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.Comment: Ph.D. dissertation. Accepted by the University of California, Santa
Cruz, in March 2014. 278 pages (295 including frontmatter
