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A tree-based Operational Semantics for Interactive Multimedia Scores

A tree-based Operational Semantics for Interactive Multimedia Scores

Talk presented at the seminar on formal methods and languages.

Jaime Arias Almeida

October 24, 2017
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  1. A Tree-Based Operational Semantics for
    Interactive Multimedia Scores
    Jaime ARIAS, Myriam DESAINTE-CATHERINE, Carlos OLARTE, and Camilo RUEDA
    Seminars on Formal Methods and Languages
    Inria Grenoble - Rhône-Alpes
    October 2017

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  2. Static Score
    Play
    2
    =

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  3. Interactive Scores
    3
    Les Baltazars. Nocturne nº2 - Tumbleweed
    During the performance of a scenario, the performer
    has the possibility to influence its execution by
    triggering interactive points (IPs).
    IPs are defined by the composer during the
    composition and allow for agogic modifications (i.e.,
    the possibility to change the start and stop times of
    TOs during execution ).
    In this sense, a performance constitutes an instance of
    a finite set of possible scenarios that share the same
    temporal properties.

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  4. Interactive Scores
    4
    i-score - https://ossia.io

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  5. Interactive Scores
    5
    f
    f
    f
    f
    T D F S

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  6. Interactive Scores
    6
    The underlying model of i-score does not support:
    1. Flexible control structures (e.g., conditionals, loops)
    2. Mechanisms for the automatic verification
    Several researchers have made many efforts to overcome these limitations:
    ● Petri nets: Allombert 2009
    ● Process calculi: Olarte 2009, Toro 2014
    but there are no practical solutions for the automatic verification and real-time performance, and the models
    cannot be straightforwardly implemented or extended.

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  7. Outline 1. ReactiveML
    1.1. Syntax
    1.2. Tree Representation
    1.3. Operational Semantics
    1.4. Logical Characterization
    2. Concluding Remarks
    7

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  8. ReactiveIS
    8
    https://github.com/himito/reactiveIS

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  9. Syntax
    9

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  10. Syntax
    10

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  11. Conditions
    11
    WaitFromStart(WH,1,1)

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  12. Program (Score) Tree
    12

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  13. Program (Score) Tree
    13

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  14. State Tree
    14

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  15. Tree Homomorphism
    15

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  16. State Tree Operation: Start
    16

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  17. State Tree Operation: Stop
    17

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  18. Operational Semantics
    18
    P
    T
    S
    T
    C
    I
    C
    O
    C
    S H

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  19. Operational Semantics
    19

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  20. Operational Semantics
    20

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  21. Operational Semantics
    21

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  22. Operational Semantics
    22

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  23. Operational Semantics
    23

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  24. Properties of the SOS
    24

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  25. Logical Characterization
    25
    L L S (SELL)

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  26. Logical Characterization
    This opens the possibility of reasoning about interactive scores by using well established techniques in
    proof theory.
    We can verify, for example, if all the structures will be eventually played.
    26

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  27. Concluding
    Remarks
    27

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  28. Summary
    ● New programming language for the specification, verification and interpretation of interactive
    scores.
    ● ReactiveIS extends the full capacity of temporal organization of i-score.
    ● It is possible to extend the language for the specification of conditionals and loops.
    ● The operational semantics based on labelled trees are simpler and more intuitive than the current
    model in HTSPN of i-score.
    ● The declarative interpretation of ReactiveIS programs as formulas in SELL is adequate.
    28

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  29. Future Work
    ● Coq or Maude for proving the correctness of the semantics.
    ● Automatic checking of bound times of execution.
    ● Front-end for the specification of properties.
    ● Extension for conditional and loops.
    29

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  30. Thank you for your attention
    30

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  31. References
    1. Arias, J., Desainte-Catherine, M., Olarte, C., & Rueda, C. (2015). Foundations for Reliable and Flexible Interactive
    Multimedia Scores. In T. Collins, D. Meredith, & A. Volk (Eds.), 5th International Conference on Mathematics and
    Computation in Music, MCM 2015, London, UK, June 22-25, 2015 (Vol. 9110, pp. 29–41). Springer.
    https://doi.org/10.1007/978-3-319-20603-5_3
    2. Allombert, A. (2009). Aspects Temporels d’un Système de Partitions Musicales Interactives pour la Composition
    et l’Exécution. Université de Bordeaux. Retrieved from
    http://ori-oai.u-bordeaux1.fr/pdf/2009/ALLOMBERT_ANTOINE_2009.pdf
    3. Olarte, C., & Rueda, C. (2009). A Declarative Language for Dynamic Multimedia Interaction Systems. In E. Chew,
    A. Childs, & C.-H. Chuan (Eds.), 2nd International Conference on Mathematics and Computation in Music, MCM
    2009, New Haven, CT, USA, June 19-22, 2009 (Vol. 38, pp. 218–227). Springer Berlin Heidelberg.
    https://doi.org/10.1007/978-3-642-02394-1_20
    4. Toro, M., Desainte-Catherine, M., & Rueda, C. (2014). Formal semantics for interactive music scores: a
    framework to design, specify properties and execute interactive scenarios. Journal of Mathematics and Music,
    8(1), 93–112. https://doi.org/10.1080/17459737.2013.870610
    31

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