Finite Functional Programming

2026-04-28

AI Summary

This work proposes a novel programming paradigm that unifies functional and logic programming to support aggregation and weighted logical reasoning. The core idea models predicates as functions with finite support, represented via input–output tables. By integrating higher-order functions, a graded effect system, and relevance types, the approach guarantees variable grounding and computational finiteness. This framework naturally generalizes logic languages such as Datalog, enabling uniform treatment of both Boolean and non-Boolean logic programs. Furthermore, it provides a concise type system that effectively verifies the finite-support property, thereby establishing a formal foundation for weighted and aggregate reasoning.

Abstract

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.

Problem

• functional programming
• logic programming
• finite support
• Datalog
• pointed sets

Innovation

• finite support
• functional logic programming
• pointed sets
• graded effects
• relevance types