POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Handbook of theoretical computer science (vol. B)
The geometry of optimal lambda reduction
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Handbook of logic in computer science (vol. 2)
Intersection type assignment systems
Selected papers of the thirteenth conference on Foundations of software technology and theoretical computer science
Rank 2 intersection type assignment in term rewriting
Fundamenta Informaticae
Normalization results for typeable rewrite systems
Information and Computation
Information and Computation
Interaction nets and term-rewriting systems
Theoretical Computer Science - Special issue: trees in algebra and programming
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Partial Intersection Type Assignment in Applicative Term Rewriting Systems
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Graph Notation for Concurrent Combinators
TPPP '94 Proceedings of the International Workshop on Theory and Practice of Parallel Programming
Une Extension de la Theorie des Types en lambda-Calcul
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
From Term Rewriting to Generalised Interaction Nets
PLILP '96 Proceedings of the 8th International Symposium on Programming Languages: Implementations, Logics, and Programs
CONCUR '93 Proceedings of the 4th International Conference on Concurrency Theory
From Action Calculi to Linear Logic
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Simple Type Inference for Term Graph Rewriting Systems
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Polymorphic Intersection Type Assignment for Rewrite Systems with Abstractions and beta-Rule
TYPES '99 Selected papers from the International Workshop on Types for Proofs and Programs
Realizing impure functions in interaction nets
ICGT'10 Proceedings of the 5th international conference on Graph transformations
Realizing monads in interaction nets via generic typed rules
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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Interaction nets have proved to be a useful tool for the study of computational aspects of various formalisms (e.g. λ-calculus, term rewriting systems), but they are also a programming paradigm in themselves, and this is actually how they were introduced by Lafont. In this paper we consider semi-simple interaction nets as a programming language, and present a type assignment system using intersection types. First we show that interactions preserve types (i.e., the system enjoys subject reduction), and we compare this type assignment system with the intersection systems for λ-calculus and term rewriting systems. Then we define a recursion scheme that ensures termination of all interaction sequences. By relaxing the scheme and using the type assignment system, we derive another sufficient condition for termination of interaction nets. Finally, we show that although the type system based on general intersection types is not decidable, its restriction to rank 2 types is, and we give an algorithm that computes principal types for nets.