Eager Functions as Processes

TL;DR

This paper explores how different encodings of the call-by-value lambda calculus into the pi-calculus can align behavioral equivalences, using unique solutions of equations as a key technical tool.

Contribution

It demonstrates that tuning the encoding to specific pi-calculus subcalculi aligns lambda calculus equivalences with pi-calculus behavioral equivalences, extending the technique of unique solutions of equations.

Findings

Equivalence on lambda-terms matches eager normal-form bisimilarity in specific pi-calculus encodings.

The approach extends to preorders, not just equivalences.

The paper showcases the applicability of the unique solutions of equations technique.

Abstract

We study Milner's encoding of the call-by-value $\lambda$-calculus into the $\pi$-calculus. We show that, by tuning the encoding to two subcalculi of the $\pi$-calculus (Internal $\pi$ and Asynchronous Local $\pi$), the equivalence on $\lambda$-terms induced by the encoding coincides with Lassen's eager normal-form bisimilarity, extended to handle $\eta$-equality. As behavioural equivalence in the $\pi$-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.