The Definition of Standard ML
Pattern Matching as Cut Elimination
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Locus Solum: From the rules of logic to the logic of rules
Mathematical Structures in Computer Science
ACM Transactions on Programming Languages and Systems (TOPLAS)
The λ-calculus with constructors: Syntax, confluence and separation
Journal of Functional Programming
Confluence of pattern-based calculi
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
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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.