Interaction Nets¶
Compute by replacing principal-port-connected pairs of fixed-arity graph agents with interface-preserving local nets under a one-rule-per-agent-pair discipline, so distinct redexes are disjoint and reductions are strongly confluent by construction.
Core Idea¶
Interaction nets are a restricted graph-rewriting model of computation introduced by Yves Lafont. A program state is a port graph whose vertices are labeled agents. Every agent has exactly one distinguished principal port and a fixed number of auxiliary ports determined by its symbol. Computation occurs only when two agents meet principal port to principal port, forming an active pair. A rule replaces that pair with another net while preserving all connections by which the pair met the surrounding graph.
Scope of Application¶
The core scope is theoretical computer science: graph rewriting, models of computation, declarative programming, functional-language implementation, linear logic, and parallel reduction. Interaction nets can serve as a high-level visual programming formalism or as a low-level target into which another calculus is compiled. Their interface-preserving rules support compositional construction; their explicit resource agents expose copying and erasure; and their local steps map naturally to pointer-rewiring implementations.
Clarity¶
A candidate is an interaction-net system only if all of these questions have satisfactory answers:
- What is the signature, and what fixed arity belongs to each agent symbol? 2. Which port is the unique principal port of every agent occurrence? 3. Are edges linear—at most one edge incident to each port—and which free ports form the interface? 4. Does rewriting trigger only on principal–principal active pairs?
Manages Complexity¶
Interaction nets manage rewriting complexity by making critical overlap impossible at the primitive level. In a general rewrite system, proving confluence may require enumerating and joining critical pairs. Here the one-principal-port restriction prevents one agent from participating in two active pairs, while the one-rule-per-symbol-pair restriction removes ambiguity at a redex. The calculus obtains local diamond behavior from representation design rather than a global theorem proved separately for each program.
Abstract Reasoning¶
Redex-independence inference. If two applicable active pairs are distinct, they share no agent. Their one-step reductions commute. An evaluator may schedule either first or execute both in parallel without changing the joined semantic state.
Unique-normal-form inference. Strong confluence implies at most one normal form when one is reachable. It does not prove that reduction terminates, that a normal form exists, or that a scheduler will reach it under an unfair strategy.
Knowledge Transfer¶
Literal transfer occurs among interaction-net systems with different signatures. Arithmetic agents, lambda-calculus agents, linear-logic connectives, universal interaction combinators, process-network nodes, and implementation-oriented instructions preserve the same one-principal-port, active-pair, unique-rule, interface-preserving rewrite skeleton. The domain vocabulary changes while the model of computation remains identical.
Transfer also occurs between graphical and textual presentations. A name can represent a wire, a term can represent an agent tree rooted at a port, and an equation can connect two roots.
Relationships to Other Abstractions¶
Current abstraction Interaction Nets Domain-specific
Parents (1) — more general patterns this builds on
-
Interaction Nets is a kind of Network Prime
The proposed direct parent is live
prime:network.
Hierarchy path (1) — routes to 1 parentless root
- Interaction Nets → Network → Reservoir-Flux Network → Conservation Laws → Invariance
Neighborhood in Abstraction Space¶
Interaction Nets sits in a sparse region of the domain-specific corpus (94th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (1565 abstractions)
Nearest neighbors
- Activity Diagram — 0.77
- Interface segregation principle — 0.77
- Multi-User Dungeon — 0.77
- Assembloid — 0.77
- NAND Logic — 0.76
Computed from structural-signature embeddings · 2026-09-08