Realizing Monads in Interaction Nets via Generic Typed Rules

Interaction net systems are a model of computation based on graph rewriting. They enjoy various nice properties which make them a promising basis for a functional programming language. However, mechanisms to model impure functions are indispensable for a practical language. A natural approach to achieve this goal is the systematic use of monads. Yet, specifying the appropriate monads for impure language features is hard, due to the very restricted form of basic interaction rules. What is missing in particular, are appropriate means to specify higher-order functions and some typing mechanism that restricts computations to reasonable settings. In this paper, we propose two extensions of interaction nets which solve these problems. First we extend interaction rules with generic rules, thus adding a form of higher-order functions. Moreover, we define constraints on these rules to ensure the preservation of uniform confluence. In addition, we propose a simple type system in order to appropriately restrict the matching of generic rules. Finally, we show how the combination of these features, i.e., generic typed rules, can indeed be employed to model impure functions in interaction nets via monads in an intuitive and simple manner.