Normal Higher-Order Termination
TL;DR: The termination proof methods based on reduction orderings are extended to higher-order rewriting systems based on higher- order pattern matching and a weakly polymorphic, algebraic extension of Church’s simply typed λ-calculus is accommodated.
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Abstract: We extend the termination proof methods based on reduction orderings to higher-order rewriting systems based on higher-order pattern matching. We accommodate, on the one hand, a weakly polymorphic, algebraic extension of Church’s simply typed λ-calculus and, on the other hand, any use of eta, as a reduction, as an expansion, or as an equation. The user’s rules may be of any type in this type system, either a base, functional, or weakly polymorphic type.
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Citations
Term Rewriting Systems
Enno Ohlebusch
- 01 Jan 2002
TL;DR: This chapter presents the basic concepts of term rewriting that are needed in this book and suggests several survey articles that can be consulted.
964
Polymorphic Rewrite Rules: Confluence, Type Inference, and Instance Validation
Makoto Hamana
- 09 May 2018
TL;DR: A new framework of polymorphic rewrite rules having predicates to restrict their instances is presented, suitable for formulating and analysing fundamental calculi of programming languages.
9
Polymorphic computation systems: Theory and practice of confluence with call-by-value
TL;DR: A new framework of polymorphic computation rules that can accommodate a distinction between values and non-values is presented, suitable for analysing fundamental calculi of programming languages and implemented in the automated confluence checking tool PolySOL.
7
•Posted Content
Modular Termination for Second-Order Computation Rules and Application to Algebraic Effect Handlers
TL;DR: A new modular proof method of termination for second-order computation is presented, and its implementation SOL.l is reported, which shows that the tool SOLl is effective to solve higher-order termination problems.
•Journal Article
On Dependency Pair Method for Proving Termination of Higher-Order Rewrite Systems(Computation and Computational Models)
TL;DR: In this paper, the authors extend the dependency pair technique for proving termination of higher-order rewrite systems and introduce a new notion of dependency forest that characterize infinite reductions and infinite R-chains.
1
References
CHAPTER 6 – Rewrite Systems
Nachum Dershowitz
- 01 Jan 1990
TL;DR: In this paper, the authors focus on rewrite systems, which are directed equations used to compute by repeatedly replacing sub-terms of a given formula with equal terms until the simplest form possible is obtained.
1.6K
Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems: Abstract Properties and Applications to Term Rewriting Systems
TL;DR: This paper gives new results, and presents old ones, concerning ChurchRosser theorems for rewrmng systems, depending solely on axioms for a binary relatton called reduction, and how these criteria yield new methods for the mechanizaUon of equattonal theories.
1.2K
Term Rewriting Systems
Enno Ohlebusch
- 01 Jan 2002
TL;DR: This chapter presents the basic concepts of term rewriting that are needed in this book and suggests several survey articles that can be consulted.
964
Orderings for term-rewriting systems☆
TL;DR: Methods of proving that a term-rewriting system terminates are presented, based on the notion of "simplification orderings", orderings in which any term that is homeomorphically embeddable in another is smaller than the other.
740
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