Time refinement in a functional synchronous language

Mandel, Louis; Pasteur, Cédric; Pouzet, Marc

doi:10.1016/j.scico.2015.07.002

Cited by 5 publications

(7 citation statements)

References 8 publications

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“…Particularly recent relevant work to us is the research on time refinement [42], causality analysis [8], constructive semantics [44], and the work of Adrien Guatto [30]. Indeed, Guatto's work is quite close in spirit to our proposal, as he introduces a synchronous language with integer clocks, while most of his metatheory is based on techniques developed in the functional programming community, such as step indexing [3,12,46].…”

Section: Related Workmentioning

confidence: 88%

The w-calculus: a synchronous framework for the verified modelling of digital signal processing algorithms

Arias

Jouvelot

Ribstein³

et al. 2021

Proceedings of the 9th ACM SIGPLAN International Workshop on Functional Art, Music, Modelling, and Design

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We introduce the W-calculus, an extension of the call-byvalue λ-calculus with synchronous semantics, designed to be flexible enough to capture different implementation forms of Digital Signal Processing algorithms, while permitting a direct embedding into the Coq proof assistant for mechanized formal verification. In particular, we are interested in the different implementations of classical DSP algorithms such as audio filters and resonators, and their associated high-level properties such as Linear Time-invariance.We describe the syntax and denotational semantics of the W-calculus, providing a Coq implementation. As a first application of the mechanized semantics, we prove that every program expressed in a restricted syntactic subset of W is linear time-invariant, by means of a characterization of the property using logical relations. This first semantics, while convenient for mechanized reasoning, is still not useful in practice as it requires re-computation of previous steps. To improve on that, we develop an imperative version of the semantics that avoids recomputation of prior stream states. We empirically evaluate the performance of the imperative semantics using a staged interpreter written in OCaml, which, for an input program in W , produces a specialized OCaml program, which is then fed to the optimizing OCaml compiler. The approach provides a convenient path from the high-level semantical description to low-level efficient code.

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Section: Related Workmentioning

confidence: 88%

The w-calculus: a synchronous framework for the verified modelling of digital signal processing algorithms

Arias

Jouvelot

Ribstein³

et al. 2021

Proceedings of the 9th ACM SIGPLAN International Workshop on Functional Art, Music, Modelling, and Design

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“…Furthermore, a natural extension of spacetime is to reify the queue inside the language itself instead of relying on the host language. The key idea of this extension is to merge the time hierarchy of synchronous languages [14,24] and the space hierarchy induced by deep guards in logic programming [18] and Oz computation spaces [43]. First-class queue will allow users to program restart-based search strategies directly in spacetime instead of partly relying on the host language.…”

Section: Discussionmentioning

confidence: 99%

“…The lifting to sequence of universes is inspired by ReactiveML [24]. The reaction rules are defined in Figure 4.…”

Section: Semantics Across Instantsmentioning

confidence: 99%

Spacetime Programming: A Synchronous Language for Composable Search Strategies

Talbot

2019

Preprint

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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.

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“…Our universe extension synthesizes time hierarchy from synchronous programming and spatial hierarchy from logic programming. Time hierarchies were first developed in Quartz [GBS13] and ReactiveML [Pas13,MPP15] to execute a process on a faster time scale. They propose that in one instant of the global clock, we can execute more than one local step of a process.…”

Section: Hierarchy In Spacetime With Universesmentioning

confidence: 99%

Spacetime programming: a synchronous language for constraint search

Talbot

2023

Constraints

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Constraint programming is a paradigm for computing with mathematical relations named constraints. It is a declarative approach to describe many real-world problems including scheduling, vehicles routing, biology and musical composition. Constraint programming must be contrasted with procedural approaches that describe how a problem is solved, whereas constraint models describe what the problem is. The part of how a constraint problem is solved is left to a general constraint solver. Unfortunately, there is no solving algorithm efficient enough to every problem, because the search strategy must often be customized per problem to attain reasonable efficiency. This is a daunting task that requires expertise and good understanding on the solver's intrinsics. Moreover, higher-level constraint-based languages provide limited support to specify search strategies.In this dissertation, we tackle this challenge by designing a programming language for specifying search strategies. The dissertation is constructed around two axes: (i) a novel theory of constraint programming based on lattice theory, and (ii) a programming language, called spacetime programming, building on lattice theory for its data structures and on synchronous programming for its computational model.The first part formalizes the components of inference and search in a constraint solver. This allows us to scrutinize various constraint-based languages through the same underlying foundations. In this respect, we give the semantics of several paradigms including constraint logic programming and concurrent constraint programming using lattices. The second part is dedicated to building a practical language where search strategies can be easily composed. Compositionality consists of taking several distinct strategies and, via some operators, to compose these in order to obtain a new strategy. Existing proposals include extensions to logic programming, monadic constraint programming and search combinators, but all suffer from different drawbacks as explained in the dissertation. The original aspect of spacetime programming is to make use of a temporal dimension, offered by the synchronous paradigm, to compose and synchronize search strategies on a shared logical clock.This paradigm opens the door to new and more complex search strategies in constraint programming but also in applications requiring backtracking search. We demonstrated its usefulness in an interactive computer-aided composition system where we designed a search strategy to help the composer navigating in the state space generated by a musical constraint problem. We also explored a model checking algorithm where a model dynamically generates a constraint satisfaction problem (CSP) representing the reachability of some states. Although these applications are experimental, they hint at the suitability of spacetime programming in a larger context. v AcknowledgementsJe remercie très chaleureusement Emmanuel Chailloux qui, après un Skype mémorable, m'a accepté pour ma dernière année en Master, et qui m'a ...

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Time refinement in a functional synchronous language

Cited by 5 publications

References 8 publications

The w-calculus: a synchronous framework for the verified modelling of digital signal processing algorithms

The w-calculus: a synchronous framework for the verified modelling of digital signal processing algorithms

Spacetime Programming: A Synchronous Language for Composable Search Strategies

Spacetime programming: a synchronous language for constraint search

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