Higher-order unification revisited: Complete sets of transformations
Journal of Symbolic Computation
Combinatory reduction systems: introduction and survey
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Higher-order rewrite systems and their confluence
Theoretical Computer Science - Special issue: rewriting systems and applications
Higher order unification via explicit substitutions
Information and Computation
Confluence and Superdevelopments
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
Comparing Combinatory Reduction Systems and Higher-order Rewrite Systems
HOA '93 Selected Papers from the First International Workshop on Higher-Order Algebra, Logic, and Term Rewriting
Higher-order unification and matching
Handbook of automated reasoning
Handbook of automated reasoning
A survey of strategies in rule-based program transformation systems
Journal of Symbolic Computation
A pattern matching compiler for multiple target languages
CC'03 Proceedings of the 12th international conference on Compiler construction
ESOP'06 Proceedings of the 15th European conference on Programming Languages and Systems
The rewriting calculus as a combinatory reduction system
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
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To perform higher-order matching, we need to decide the βη-equivalence on λ-terms. The first way to do it is to use simply typed λ-calculus and this is the usual framework where higher-order matching is performed. Another approach consists in deciding a restricted equivalence based on finite superdevelopments. We consider higher-order matching modulo this equivalence over untyped λ-terms for which we propose a terminating, sound and complete matching algorithm. This is in particular of interest since all second-order β-matches are matches modulo superdevelopments. We further propose a restriction to second-order matching that gives exactly all second-order matches.