Ties between Parametrically Polymorphic Type Systems and Finite Control Automata

TL;DR

This paper explores the deep connections between parametrically polymorphic type systems and finite control automata, revealing optimal results, new insights, and potential applications in software engineering beyond fluent API generation.

Contribution

It establishes a formal correspondence and bisimulation between polymorphic type systems and various finite automata, providing new theoretical results and practical implications.

Findings

Two recent results on fluent API generation are shown to be optimal.

New results on the studied type systems are presented.

Potential software engineering applications are identified.

Abstract

We present a correspondence and bisimulation between variants of parametrically polymorphic type systems and variants of finite control automata, such as FSA, PDA, tree automata and Turing machine. Within this correspondence we show that two recent celebrated results on automatic generation of fluent API are optimal in certain senses, present new results on the studied type systems, formulate open problems, and present potential software engineering applications, other than fluent API generation, which may benefit from judicious use of type theory.