arXiv subjects

Barry Jay

Publications and source records attributed to Barry Jay.

3 recordsLinked to original sources

arXiv2026

Simple Types for Polymorphic Functions

This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be hidden by abstract types, such as list types and function types. Even without any quantified types, it supports polymorphism beyond that of the Hindley-Milner type system that underpins functional programming, and an effective type inference algorithm. Also, the simplicity of the formalism should make other static program analyses easier.

cs.LO↗

arXiv2014

Confusion in the Church-Turing Thesis

The Church-Turing Thesis confuses numerical computations with symbolic computations. In particular, any model of computability in which equality is not definable, such as the lambda-models underpinning higher-order programming languages, is not equivalent to the Turing model. However, a modern combinatory calculus, the SF-calculus, can define equality of its closed normal forms, and so yields a model of computability that is equivalent to the Turing model. This has profound implications for programming language design.

cs.LO↗

arXiv2014

A Concurrent Pattern Calculus

Concurrent pattern calculus (CPC) drives interaction between processes by comparing data structures, just as sequential pattern calculus drives computation. By generalising from pattern matching to pattern unification, interaction becomes symmetrical, with information flowing in both directions. CPC provides a natural language to express trade where information exchange is pivotal to interaction. The unification allows some patterns to be more discriminating than others; hence, the behavioural theory must take this aspect into account, so that bisimulation becomes subject to compatibility of patterns. Many popular process calculi can be encoded in CPC; this allows for a gain in expressiveness, formalised through encodings.

cs.LO↗