Structured reactive programming with polymorphic temporal tiles

Abstract

In functional reactive programming (FRP), system inputs and outputs are generally modeled as functions over continuous time (behaviors) whose future values are governed by sudden changes (events). In this approach, discrete events are embedded into piece-wise continuous behaviors. In the field of reactive music system programming, we develop an orthogonal approach that seems to better fit our need. Much like piano keys can be played and combined both in sequence and in parallel, we model system inputs and outputs as spatio temporal combinations of what we call temporal values: continuous functions over time whose domain lays between two events: a start and a stop event. Various high level data types and program constructs can then be derived from such a model. They are shown to satisfy robust algebraic and category theoretic properties. Altogether, this eventually provides a simple, robust and elegant programming front-end, temporal tile programming, for reading, memorizing, stretching, combining and transforming flows of inputs into flows of outputs. Although at its infancy, the resulting approach has been experimentally validated for reactive and real-time music system programming.

Unified media programming: an algebraic approach

“…In computer science, they already appears in connection with Girard's Linear Logic [6] and related studies of reversible computations [1,3]. More recently, inverse semigroup have been applied to music modeling [2,9,12].…”

“…In this paper, we develop a semantics model for the synthesis of temporal media as defined by Hudak [7] such as animations, as illustrated in this paper, but also applicable to music, as illustrated in former work [2] or in Euterpea [8].…”

“…The language [..] enable [..] "bodysyntonic reasoning", where students can understand, predict and reason about the turtle's motion by imagining what they would do if they were the turtle. 2 .…”

Spatio-Temporal Domains: An Overview

“…This suggests that semantic features can be distributed between typical operational features (time and space values) and denotational features (other data values). However, in many modern computerized systems such as, for instance, interactive music or animation systems [14,18,2,3], timing or spacing information plays a crucial rôle in the definition of system's inputs and outputs. There, many data values are implicitly parameterized by some space and/or time information: think of an augmented music system taking as input the melody played by a musician dancing on a stage.…”

“…(1) a synchronous layer of programming constructs available when components' inputs and outputs are located and timed on the same spacetime scale and received or produced in a synchronous way (Section 5), (2) an asynchronous layer of programming constructs available when component's inputs and outputs are located and timed on possibly distinct spacetime scales (Section 6).…”