TY - GEN
T1 - Normalisation for dynamic pattern calculi
AU - Bonelli, Eduardo
AU - Kesner, Delia
AU - Lombardi, Carlos
AU - Ríos, Alejandro
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Neededness
KW - Pattern calculi
KW - Reduction strategies
KW - Sequentiality
UR - http://www.scopus.com/inward/record.url?scp=84880220243&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84880220243&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.RTA.2012.117
DO - 10.4230/LIPIcs.RTA.2012.117
M3 - Conference contribution
AN - SCOPUS:84880220243
SN - 9783939897385
T3 - Leibniz International Proceedings in Informatics, LIPIcs
SP - 117
EP - 132
BT - 23rd International Conference on Rewriting Techniques and Applications, RTA 2012
T2 - 23rd International Conference on Rewriting Techniques and Applications, RTA 2012
Y2 - 30 May 2012 through 1 June 2012
ER -