A token-passing net implementation of optimal reduction with embedded read-back

In this paper, we introduce a new interaction net implementation of optimal reduction for pure untyped lambda calculus. Unlike others, our implementation allows to reach normal form regardless of interaction net reduction strategy using the approach of so-called token-passing nets. Another new feature is the read-back mechanism also implemented without leaving the formalism of interaction nets.

💡 Research Summary

The paper presents a novel interaction‑net implementation of optimal reduction for the pure untyped λ‑calculus that is based on token‑passing nets and incorporates a built‑in read‑back mechanism. Traditional optimal reduction techniques, such as Lamping’s algorithm and its later interaction‑net formulations, typically require a specific reduction strategy to avoid disconnected sub‑nets; otherwise the net may get stuck before reaching normal form. The authors overcome this limitation by introducing a “waiting” construct and a non‑deterministic agent Amb, allowing the net to block unnecessary β‑redexes until they are explicitly needed, regardless of the reduction order.

The core of the system is an extended signature Σ_W = Σ_O ∪ {Call, Eval, Wait, Hold, Decide}. Call has arity 0, Eval arity 1, and the remaining agents have arity 2. The classic interaction rule @ i