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Combinatory Reduction Systems: Introduction and Survey
Perpetual Reductions in Lambda-Calculus
This paper surveys a part of the theory ofs-reduction in?-calculus which might aptly be calledperpetual reductions. The theory is concerned withperpetual reduction strategies, i.e., reduction
Teaching logic using a state-of-the-art proof assistant
TLDR
The system ProofWeb is currently being developed in Nijmegen and Amsterdam for teaching logic to undergraduate computer science students, based on the higher order proof assistant Coq, and is made available to the students through an interactive web interface.
Comparing Combinatory Reduction Systems and Higher-order Rewrite Systems
TLDR
It is concluded that as far as rewrite theory is concerned, Combinatory Reduction Systems and Higher-Order Rewrite Systems are equivalent, the only difference being that Combinatories Reduction Systems employ a more ‘lazy’ evaluation strategy.
On normalisation
Using a characterisation of strongly normalising $\lambda$-terms, we give new and simple proofs of the following: all developments and superdevelopments are finite, a certain rewrite strategy is
Weak Orthogonality Implies Confluence: The Higher Order Case
In this paper we prove confluence for weakly orthogonal Higher-Order Rewriting Systems. This generalises all the known ‘confluence by orthogonality’ results.
Higher-Order Rewriting
TLDR
It is proved on one hand that natural intersection type preorders induces natural λ-structures, and on the other hand thatnatural λ -structures admits presentations through intersectiontype preorders.
A Higher-Order Iterative Path Ordering
TLDR
An iterative version of HORPO is presented by means of an auxiliary term rewriting system, following an approach originally due to Bergstra and Klop, and well-foundedness of the iterative definition is studied.
Lambda-Calculus and Combinators, An Introduction, 2nd Edition, J. Roger Hindley and Jonathan P. Seldin, Cambridge University Press, 2008. Hardback, ISBN 9780521898850
  • F. Raamsdonk
  • Mathematics
    Theory and Practice of Logic Programming
  • 1 March 2009
TLDR
This book is the second edition of the classical book Introduction to Combinators and λ-calculus by the same authors, and it gives a clear and well-written presentation of untyped λ -calculus and CL, typed versions of both systems, and their model theory.
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