Uniqueness typing and affine (or linear) typing are dual type systems. Uniqueness gives a guarantee that an term has not been shared, while affinity imposes a restriction that a term may not be shared. We show that we can unify both concepts through polymorphism.

We present two systems for rst-order typing of graph expressions, in natural deduction style: conventional typing and (polymorphic) uniqueness typing. In both type systems, typing is preserved during evaluation, and types can be determined eeectively.

this paper uses the tsuji’s characteristic to investigate the uniqueness of transcen- dental meromorphic function with shared values in an angular domain dealing with the multiple values which improve a result of j. zheng.

this paper is devoted to the proof of the unique solvability ofthe inverse problems for second-order differential operators withregular singularities. it is shown that the potential functioncan be determined from spectral data, also we prove a uniquenesstheorem in the inverse problem.

‎We consider the uniqueness problem of algebroid functions‎ ‎on an angular domain‎. ‎Several theorems are established to extend the uniqueness theory of meromorphic functions to algebroid functions‎.

Uniqueness typing can be used to add side effects to a functional programming language without losing referential transparency. Unfortunately uniqueness types often involve implications between uniqueness attributes, which complicates type inference and incorporating modern extensions such as arbitrary rank types. In this paper we show how to avoid these difficulties by recoding attribute inequ...

A topological approach of determining the best one out of four solutions of the Hermitian interpolation problem for quintic Pythagorean hodograph curves is presented. An existence theorem is proved together with complete analysis of uniqueness/nonuniqueness properties. A simple formula of obtaining the best solution without using any curve fairing or curvature integral is also presented.

There is a longstanding conjecture, due to Gregory Cherlin and Boris Zilber, that all simple groups of finite Morley rank are simple algebraic groups. One of the major theorems in the area is Borovik’s trichotomy theorem. The ‘trichotomy’ here is a case division of the generic minimal counterexamples within odd type, that is, groups with a large and divisible Sylow◦ 2-subgroup. The so-called ‘u...

We present a new approach to implementing arrays in a pure lazy functional programming language. The arrays can be updated destructively by using uniqueness typing, and the elements can be unboxed. We describe the implementation of these arrays in the functional programming language Clean 1.1. The performance of two sorting algorithms and a fast fourier transformation written in Clean using arr...