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Report on the programming language Haskell: a non-strict, purely functional language version 1.2
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A call-by-need lambda calculus
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The Definition of Standard ML
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The Longest Perpetual Reductions in Orthogonal Expression Reduction Systems
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Weak Orthogonality Implies Confluence: The Higher Order Case
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Orthogonal Higher-Order Rewrite Systems are Confluent
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
A Lambda-Calculus `a la de Bruijn with Explicit Substitutions
PLILPS '95 Proceedings of the 7th International Symposium on Programming Languages: Implementations, Logics and Programs
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STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
A de Bruijn Notation for Higher-Order Rewriting
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
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RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
A Weak Calculus with Explicit Operators for Pattern Matching and Substitution
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Polynomial Time Termination and Constraint Satisfaction Tests
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
Confluence and Superdevelopments
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
Optimal Normalization in Orthogonal Term Rewriting Systems
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
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RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
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ALP '97-HOA '97 Proceedings of the 6th International Joint Conference on Algebraic and Logic Programming
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CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
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Expression Reduction Systems is a formalism for higher-order rewriting, extending Term Rewriting Systems and the lambda-calculus. Here we give an overview of results in the literature concerning ERSs. We review confluence, normalization and perpetuality results for orthogonal ERSs. Some of these results are extended to orthogonal conditional ERSs. Further, ERSs with patterns are introduced and their confluence is discussed. Finally, higher-order rewriting is translated into equational first-order rewriting. The technique develops an isomorphic model of ERSs with variable names, based on de Bruijn indices.