A Curry-Howard Approach to Church's Synthesis

Authors Pierre Pradic, Colin Riba

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Pierre Pradic
Colin Riba

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Pierre Pradic and Colin Riba. A Curry-Howard Approach to Church's Synthesis. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Church's synthesis problem asks whether there exists a finite-state stream transducer satisfying a given input-output specification. For specifications written in Monadic Second-Order Logic over infinite words, Church's synthesis can theoretically be solved algorithmically using automata and games. We revisit Church's synthesis via the Curry-Howard correspondence by introducing SMSO, a non-classical subsystem of MSO, which is shown to be sound and complete w.r.t. synthesis thanks to an automata-based realizability model.
  • Intuitionistic Arithmetic
  • Realizability
  • Monadic Second-Order Logic on Infinite Words


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