Publications of Fer-Jan de Vries
-
A. Kurz, D. Petrisan,
P. Severi and F.J. de Vries.
An Alpha-Corecursion Principle
for the Infinitary Lambda Calculus
to appear in proceedings of CMCS 2012: the 11th International Workshop on Coalgebraic Methods in Computer Science.
31 March - 1 April 2012, Tallinn, Estonia.
pdf
Abstract Gabbay and Pitts proved that lambda-terms up to alpha-equivalence constitute an initial algebra for a certain endofunctor on
the category of nominal sets. We show that the terms of the infinitary
lambda-calculus form the final coalgebra for the same functor. This allows us to give a corecursion principle for alpha-equivalence classes of
finite and infinite terms. As an application, we give corecursive definitions of substitution and of infinite normal forms (Bohm, Levy-Longo
and Berarducci trees).
-
P. Severi and F.J. de Vries.
Weakening the Axiom of Overlap in
Infinitary Lambda Calculus
in proceedings of RTA2011: the 22nd International Conference on
Rewriting Techniques and Applications. Editor Manfred Schmidt-Schauß. Novi
Sad. May 30 - June 1, 2011. Leibniz International
Proceedings in Informatics (LIPIcs) volume 10. Pages 313--328.
pdf
Abstract In this paper we present a set of necessary and sufficient conditions on a set of lambda terms
to serve as the set of meaningless terms in an infinitary bottom extension of lambda calculus.
So far only a set of sufficient conditions was known for choosing a suitable set of meaningless
terms to make this construction produce confluent extensions. The conditions covered the three
main known examples of sets of meaningless terms. However, the much later construction of
many more examples of sets of meaningless terms satisfying the sufficient conditions renewed the
interest in the necessity question and led us to reconsider the old conditions.
The key idea in this paper is an alternative solution for solving the overlap between beta
reduction and bottom reduction. This allows us to reformulate the Axiom of Overlap, which now
determines together with the other conditions a larger class of sets of meaningless terms. We
show that the reformulated conditions are not only sufficient but also necessary for obtaining a
confluent and normalizing infinitary lambda beta bottom calculus. As an interesting consequence
of the necessity proof we obtain for infinitary lambda calculus with beta and bot reduction that
confluence implies normalization.
-
P. Severi and F.J. de Vries.
Decomposing the Lattice of Meaningless Sets
in the Infinitary Lambda Calculus
in proceedings of WoLLIC 2011, Logic, Language, Information and Computation -
18th International Workshop, Philadelphia, PA, USA, May 18-20, 2011. Editors
Lev D. Beklemishev and Ruy de Queiroz. SLNAI 6642, pages 210-227, 2011.
pdf
Abstract The notion of a meaningless set has been defined for infinitary lambda calculus axiomatically. Standard examples of meaningless
sets are sets of terms that have no head normal form, the set of terms
without weak head normal form and the set of rootactive terms. The
collection of meaningless sets is a lattice. In this paper, we study the
way this lattices decompose as union of more elementary key intervals.
We also analyse the distribution of the sets of meaningless terms in the
lattice by selecting some sets as key vertices and study the cardinality in
the intervals between key vertices. As an application, we prove that the
lattice of meaningless sets is neither distributive nor modular. Interest-
ingly, the example translates into a counterexample that the lattice of
lambda theories is not modular.
-
J.R. Kennaway, P. Severi, M.R. Sleep, and F.J. de Vries.
Infinite rewriting: from syntax to semantics,
in proceedings of Processes, Terms and Cycles: Steps on the Road to
Infinity: Essays dedicated to Jan Willem Klop on the Occasion of
His 60th Birthday, editors: A. Middeldorp, V. van Oostrom,
F. van Raamsdonk and R. de Vrijer. SLNCS 3838, pages 148-172, 2005.
pdf
-
P. Severi and F.J. de Vries.
Separability of infinite lambda terms
in proceedings of the LCTTNL Workshop: The
second workshop on Lambda Calculus, Type Theory and Natural
Language, King's College London, 12th September 2005. Page 1-12.
pdf
Abstract Infinite lambda calculi extend finite lambda
calculus with infinite terms and transfinite reduction.
In this paper we extend some classical results of finite lambda calculus
to infinite terms.
First we extend to infinite terms is
B\"ohm Theorem which states the
separability of two finite $\beta \eta$-normal forms.
Next we extend to infinite terms is
the equivalence of
the prefix relation up to infinite eta expansions and
the contextual preorder that observes
head normal forms.
Finally we
prove that the theory given
by
equality of $\infty \eta$-B\"ohm trees
is the
largest theory induced by
the confluent and normalising
infinitary lambda calculi extending the calculus of
B\"ohm trees.
-
P. Severi and F.J. de Vries.
Order Structures on Böhm-like Models
Conference paper in Luke Ong, editor, Computer Science Logic: 19th
International Workshop, CSL 2005, 14th Annual Conference of the
EACSL, Oxford, UK. August 22-25, 2005.
(Lecture Notes
in Computer Science 3634), Springer-Verlag. Page 103-116. 2005.
dvi, ps and pdf
Abstract
We are interested in the question whether the models
induced by the infinitary lambda calculus are orderable,
that is whether they have a partial order with a least element
making the context operators monotone.
The first natural candidate is the
prefix relation: a prefix of a term is obtained
by replacing some subterms by $\bot$.
We prove that six models
induced by the
infinitary lambda calculus (which includes
Böhm and Lévy-Longo trees)
are orderable by the prefix relation.
The following two orders we consider are the compositions of
the prefix relation with either transfinite $\eta$-reduction or
transfinite $\eta$-expansion.
We prove that these orders make the context operators of
the $\eta$-Böhm trees and the $\infty \eta$-Böhm trees monotone.
The model of Berarducci trees is not monotone with respect
to the prefix relation. However, somewhat
unexpectedly, we found that the Berarducci trees are orderable
by a new order related to the prefix relation
in which subterms are not replaced by $\bot$
but by a lambda term $\Ogreterm$ called the ogre
which devours all its inputs.
The proof of this uses simulation and coinduction.
Finally, we show that there are
$2^c$ unorderable models induced by the infinitary
lambda calculus where $c$ is the cardinality of the continuum.
P. Severi and F.J. de Vries.
Continuity and Discontinuity in Lambda Calculus
Conference paper in Pawel Urzyczyn, editor, Typed Lambda Calculus and
Applications, Proceedings of the 7th International Conference,
TLCA 2005,
Nara Japan, April 21-23 2005. (Lecture Notes
in Computer Science 3461), Springer-Verlag. Page 369-385. 2005.
dvi, ps and pdf
Abstract
This paper studies continuity of the normal form and the
context operators as functions in the infinitary
lambda calculus. We consider the
Scott topology on the cpo of the finite and infinite terms
with the prefix relation.
We prove that the only continuous parametric trees
are Böhm and Lévy-Longo trees.
We also prove a general statement: if the normal form
function is continuous then so is the model induced
by the normal form; as well as the
converse for parametric trees.
This allows us to deduce that
the only continuous models induced by the
parametric trees
are the ones of Böhm and Lévy-Longo trees.
As a first application, we prove that there is an injective embedding
from the infinitary lambda calculus of the infinite eta-Böhm
trees in D-infinity.
As a second application,
we study the relation between
the Scott topology on the prefix relation and
the tree topologies.
This allows us to prove that the only
parametric tree topologies in which all context
operators are continuous and the approximation property holds
are the ones of Böhm and
Lévy-Longo.
As a third application, we give an explicit characterisation
of the open sets of the Böhm and Lévy-Longo tree topologies.
J.R. Kennaway and F.J. de Vries.
Infinitary Rewriting.
Chapter 12 in Terese, editor, Term Rewriting
Systems (Cambridge Tracts in Theoretical Computer Science
55), Cambridge University Press. Page 668-711. 2003. Erratum.
dvi, ps and pdf
Abstract
In this chapter we will give the basic
definitions and properties of infinite terms and infinite reduction
sequences, for both term rewrite systems and the lambda calculus.
We will then study confluence properties in orthogonal systems,
which turns out to be significantly more complicated than in the
finitary case. In general, these systems are only confluent up to
an identification of a certain class of terms. The breakdown of
confluence leads us to consider the concept of a meaningless term,
which further suggests a link with the lambda-calculus concept of
Böhm reduction, and to denotational semantics for
TRSs.
M. Dezani-Ciancaglini, P. Severi and F.J. de Vries.
Infinitary Lambda Calculus and
Discrimination of Berarducci trees.
Theoretical Computer Science 298(2):275 - 302, 2003.
dvi, ps and pdf
Abstract We propose an extension of lambda
calculus for which the Berarducci trees equality coincides with
observational equivalence, when we observe rootstable or rootactive
behavior of terms. In one direction the proof is an adaptation of
the classical Böhm out technique. In the other direction the
proof is based on confluence for strongly converging reductions in
this extension.
P. Severi and F.J. de Vries.
An Extensional Böhm
Model.
Conference paper in Sophie Tison, editor, Rewiting Techniques and
Applications, Proceedings of the 13th International Conference,
RTA 2002, Copenhagen Denmark, July 2002. (Lecture Notes
in Computer Science 2378), Springer-Verlag. Page 159-173. 2002.
dvi, ps and pdf (15 pages)
Abstract We show the existence of an infinitary
confluent and normalising extension of the finite extensional
lambda calculus with beta and eta. Besides infinite beta reductions
also infinite eta reductions are possible in this extension, and
terms without head normal form can be reduced to bottom. As
corollaries we obtain a simple, syntax based construction of an
extensional Böhm model of the finite lambda calculus; and a
simple, syntax based proof that two lambda terms have the same
semantics in this model if and only if they have the same
eta-Böhm tree if and only if they are observationally
equivalent wrt to beta normal forms. The confluence proof reduces
confluence of beta bottom and eta via infinitary commutation and
postponement arguments to confluence of beta and bottom and
confluence of eta. We give counterexamples against confluence of
similar extensions based on the identification of the terms without
weak head normal form and the terms without top normal form
(rootactive terms) respectively.
S. van Bakel, F. Barbanera, M. Dezani-Ciancaglini, F.J. de
Vries.
Intersection Types for Lambda
Trees.
Theoretical Computer Science 272(1-2): 3-40, 2002.
ps and pdf (42 pages)
Abstract We introduce a type assignment system
which is parametric with respect to five families of trees obtained
by evaluating lambda terms (Böhm trees, Lévy-Longo trees, etc.).
then we prove, in an (almost ) uniform way that each type
assignment system fully describes the observational equivalences
induced by the corresponding tree representation of lambda trees.
More precisely, for each family of trees, two lambda terms have the
same tree if and only if they get assigned the same types in the
corresponding type assignment system.
M. Dezani-Ciancaglini, P. Severi and F.J. de Vries.
Böhm's theorem for Berarducci
trees.
In Proceedings CATS 2000 Computing: the Australasian Theory
Symposium, Canberra, Australia, February 1-2, 2000. Electronic
Notes in Theoretical Computer Science, volume 31, 24 pages,
2000.
dvi (24 pages)
J.R. Kennaway, V. van Oostrom, F.J. de Vries.
Meaningless terms in
rewriting.
Journal of Logic and Functional Programming. The MIT Press.
Article 1, 35 pages. Volume 1999.
dvi, ps and pdf (35 pages)
Abstract We present an axiomatic approach to the concept of meaninglessness in
finite and transfinite term rewriting and lambda calculus. We
justify our axioms in several ways. They can be intuitively
justified from the viewpoint of rewriting as computation. They are
shown to imply important properties of meaninglessness: genericity
of the class of meaningless terms, confluence modulo equality of
meaningless terms, the consistency of equating all
meaningless terms, and the construction of Böhm trees and models
of rewrite systems. Finally, we show that they can be easily
verified for many existing notions of meaninglessness, and easily
refuted for some notions that are known not to be good
characterisations of meaninglessness.
F. Barbanera, M. Dezani-Ciancaglini, F.J. de Vries.
Types for trees.
In Proceedings IFIP Working Conference on Programming Concepts and
Methods (PROCOMET '98), Shelter Island, New York, Chapman and
Hall, pages 6-29, 1998.
J.R. Kennaway, J.W. Klop, M.R. Sleep, F.J. de Vries.
Infinitary lambda
calculus.
Theoretical Computer Science 175(1):93-125, 1997.
dvi, ps and pdf (38 pages)
Abstract In a previous paper we have established the theory
of transfinite reduction for orthogonal term rewriting systems.
In this paper we perform the same task for the lambda calculus.
From the viewpoint of infinitary rewriting,
the Böhm model of the lambda calculus can be seen as an infinitary
term model.
In contrast to term rewriting,
there are several different possible notions of infinite term,
which give rise to different Böhm-like models,
which embody different notions of lazy or eager computation.
F.J. de Vries.
Böhm trees, bisimulations and
observations in lambda calculus.
In Proceedings of the Second Fuji International Workshop on
Functional and Logic Programming Workshop Shonan Village Center,
Japan 1-4 November 1996. Editors: T. Ida, A. Ohori and M. Takeichi.
World Scientific, Singapore, pages 230-245, 1997.
J.R. Kennaway, J.W. Klop, M.R. Sleep and F.J. de Vries.
Comparing curried and uncurried rewrite
systems.
Journal of Symbolic Computation, 21(1):15-39, 1996.
dvi, ps and pdf (25 pages)
J.R. Kennaway, V. van Oostrom, F.J. de Vries.
Meaningless terms in
rewriting.
In Proceedings of the Fifth International Conference on Algebraic
and Logic Programming Aachen (Germany), September 25-27, 1996.
Series: Lecture Notes in Computer Science 1139, Springer-Verlag,
pages 254-268, 1996.
J.R. Kennaway, J.W. Klop, M.R. Sleep, F.J. de Vries.
Infinite lambda calculus and Böhm
models.
In Proceedings Rewriting Techniques and Applications,
Kaiserslautern, 1995. Series: Lecture Notes in Computer Science
914, Springer-Verlag, pages 257-270, 1995.
J.R. Kennaway, J.W. Klop, M.R. Sleep, F.J. de Vries.
From Finite to Infinite Lambda
Calculi.
Bulletin of the section of Logic, University of Lodz, Department of
Logic (Special issue dedicated to the Workshop on Non-standard
Logics and Logical Aspects of Computer Science, Kanazawa, Japan,
Dec. 5-8. 1994, editor Hiroakira Ono), 24(1)13-20, 1995.
pdf (8 pages)
Abstract
In a previous paper we have established the theory of transfinite reduction for
orthogonal term rewriting systems. In this paper we perform the same task for
the lambda calculus. This results in several new Bohm models of the lambda
calculus and new unifying descriptions of existing models.
D.J.N van Eijck and F.J. de Vries.
Reasoning about Update
Logic.
Journal of Philosophical Logic, 24(1):19-47, 1995.
dvi, ps and pdf (19 pages)
E. Horita and F.J. de Vries. A fully abstract denotational
model for communicating processes with label-passing. In
Proceedings of Concurrency Theory and Its Application,
RIMS Kokyuroku 902, page 26-48, 1995. J.R. Kennaway, J.W. Klop, M.R. Sleep and F.J. de Vries.
Transfinite Reductions in Orthogonal Term
Rewriting Systems.
Information and Computation, 119(1):18-38, 1995.
ps and pdf (36
pages)
Abstract We define the notion of transfinite term rewriting:
rewriting in which terms may be infinitely large
and rewrite sequences may be of any ordinal length.
For orthogonal rewrite systems,
some fundamental properties known in the finite case
are extended to the transfinite case.
Among these are the Parallel Moves lemma
and the Unique Normal Form property.
The transfinite Church-Rosser property fails in general,
even for orthogonal systems,
including such well-known systems as Combinatory Logic.
Syntactic characterisations are given of some classes of orthogonal
TRSs which do satisfy the transfinite Church-Rosser property.
We also prove a weakening of the transfinite Church-Rosser property for all orthogonal systems,
in which the property is only required to hold
up to a certain equivalence relation on terms.
Finally, we extend the theory of needed reduction from the finite
to the transfinite case.
The reduction strategy of needed reduction is normalising in the finite case,
but not in the transfinite case.
To obtain a normalising strategy,
it is necessary and sufficient to add a requirement of fairness.
Parallel outermost reduction is such a strategy.
Z. Ariola, J.R. Kennaway, J.W. Klop, M.R. Sleep and F.J. de
Vries.
On defining the
undefined.
In the proceedings: TACS'94 (Theoretical Aspects of Computer
Software) International conference in Sendai. Series: Lecture Notes
in Computer Science 789, Springer-Verlag, pages 543-554,
1994.
J.R. Kennaway, J.W. Klop, M.R. Sleep and F.J. de Vries.
On the Adequacy of Graph Rewriting for
Simulating Term Rewriting.
Transactions on Programming Languages and Systems, 16(3):493-523,
1994.
ps (29 pages)
F.J. de Vries and J. Yamada.
On termination of rewriting with real
numbers.
In proceedings: Functional Programming II, JSSST'94.
Editor Masato Takeichi. Series: Lecture Notes on Software Gaku 10.
Publisher: Kindai-kagaku-sya, Tokyo. Pages 233-247, 1994.
ps (18 pages), pdf (18 pages) and Addendum (Oct 13, 2004)
J.R. Kennaway, J.W. Klop, M.R. Sleep and F.J. de Vries.
An Introduction to Term Graph
Rewriting.
Chapter 1 in M.R. Sleep, M.J. Plasmeijer and M.C. van Eekelen, editors, Term
Graph Rewriting: Theory and Practice, John Wiley ™Sons Ltd,
pages 1-13, 1993.
J.R. Kennaway, J.W. Klop, M.R. Sleep and F.J. de Vries.
An infinitary Church-Rosser property for
non-collapsing orthogonal term rewriting systems.
Chapter 4 in M.R. Sleep, M.J. Plasmeijer and
M.C. van Eekelen, editors, Term Graph Rewriting: Theory and
Practice, John Wiley ™ Sons Ltd, pages 47-59, 1993.
J.R. Kennaway, J.W. Klop, M.R. Sleep and F.J. de Vries.
Event Structures and Orthogonal Term Graph
Rewriting.
Chapter 11 in M.R. Sleep, M.J. Plasmeijer and M.C. van Eekelen, editors, Term
Graph Rewriting: Theory and Practice, John Wiley ™Sons Ltd,
pages 141-155, 1993.
J.R. Kennaway, J.W. Klop, M.R. Sleep and F.J. de Vries.
On the adequacy of graph rewriting for
simulating term rewriting.
Chapter 12 in M.R. Sleep, M.J. Plasmeijer and M.C. van Eekelen, editors, Term
Graph Rewriting: Theory and Practice, John Wiley ™ Sons Ltd,
pages 157-169, 1993.
D.J.N van Eijck and F.J. de Vries.
Dynamic interpretation and Hoare
deduction.
Journal of Logic, Language and Information, 1(1):1-44, 1992.
dvi, ps and pdf (43 pages)
D.J.N van Eijck and F.J. de Vries.
Dynamic interpretation and Hoare deduction
(Extended Abstract).
In S. Moore and A.Z. Wyner, editors, Proceedings of
Semantics and Linguistic Theory, SALT I, CLC Publications, Cornell University, Ithaca,
N.Y., 10:65-85, 1991.
J.R. Kennaway, J.W. Klop, M.R. Sleep and F.J. de Vries.
Transfinite reductions in orthogonal term
rewriting systems.
In R.V. Book, editor, Proceedings of Rewriting Techniques and
Applications, Como, Lecture Notes in computer Science 488, pages
1-12, 1991.
pdf (12 pages)
F.J. de Vries.
Type theoretical topics in topos
theory.
PhD Thesis, University of Utrecht, April 13, 1989. Supervisor Prof
D. van Dalen.
D. van Dalen and F.J. de Vries.
Intuitionistic Free Abelian
Groups.
Zeitschrift für Mathematischen Logik und Grundlagen der
Mathematik, 34(1):3-12, 1988.
F.J. de Vries.
A functional program for the Fast Fourier
Transform.
SigmaPlan Notices, 23(1):67-74, 1988.
J. Giesl, J.R, V. van Oostrom, F.J. de Vries. Strong
convergence of term rewriting using strong dependency pairs.
Extended abstract. In Proceedings of Termination Workshop, Schloss
Dagstuhl, 1999.
pdf (2 pages plus erratum)
F.J. de Vries. Projection spaces and recursive domain
equations. Information Processing Society of Japan SIG Notes. 95(114):37-38, 1995
. J.R. Kennaway, J.W. Klop, M.R. Sleep and F.J. de Vries. From
finite lambda calculus to infinite lambda calculi (abstract)
Information Processing Society of Japan, SIG Notes
94-PRG-19-6:43-50, 1994. J.R. Kennaway, J.W. Klop, M.R. Sleep and F.J. de Vries.
On comparing curried and uncurried
rewrite systems. In H.P. Barendregt, M. Bezem and J.W. Klop,
editors, Festschrift dedicated to the sixtieth anniversary of Dirk
van Dalen, Quaestiones Infinitae, Logic Series, Department of
Philosophy, University of Utrecht, pages 57-78, 1993.
P. Severi and F.J. de Vries.
A lambda calculus for
D-infinity.
Presented at the Workshop at Domain Theory held at the honour
of Dana Scott's 70th birthday.
Technical Report tr-2002-29, University of Leicester, June
2002.
dvi (10 pages),
ps (10 pages)
Abstract We define an extension of lambda
calculus which is fully abstract for Scott's D-infinity models. We
do so by constructing an infinitary lambda calculus which not only
has the confluence property, but also is normalising: every term
has its inf-eta-Böhm tree as unique normal form. The extension
incorporates a strengthened form of eta-reduction besides infinite
terms, infinite reductions and a bottom rule allowing to replace
terms without head normal form by bottom. The new eta!-reduction is
the key idea of this paper. It allows us to capture in a compact
and natural way Barendregt's complex infinite eta-operation on
Böhm trees. As a corollary we obtain a new congruence proof
for Böhm tree equivalence modulo infinite
eta-expansion.
P. Severi and F.J. de Vries.
An Extensional Böhm
Model.
In the Proceedings of RTA'02, Springer Lecture Notes in Computer Science 2378.
Technical Report tr-2002-28, University of Leicester, June
2002.
dvi (15 pages),
ps (15 pages)
Abstract We show the existence of an infinitary
confluent and normalising extension of the finite extensional
lambda calculus with beta and eta. Besides infinite beta reductions
also infinite eta reductions are possible in this extension, and
terms without head normal form can be reduced to bottom. As
corollaries we obtain a simple, syntax based construction of an
extensional Böhm model of the finite lambda calculus; and a
simple, syntax based proof that two lambda terms have the same
semantics in this model if and only if they have the same
eta-Böhm tree if and only if they are observationally
equivalent wrt to beta normal forms. The confluence proof reduces
confluence of beta, bottom and eta via infinitary commutation and
postponement arguments to confluence of beta and bottom and
confluence of eta. We give counterexamples against confluence of
similar extensions based on the identification of the terms without
weak head normal form and the terms without top normal form
(rootactive terms) respectively.
S. Byun, J.R. Kennaway, V. van Oostrom, F.J. de Vries.
Separability and translatability of
sequential term rewrite systems into the lambda
calculus.
Technical Report tr-2001-16, University of Leicester, April
2001.
dvi (35 pages),
ps (35 pages)
Abstract Orthogonal term rewrite systems do not
currently have any semantics other than syntactically-based ones
such as term models and event structures. For a functional language
which combines lambda calculus with term rewriting, a semantics is
most easily given by translating the rewrite rules into lambda
calculus and then using well-understood semantics for the lambda
calculus. We therefore study in this paper the question of which
classes of TRSs do or do not have such translations. We demonstrate
by construction that forward branching orthogonal term rewrite
systems are translatable into the lambda calculus. The translation
satisfies some strong properties concerning preservation of
equality and of some inequalities. We prove that the forward
branching systems are exactly the systems permitting such a
translation which is, in a precise sense, uniform in the right-hand
sides. Connections are drawn between translatability, sequentiality
and separability properties. Simple syntactic proofs are given of
the non-translatability of a class of TRSs, including Berry's F and
several variants of it.
J.R. Kennaway and F.J. de Vries.
Infinitary Rewriting.
Technical Report tr-2001-13, University of Leicester, March
2001.
dvi (48 pages),
ps (48 pages)
Abstract In this chapter we will give the basic
definitions and properties of infinite terms and infinite reduction
sequences, for both term rewrite systems and the lambda calculus.
We will then study confluence properties in orthogonal systems,
which turns out to be significantly more complicated than in the
finitary case. In general, these systems are only confluent up to
an identification of a certain class of terms. The breakdown of
confluence leads us to consider the concept of a meaningless term,
which further suggests a link with the lambda-calculus concept of
Böhm reduction, and to denotational semantics for
TRSs.
M. Dezani-Ciancaglini, P. Severi and F.J. de Vries.
Infinitary Lambda Calculus and
Discrimination.
Technical Report tr-2001-06, University of Leicester, February
2001.
dvi (33 pages),
ps (33 pages)
Abstract We propose an extension of lambda
calculus for which the Berarducci trees equality coincides with
observational equivalence, when we observe rootstable or rootactive
behavior of terms. In one direction the proof is an adaptation of
the classical Böhm out technique. In the other direction the
proof is based on confluence for strongly converging reductions in
this extension.
J.R. Kennaway, V. van Oostrom, F.J. de Vries. Meaningless
terms in rewriting, revised version. Technical Report: Utrecht
Universiteit, Artificial Intelligence Preprint Series No: 003, May,
1999. F. Barbanera, M. Dezani-Ciancaglini, F.J. de Vries. Types
for Trees. Technical Report: Dipartimento di Unformatica,
Universita' di Torino, 1997. J.R. Kennaway, V. van Oostrom, F.J. de Vries. Meaningless
terms in rewriting Technical Report: Vrije Universiteit,
Amsterdam, IR-418, 23 pages, January, 1997. J.R. Kennaway, J.W. Klop, M.R. Sleep, F.J. de Vries.
Infinite lambda calculus, Report CS-R9535, CWI, Amsterdam,
1995. E. Horita and F.J. de Vries. A fully abstract denotational
model for communicating processes with label-passing. ECL
Technical Report. NTT Kyoto, 1994. J.R. Kennaway, J.W. Klop, M.R. Sleep, F.J. de Vries. On
comparing curried and uncurried rewrite systems. Revised
version of Festschrift version. Report CS-R9350, CWI, Amsterdam,
1993. D.J.N. van Eijck and F.J. de Vries. Reasoning about Update
Logic, (Completely revised version of report CS-R9155), Report
CS-R9312, CWI, Amsterdam, 1993. Kennaway J.R., Klop J.W., Sleep M.R., Vries F.-J. de,
Transfinite reductions in orthogonal term rewriting systems,
Report SYS-C93-10, School of Information Systems, Univ. of East
Anglia, Norwich, England. Revised version of 17. J.R. Kennaway, J.W. Klop, M.R. Sleep, F.J. de Vries. On the
Adequacy of Graph Rewriting for Simulating Term Rewriting,
Report CS9204, CWI, Amsterdam, 1992. Similar as 10. J.R. Kennaway, J.W. Klop, M.R. Sleep, F.J. de Vries. On the
Adequacy of Graph Rewriting for Simulating Term Rewriting,
Report IR-287, Vrije Universiteit Amsterdam. D.J.N. van Eijck and F.J. de Vries. A sound and complete
calculus for Update Logic, report CS-R9155, CWI, Amsterdam,
1991. J.R. Kennaway, J.W. Klop, M.R. Sleep, F.J. de Vries. Event
structures and orthogonal term graph rewriting, in M.J.
Plasmeijer and M.R. Sleep, editors, Sema Graph '91, Part II,
Technical Report 91-25, Department of Informatics, University of
Nijmegen, 1991. J.R. Kennaway, J.W. Klop, M.R. Sleep, F.J. de Vries. Finite
orthogonal graph rewriting is adequate for rational orthogonal term
rewriting, in M.J. Plasmeijer and M.R. Sleep, editors, Sema
Graph '91, Part I, Technical Report 91-25, Department of
Informatics, University of Nijmegen, 1991. D.J.N. van Eijck and F.J. de Vries. Dynamic interpretation
and Hoare deduction, report CS-R9115, CWI, Amsterdam,
1991. J.R. Kennaway, J.W. Klop, M.R. Sleep, F.J. de Vries. An
infinitary Church-Rosser property for non-collapsing orthogonal
term rewriting systems, report CS-R9043, CWI, Amsterdam,
1990. J.R. Kennaway, J.W. Klop, M.R. Sleep, F.J. de Vries.
Transfinite reductions in orthogonal term rewriting systems
(Extended abstract), report CS-R9042, CWI, Amsterdam,
1990. J.R. Kennaway, J.W. Klop, M.R. Sleep, F.J. de Vries.
Transfinite reductions in orthogonal term rewriting systems
(Full version) , report CS-R9041, CWI, Amsterdam, 1990.
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pdf (47 pages)
A. Ponse and F.J. de Vries. Strong completeness for Hoare
Logics of Recursive Processes: an infinitary approach, report
CS-R8957, CWI, Amsterdam, 1989. F.J. de Vries. Applications of constructive logic to sheaf
constructions in toposes, Logic Group Preprint Series No. 25,
Department of Philosophy, University of Utrecht, October 1987. F.J. de Vries. A functional program for Gaussian
elimination, Logic Group Preprint Series No. 23, Department of
Philosophy, University of Utrecht. September 1987. F.J. de Vries. A functional program for the Fast Fourier
Transform, Logic Group Preprint Series No. 19, Department of
Philosophy, University of Utrecht, April 1987. D. van Dalen and F.J. de Vries. Intuitionistic Free Abelian
Groups, Logic Group Preprint Series No. 7, Department of
Philosophy, University of Utrecht, April 1986. F.J. de Vries. Type theory with a geometric modality and
extensions of the reals, Preprint 340, Mathematical Institute,
University of Utrecht, June 1984.
Review of Algebra in a localic topos, with applications to
ring theory by F.Borceux and G. van den Bossche, Nov 1985,
Mededelingen van het Wiskundig Genootschap. Review of Antimorphic action by W.H. Cornish, 1988,
Mededelingen van het Wiskundig Genootschap. Review of Graph-grammars and their application to computer
science by H.Ehrig, e.a. (eds), 1990, Informatie. Review of Cartesian closed categories of domains by A.
Jung, 1990, Mededelingen van het Wiskundig Genootschap.
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