Term Collections in λ and ρ-calculi

The ρ-calculus generalises term rewriting and the λ-calculus by defining abstractions on arbitrary patterns and by using a pattern-matching algorithm which is a parameter of the calculus. In particular, equational theories that do not have unique principal solutions may be used. In the latter case, all the principal solutions of a matching problem are stored in a “structure” that can also be seen as a collection of terms.Motivated by the fact that there are various approaches to the definition of structures in the ρ-calculus, we study in this paper a version of the λ-calculus with term collections.The contributions of this work include a new syntax and operational semantics for a λ-calculus with term collections, which is related to the λ-calculi with strict parallel functions studied by Boudol and Dezani et al. and a proof of the confluence of the β-reduction relation defined for the calculus (which is a suitable extension of the standard rule of β-reduction in the λ-calculus).