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An ordinal calculus for proving termination in term rewriting
[chapter]

1996
*
Lecture Notes in Computer Science
*

*In*this article, we are concerned with the proofs of

*termination*of

*rewrite*systems by the method of interpretations. ... As the corresponding

*ordinal*

*terms*are primitive recursively closed, we get a concise and intuitive proof

*for*the closure of the class of primitive recursive functions under these schemes. ... Introduction

*Proving*

*termination*of a

*rewrite*system means establishing the well-foundedness of the induced

*rewrite*ordering. ...

##
###
Problems in rewriting III
[chapter]

1995
*
Lecture Notes in Computer Science
*

Many thanks to Stefan Blom

doi:10.1007/3-540-59200-8_82
fatcat:in5aspimbrbvngnrhzcm7tfwei
*for*substantial help producing this list. ...*An*interesting system*for*doing arithmetic by*rewriting*was presented*in*[24] . Unfortunately, its*termination*has not been*proved*.*Termination*of a related system is*proved**in*[103] . ...*Termination*of string-*rewriting*systems is known to be undecidable [49] .*Termination*of a single*term*-*rewriting*rule was*proved*undecidable*in*[32; 64] . ...##
###
Inductive-data-type systems

2002
*
Theoretical Computer Science
*

*In*a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the last two authors presented a combined language made of a (strongly normalizing) algebraic

*rewrite*system and a typed lambda-

*calculus*... This result provides a computation model

*for*the combination of

*an*algebraic specification language based on abstract data types and of a strongly typed functional language with strictly positive inductive ...

*In*the sequel, we assume the reader familiar with the notions of λ-

*calculus*and

*term*

*rewriting*, as presented

*in*[4]

*for*the simply-typed λ-

*calculus*, [16]

*for*

*term*

*rewriting*and [31, 39, 49]

*for*the ...

##
###
Higher-Order Termination: From Kruskal to Computability
[chapter]

2006
*
Lecture Notes in Computer Science
*

*In*computer science,

*termination*has always been

*an*important issue

*for*showing programs correct. ...

*In*the sixties, Tait invented a new method

*for*showing cut elimination of natural deduction, based on a predicate over the set of

*terms*, such that the membership of

*an*expression to the predicate implied ... The above rule-schemas define a

*rewrite*system which is known to be

*terminating*, a result

*proved*

*in*Section 3. ...

##
###
Page 3883 of Mathematical Reviews Vol. , Issue 97F
[page]

1997
*
Mathematical Reviews
*

{

*For*the entire collection see MR 97f:68005. } 97f:68086 68Q42 03D55 Cichon, E. A.; Touzet, H.*An**ordinal**calculus**for**proving**termination**in**term**rewriting*. ... We then*prove*that*for*typeable*rewrite*systems satisfying a general scheme*for*re- cursive definitions, every typeable*term*has*an*approximant of the same type. ...##
###
More problems in rewriting
[chapter]

1993
*
Lecture Notes in Computer Science
*

How can

doi:10.1007/3-540-56868-9_39
fatcat:cibthhywyrgmvcsv73tryp3v2e
*termination*orderings*for**term**rewriting*be adapted to cover those cases*in*which graph*rewriting*is*terminating*although*term**rewriting*is not? Problem 7'5 (D. Plump). ...*An*interesting system*for*doing arithmetic by*rewriting*was presented*in*[Cohen and Watson, 1991] . Unfortunately, its*termination*has not been*proved*. Problem 66 (F. Baader, K. Schulz [1992] ). ...##
###
Open problems in rewriting
[chapter]

1991
*
Lecture Notes in Computer Science
*

-J. de Vries

doi:10.1007/3-540-53904-2_120
fatcat:bsnbx2vghrc2tmv6xcywwijbjq
*for*helping prepare this list, and Ron Book,*for*going out of his way t o m a k e it possible. ... Can strong normalization*termination*of the typed lambda*calculus*be*proved*by a reasonably straightforward mapping from typed*terms*to a well-founded ordering? ... egx; y Trans nite 0 -induction is required*for*a proof of*termination*. Must any*termination*ordering have the Howard*ordinal*as its order type, as conjectured*in*18 ? Problem 24. ...##
###
Termination of algebraic type systems: The syntactic approach
[chapter]

1997
*
Lecture Notes in Computer Science
*

*In*14], they

*prove*that the combination of the polymorphic -

*calculus*{system F{ with the curried version of a

*terminating*rst-order

*term*

*rewriting*system is

*terminating*. ... The proof consists of extending a

*termination*model of the

*term*

*rewriting*system to a

*termination*model

*for*simply typed -

*calculus*. ...

##
###
Foreword

1999
*
Theoretical Computer Science
*

Pinto provides a confluent and weakly normalizing

doi:10.1016/s0304-3975(98)00133-9
fatcat:ea62itnvanbttcep6sq5qojv5y
*rewriting*system*for**terms*representing cut-free sequent*calculus*derivations. ...*Termination*of Permutative Conversions*in*Intuitionistic Gentzen Calculi by H. Schwichtenberg*proves*the result stated*in*the title by referring to a I-*calculus*with explicit substitution. ...##
###
Termination and Confluence of Higher-Order Rewrite Systems
[chapter]

2000
*
Lecture Notes in Computer Science
*

*In*Section 4, we adapt the General Schema to this new

*calculus*and

*prove*

*in*Section 5 that the

*rewrite*systems that follow this schema are strongly normalizing (every reduction sequence is nite). ... It appears that most of the known approaches can be obtained by using

*an*appropriate substitution

*calculus*. ... Jouannaud

*for*their suggestions and remarks on previous versions of this paper. I also thank the anonymous referees

*for*their useful comments. ...

##
###
Zenon Modulo: When Achilles Outruns the Tortoise Using Deduction Modulo
[chapter]

2013
*
Lecture Notes in Computer Science
*

The theory of deduction modulo is

doi:10.1007/978-3-642-45221-5_20
fatcat:oovkbtnk7vaztfia4h7cjpdreq
*an*extension of predicate*calculus*, which allows us to*rewrite**terms*as well as propositions, and which is well suited*for*proof search*in*axiomatic theories, as it turns ... Finally, we describe*an*additional backend*for*Zenon that outputs proof certificates*for*Dedukti, which is a proof checker based on the λΠ-*calculus*modulo. ⋆ This work is supported by the BWare project ... Jouvelot*for*their detailed comments on this paper, to G. Burel*for*helpful discussions, and to the Deducteam Inria research team*for*the many interactions. ...##
###
An on-line problem database
[chapter]

1998
*
Lecture Notes in Computer Science
*

*For*the current proceedings, the main subjects were

*Term*

*rewriting*systems Symbolic and algebraic computation Uni cation and matching Completion techniques String and graph

*rewriting*Conditional and typed ...

*rewriting*

*Rewriting*-based theorem

*proving*Parallel

*rewriting*and deduction Constrained

*rewriting*and deduction Constraint s o l v i n g Higher-order

*rewriting*Lambda calculi Functional and logic programming ...

*Termination*of a single

*term*-

*rewriting*rule was

*proved*undecidable

*in*16,38 . ...

##
###
A Type-Based Termination Criterion for Dependently-Typed Higher-Order Rewrite Systems
[chapter]

2004
*
Lecture Notes in Computer Science
*

We extend these works to general

doi:10.1007/978-3-540-25979-4_2
fatcat:fptdfpb4rfctzm6t2tcr5thl4y
*rewriting*and dependent types, hence providing a powerful*termination*criterion*for*the combination of*rewriting*and β-reduction*in*the*Calculus*of Constructions. ... Several authors devised type-based*termination*criteria*for*ML-like languages allowing non-structural recursive calls. ... I thank Ralph Matthes*for*having invited me*in*Münich*in*February 2002, Andreas Abel*for*his useful comments on a previous version of this work (his technical report [2] and the discussions we had*in*...##
###
Highlights in infinitary rewriting and lambda calculus

2012
*
Theoretical Computer Science
*

We present some highlights from the emerging theory of infinitary

doi:10.1016/j.tcs.2012.08.018
fatcat:ulhkxwoambaj3pjimztxxlz6jm
*rewriting*, both*for*first-order*term**rewriting*systems and λ-*calculus*. ... We present a recent observation concerning the continuity of infinitary*rewriting*.*In*the second section we present*an*excursion to the infinitary λ-*calculus*. ...*For*finite*rewrite*sequences σ , the argument*for**termination*of this procedure is precisely as*in*[36] . ...##
###
Page 7467 of Mathematical Reviews Vol. , Issue 94m
[page]

1994
*
Mathematical Reviews
*

Also, the decidability of the existence of

*an*equivalent ground*term**rewriting*system and some other results are*proved*.” ... This paper considers the order type of*termination*orderings as they relate to the complexity of*term**rewriting*systems: specifically, they consider order types which are*ordinals*. ...
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