Abstract
We present an extension of the λ(η)-calculus with a case construct that propagates through functions like a head linear substitution, and show that this construction permits to recover the expressiveness of ML-style pattern matching. We then prove that this system enjoys the Church-Rosser property using a semi-automatic ‘divide and conquer’ technique by which we determine all the pairs of commuting subsystems of the formalism (considering all the possible combinations of the nine primitive reduction rules). Finally, we prove a separation theorem similar to Böhm’s theorem for the whole formalism.
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Arbiser, A., Miquel, A., Ríos, A.: A λ-calculus with constructors. Available from the web pages of the authors (manuscript, 2006)
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Arbiser, A., Miquel, A., Ríos, A. (2006). A Lambda-Calculus with Constructors. In: Pfenning, F. (eds) Term Rewriting and Applications. RTA 2006. Lecture Notes in Computer Science, vol 4098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11805618_14
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DOI: https://doi.org/10.1007/11805618_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36834-2
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