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The λ-calculus with constructors: Syntax, confluence and separation

Published online by Cambridge University Press:  14 September 2009

Departamento de Computación – Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina (e-mail:
PPS & Université Paris 7 – Case 7014, 2 Place Jussieu, 75251 PARIS Cedex 05, France (e-mail:
Departamento de Computación – Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina (e-mail:
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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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