opened the doors… (More)