Eager Functions as Processes

Abstract

We study Milner's encoding of the call-by-value λ-calculus into the π-calculus. We show that, by tuning the encoding to two subcalculi of the π-calculus (Internal π and Asynchronous Local π), the equivalence on λ-terms induced by the encoding coincides with Lassen's eager normal-form bisimilarity, extended to handle η-equality. As behavioural equivalence in the π-calculus we consider contextual equivalence and barbed congruence. We also extend the results to preorders. A crucial technical ingredient in the proofs is the recently-introduced technique of unique solutions of equations, further developed in this paper. In this respect, the paper also intends to be an extended case study on the applicability and expressiveness of the technique.

Using Pi-Calculus Names as Locks

“…The way ≈ w is defined should allow us to combine locks with other programming constructs in order to reason about programs featuring locks and, e.g., functions, continuations, and references. Work in this direction will build on [19,23,5,8,21].…”

“…We show that the corresponding programming discipline in the π-calculus induces a notion of behavioural equivalence between processes, which can be used to reason about processes manipulating locks. This approach has been followed to analyse several disciplines for the usage of π-calculus names: linearity [15], receptiveness [25], locality [16], internal mobility [24], functions [23,5], references [7,21].…”

Effectful Normal Form Bisimulation

“…An elementary proof of congruence properties of eager normal form bisimilarity is given in [9], where Lassen's relational construction [37] is extended to the call-by-value λ-calculus, as well as its extensions with delimited and abortive control operators. Finally, following [65], eager normal form bisimilarity has been recently characterised as the equivalence induced by a suitable encoding of the (call-by-value) λ-calculus in the π-calculus [21].…”

Eager Functions as Processes (long version)

“…This paper is an extended version of [8]. We provide here detailed proofs which were either absent or only sketched in [8], notably for: the soundness of the encoding into Iπ (Sections 4.2 and 4.3, Appendix C), completeness of the same encoding (Section 4.4), the unique solution technique for contextual relations and preorders (Section 6.2, Appendix E), as well as some more details about the full abstraction proofs for contextual preorders (Section 6.3) and the encoding into ALπ (Section 5.2). We also include more detailed discussions along the paper, notably about Milner's encoding (Section 3), the encoding into Iπ (Section 4.1), and the encoding into ALπ (Section 5.1).…”