Results 1  10
of
11
Proving and Disproving Termination of HigherOrder Functions
 IN: PROC. 5TH FROCOS
, 2005
"... The dependency pair technique is a powerful modular method for automated termination proofs of term rewrite systems (TRSs). We present two important extensions of this technique: First, we show how to prove termination of higherorder functions using dependency pairs. To this end, the dependency ..."
Abstract

Cited by 62 (20 self)
 Add to MetaCart
(Show Context)
The dependency pair technique is a powerful modular method for automated termination proofs of term rewrite systems (TRSs). We present two important extensions of this technique: First, we show how to prove termination of higherorder functions using dependency pairs. To this end, the dependency pair technique is extended to handle (untyped) applicative TRSs. Second, we introduce a method to prove nontermination with dependency pairs, while up to now dependency pairs were only used to verify termination. Our results lead to a framework for combining termination and nontermination techniques for firstand higherorder functions in a very flexible way. We implemented and evaluated our results in the automated termination prover AProVE.
Orderings and Constraints: Theory and Practice of proving termination
"... Abstract. In contrast to the current general way of developing tools for proving termination automatically, this paper intends to show an alternative program based on using on the one hand the theory of term orderings to develop powerful and widely applicable methods and on the other hand constraint ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
Abstract. In contrast to the current general way of developing tools for proving termination automatically, this paper intends to show an alternative program based on using on the one hand the theory of term orderings to develop powerful and widely applicable methods and on the other hand constraint based techniques to put them in practice. In order to show that this program is realizable a constraintbased framework is presented where ordering based methods for term rewriting, including extensions like AssociativeCommutative rewriting, ContextSensitive rewriting or HigherOrder rewriting, as well as the use of rewriting strategies, can be put in practice in a natural way. 1
Higherorder termination: From kruskal to computability
 In 13th International Conf. on Logic for Programming, Artificial Intelligence, and Reasoning. Lecture Notes in Computer Science
"... Termination is a major question in both logic and computer science. In logic, termination is at the heart of proof theory where it is usually called strong normalization (of cut elimination). In computer science, termination has always been an important issue for showing programs correct. ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Termination is a major question in both logic and computer science. In logic, termination is at the heart of proof theory where it is usually called strong normalization (of cut elimination). In computer science, termination has always been an important issue for showing programs correct.
Harnessing First Order Termination Provers Using Higher Order Dependency Pairs
, 2011
"... Many functional programs and higher order term rewrite systems contain, besides higher order rules, also a significant first order part. We discuss how an automatic termination prover can split a rewrite system into a first order and a higher order part. The results are applicable to all common sty ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
Many functional programs and higher order term rewrite systems contain, besides higher order rules, also a significant first order part. We discuss how an automatic termination prover can split a rewrite system into a first order and a higher order part. The results are applicable to all common styles of higher order rewriting with simple types, although some dependency pair approach is needed to use them.
The recursive path and polynomial ordering for firstorder and higherorder terms
 Journal submission
"... higherorder terms? ..."
(Show Context)
The recursive path and polynomial ordering∗
"... In most termination tools two ingredients, namely recursive path orderings (RPO) and polynomial interpretation orderings (POLO), are used in a consecutive disjoint way to solve the final constraints generated from the termination problem. We present a simple ordering that combines both RPO and POLO ..."
Abstract
 Add to MetaCart
In most termination tools two ingredients, namely recursive path orderings (RPO) and polynomial interpretation orderings (POLO), are used in a consecutive disjoint way to solve the final constraints generated from the termination problem. We present a simple ordering that combines both RPO and POLO and defines a family of orderings that includes both, and extends them with the possibility of having, at the same time, an RPOlike treatment for some symbols and a POLOlike treatment for the others. The ordering is extended to higherorder terms, providing an automatable use of polynomial interpretations in combination with betareduction. 1
Semantic Labelling for Proving Termination of Combinatory Reduction Systems
"... Abstract. We give a novel transformation method for proving termination of higherorder rewrite rules in Klop’s format called Combinatory Reduction System (CRS). The format CRS essentially covers the usual pure higherorder functional programs such as Haskell. Our method called higherorder semant ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We give a novel transformation method for proving termination of higherorder rewrite rules in Klop’s format called Combinatory Reduction System (CRS). The format CRS essentially covers the usual pure higherorder functional programs such as Haskell. Our method called higherorder semantic labelling is an extension of a method known in the theory of term rewriting. This attaches semantics of the arguments to each function symbol. We systematically define the labelling by using the complete algebraic semantics of CRS, Σmonoids. We also examine the power of higherorder semantic labelling by several examples. This includes an interesting example from the viewpoint of functional programming. 1
Semantic Labelling for Termination of Combinatory Reduction Systems
"... Abstract. We give a method of proving termination of Klop’s higherorder rewriting format, combinatory reduction system (CRS). Our method called higherorder semantic labelling is an extension of Zantema’s semantic labelling for firstorder term rewriting systems. We systematically define the label ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We give a method of proving termination of Klop’s higherorder rewriting format, combinatory reduction system (CRS). Our method called higherorder semantic labelling is an extension of Zantema’s semantic labelling for firstorder term rewriting systems. We systematically define the labelling by using the complete algebraic semantics of CRS. 1
Proving Termination of ACrewriting without Extended Rules
"... Polynomial interpretations and RPOlike orderings allow one to prove termination of Associative and Commutative (AC)rewriting by only checking the rules of the given rewrite system without considering the socalled extended rules. However, these methods have important limitations as termination ..."
Abstract
 Add to MetaCart
Polynomial interpretations and RPOlike orderings allow one to prove termination of Associative and Commutative (AC)rewriting by only checking the rules of the given rewrite system without considering the socalled extended rules. However, these methods have important limitations as termination proving tools.
Languages—Algebraic approaches to semantics, Denotational semantics, Operational Semantics General Terms Theory, Languages
"... We give a novel transformation for proving termination of higherorder rewrite systems in the format of Inductive Data Type Systems (IDTSs) by Blanqui, Jouannaud and Okada. The transformation called higherorder semantic labelling attaches algebraic semantics of the arguments to each function symbol ..."
Abstract
 Add to MetaCart
(Show Context)
We give a novel transformation for proving termination of higherorder rewrite systems in the format of Inductive Data Type Systems (IDTSs) by Blanqui, Jouannaud and Okada. The transformation called higherorder semantic labelling attaches algebraic semantics of the arguments to each function symbol. We systematically define the labelling and show that labelled systems give termination models in the framework of Fiore, Plotkin and Turi’s binding algebras. As applications, we give simple proofs of termination of the explicit substitution system λX and currying transformation via higherorder semantic labelling. Moreover, we prove a new result of modularity of termination of IDTSs by introducing the notion of solid IDTSs. We prove that termination is preserved under the disjoint union of an IDTS and a higherorder program scheme. Categories and Subject Descriptors F.4.2 [Grammars and