Builtin Types Viewed as Inductive Families

Abstract State of the art optimisation passes for dependently typed languages can help erase redundant information typical invariant-rich data structures and programs. These automated processes do not dramatically change structure data, even though more efficient representations could be available. Using Quantitative Type Theory as implemented in Idris 2, we demonstrate how to define an invariant-rich, typechecking-time packing runtime representation together with irrelevant invariants. The compiler then aggressively all such invariants during compilation. Unlike other approaches, complexity resulting is entirely predictable, require both have same structure, yet are able seamlessly program if were using high-level structure.