Full abstraction in the lazy lambda calculus
Information and Computation
On the adequacy of graph rewriting for simulating term rewriting
ACM Transactions on Programming Languages and Systems (TOPLAS)
Transfinite reductions in orthogonal term rewriting systems
Information and Computation
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
Non-existent Statman's double fixed point combinator does not exist, indeed
Information and Computation
Lambda calculus with explicit recursion
Information and Computation
Descendants and origins in term rewriting
Information and Computation - Special issue on RTA-98
Term Rewriting Systems
Infinitary Lambda Calculi and Böhm Models
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Some philosophical issues concerning theories of combinators
Proceedings of the Symposium on Lambda-Calculus and Computer Science Theory
Applications of Plotkin-terms: partitions and morphisms for closed terms
Journal of Functional Programming
Infinitary rewriting: meta-theory and convergence
Acta Informatica
Infinitary combinatory reduction systems
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Infinitary rewriting: from syntax to semantics
Processes, Terms and Cycles
EQUATIONAL TERM GRAPH REWRITING
Fundamenta Informaticae
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Simple models for recursive schemes
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Recursive schemes, krivine machines, and collapsible pushdown automata
RP'12 Proceedings of the 6th international conference on Reachability Problems
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We present an introduction to infinitary lambda calculus, highlighting its main properties. Subsequently we give three applications of infinitary lambda calculus. The first addresses the non-definability of Surjective Pairing, which was shown by the first author not to be definable in lambda calculus. We show how this result follows easily as an application of Berry's Sequentiality Theorem, which itself can be proved in the setting of infinitary lambda calculus. The second pertains to the notion of relative recursiveness of number-theoretic functions. The third application concerns an explanation of counterexamples to confluence of lambda calculus extended with non-left-linear reduction rules: Adding non-left-linear reduction rules such as @dxx-x or the reduction rules for Surjective Pairing to the lambda calculus yields non-confluence, as proved by the second author. We discuss how an extension to the infinitary lambda calculus, where Bohm trees can be directly manipulated as infinite terms, yields a more simple and intuitive explanation of the correctness of these Church-Rosser counterexamples.