A Curry-Howard Approach to Church's Synthesis

Cécilia Pradic (1, 2, 3) , Colin Riba (2, 3)

1 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 PLUME - Preuves et Langages

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.

Mots clés: Intuitionistic Arithmetic; Monadic Second-Order Logic on Infinite Words; Realizability

Domaines: Logique en informatique [cs.LO]

Cécilia Pradic, Colin Riba. A Curry-Howard Approach to Church's Synthesis. FSCD'17, Sep 2017, Oxford, United Kingdom. ⟨10.4230/LIPIcs.FSCD.2017.29⟩. ⟨hal-01511837v2⟩