arXiv subjects

Michael Arntzenius

Publications and source records attributed to Michael Arntzenius.

4 recordsLinked to original sources

arXiv2026

Finite Functional Programming

We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite support allows representing functions as input-output tables. Generalizing from boolean functions to other pointed sets neatly handles aggregation and weighted logic programming. We refer to the combination of finitely supported functions, represented as data, with higher order functions, represented as code, as finite functional programming. We give a simple type system to check finite support, using graded effects to check variable grounding and relevance types to model pointed sets.

cs.PL↗

arXiv2025

Fair intersection of seekable iterators

miniKanren's key semantic advance over Prolog is to implement a complete yet efficient search strategy, fairly interleaving execution between disjuncts. This fairness is accomplished by bounding how much work is done exploring one disjunct before switching to the next. We show that the same idea -- fairness via bounded work -- underlies an elegant compositional approach to implementing worst-case optimal joins using a seekable iterator interface, suitable for shallow embedding in functional languages.

cs.PL↗

arXiv2025

Stream programs are monoid homomorphisms with state

We define a broad class of deterministic stream functions and show they can be implemented as homomorphisms into a "state" monoid. The homomorphism laws are simpler than the conditions of previous semantic frameworks for stream program optimization, yet retain support for rich equational reasoning over expressive dataflow programs, including sequential composition, parallel composition, and feedback. We demonstrate this using examples of partitioned database joins, stratified negation, and a simplified model of TCP.

cs.PL↗

arXiv2024

Finite-Choice Logic Programming

Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of choices while maintaining structural and logical constraints -- there is no single canonical model. The notion of stable models for logic programs with negation has successfully captured programmer intuition about the set of valid solutions for such problems, giving rise to a family of programming languages and associated solvers known as answer set programming. Unfortunately, the definition of a stable model is frustratingly indirect, especially in the presence of rules containing free variables. We propose a new formalism, finite-choice logic programming, that uses choice, not negation, to admit multiple solutions. Finite-choice logic programming contains all the expressive power of the stable model semantics, gives meaning to a new and useful class of programs, and enjoys a least-fixed-point interpretation over a novel domain. We present an algorithm for exploring the solution space and prove it correct with respect to our semantics. Our implementation, the Dusa logic programming language, has performance that compares favorably with state-of-the-art answer set solvers and exhibits more predictable scaling with problem size.

cs.PL↗