Executable Refinement Types

TL;DR

This dissertation develops executable refinement types that enhance structural types with semi-decidable predicates, providing new theoretical insights and practical tools for undecidable type systems, including a hybrid type checker and a prototype implementation.

Contribution

It introduces a comprehensive framework for executable refinement types, including type soundness, hybrid checking, a decidable reconstruction algorithm, and a prototype implementation.

Findings

Type soundness and logical relation established for executable refinement types

Hybrid type checking outperforms static approximations in some cases

Decidable type reconstruction algorithm implemented in Sage

Abstract

This dissertation introduces executable refinement types, which refine structural types by semi-decidable predicates, and establishes their metatheory and accompanying implementation techniques. These results are useful for undecidable type systems in general. Particular contributions include: (1) Type soundness and a logical relation for extensional equivalence for executable refinement types (though type checking is undecidable); (2) hybrid type checking for executable refinement types, which blends static and dynamic checks in a novel way, in some sense performing better statically than any decidable approximation; (3) a type reconstruction algorithm - reconstruction is decidable even though type checking is not, when suitably redefined to apply to undecidable type systems; (4) a novel use of existential types with dependent types to ensure that the language of logical formulae is closed under type checking (5) a prototype implementation, Sage, of executable refinement types such that all dynamic errors are communicated back to the compiler and are thenceforth static errors.