Normalisation for dynamic pattern calculi

BONELLI, EDUARDO; KESNER, DELIA; LOMBARDI, CARLOS; RÍOS, ALEJANDRO

Leibniz International Proceedings in Informatics, LIPIcs

Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik

Año: 2012 vol. 15 p. 117 - 132

1868-8969

The Pure Pattern Calculus (PPC) [10, 11] extends the λ-calculus, as well as the family of algebraic pattern calculi [20, 6, 12], with first-class patterns i.e. patterns can be passed as arguments, evaluated and returned as results. The notion of matching failure of PPC in [11] not only provides a mechanism to define functions by pattern matching on cases but also supplies PPC with parallel-or-like, non-sequential behaviour. Therefore, devising normalising strategies for PPC to obtain well-behaved implementations turns out to be challenging. This paper focuses on normalising reduction strategies for PPC. We define a (multistep) strategy and show that it is normalising. The strategy generalises the leftmost-outermost strategy for λ-calculus and is strictly finer than parallel-outermost. The normalisation proof is based on the notion of necessary set of redexes, a generalisation of the notion of needed redex encompassing non-sequential reduction systems. © Eduardo Bonelli, Delia Kesner, Carlos Lombardi, and Alejandro Ríos.