# Spacetime Programming: A Synchronous Language for Composable Search Strategies

## TL;DR

This paper introduces spacetime programming, a new synchronous language extension for composing and implementing search strategies in constraint solvers, improving modularity and practical performance.

## Contribution

It presents the design, semantics, and proofs of spacetime programming, enabling deterministic and reactive composition of search strategies with a prototype compiler.

## Key findings

- Spacetime programs are deterministic and reactive.
- Prototype compiler produces strategies with low overhead.
- Enhances compositionality in constraint-based search strategies.

## Abstract

Search strategies are crucial to efficiently solve constraint satisfaction problems. However, programming search strategies in the existing constraint solvers is a daunting task and constraint-based languages usually have compositionality issues. We propose spacetime programming, a paradigm extending the synchronous language Esterel and timed concurrent constraint programming with backtracking, for creating and composing search strategies. In this formalism, the search strategies are composed in the same way as we compose concurrent processes. Our contributions include the design and behavioral semantics of spacetime programming, and the proofs that spacetime programs are deterministic, reactive and extensive functions. Moreover, spacetime programming provides a bridge between the theoretical foundations of constraint-based concurrency and the practical aspects of constraint solving. We developed a prototype of the compiler that produces search strategies with a small overhead compared to the hard-coded ones.