arXiv subjects

Constantine Theocharis

Publications and source records attributed to Constantine Theocharis.

2 recordsLinked to original sources

arXiv2026

Type Theory With Erasure

Erasure enriches type theory with a distinction between runtime relevant and irrelevant data, allowing the compilation step to safely erase the latter. Versions of this feature are implemented by many systems, including Agda, Idris, and Rocq. We present a structural version of type theory with erasure, formulated as a second-order generalised algebraic theory (SOGAT). Erasure is encoded as a phase distinction between runtime and erased terms, in the form of a proposition that can appear in a context. This formulation has several advantages: it has models based on categories with families, is compatible with other structural features such as staging, and provides a better guideline for implementation. Through the model theory of SOGATs, we study the semantics of type theory with erasure in families of sets, which generalises to any Grothendieck topos equipped with a tiny proposition. We establish conservativity over Martin-Löf type theory (MLTT) in both phases. For code extraction, we construct a presheaf model that produces untyped lambda calculus programs and prove its correctness through gluing. Our results are formalised in Agda and we provide a toy elaborator implementation.

cs.PL↗

arXiv2025

Custom Representations of Inductive Families

Inductive families provide a convenient way of programming with dependent types. Yet, when it comes to compilation, their default linked-tree runtime representations, as well as the need to convert between different indexed views of the same data, can lead to unsatisfactory runtime performance. In this paper, we introduce a language with dependent types, and inductive families with customisable representations. Representations are a version of Wadler's views, refined to inductive families like in Epigram, but with compilation guarantees: a represented inductive family will not leave any runtime traces behind, without relying on heuristics such as deforestation. This way, we can build a library of convenient inductive families based on a minimal set of primitives, whose re-indexing and conversion functions are erased during compilation. We show how we can express optimisation techniques such as representing Nat-like types as GMP-style big integers, without special casing in the compiler. With dependent types, reasoning about data representations is also possible through a provided modality. This yields computationally irrelevant isomorphisms between the original and represented data.

cs.PL↗