We present two type systems for term graph rewriting: conventional typing and (polymorphic) uniqueness typing. The latter is introduced as a natural extension of simple algebraic and higher-order uniqueness typing. The systems are given in natural deduction style using an inductive syntax of graph denotations with familiar constructs such as let and case. The conventional system resembles tradi...

This paper is an up-to-date introduction to the problem of uniqueness versus non-uniqueness of infinite clusters for percolation on Z d and, more generally, on transitive graphs. For iid percolation on Z, uniqueness of the infinite cluster is a classical result, while on certain other transitive graphs uniqueness may fail. Key properties of the graphs in this context turn out to be amenability ...

The purpose of this article is to investigate the uniqueness of meromorphic functions sharing five small functions on annuli.

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This paper will present an analysis for detecting single uses of values in functional programs during call-by-need reduction. There are several reasons why such information can be useful. The Clean language uses a uniqueness type system for detecting single-threaded uses which allow destructive updating. Single-use information has also been proposed for compile-time garbage collection. Turner, ...

We present uniqueness typing as an extension of a familiar Curry style typing system for graph rewrite systems. This provides a method for combining purely functional programming with operations having side-eeects, while preserving the functional nature of the language. We give a technical account as well as the underlying intuition. The system is shown to be eeective in the sense that a unique...

In this paper we describe a Curry-like type system for graphs and extend it with uniqueness information to indicate that certain objects are onlyìocally accessible'. The correctness of type assignment guarantees that no external access on such an object will take place in the future. We prove that types are preserved under reduction (for both type systems) for a large class of rewrite systems. ...