LMSO: A Curry-Howard Approach to Church's Synthesis via Linear Logic

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

We propose LMSO, a proof system inspired from Linear Logic, as a proof-theoretical framework to extract finite-state stream transducers from linear-constructive proofs of omega-regular specifications. We advocate LMSO as a stepping stone toward semi-automatic approaches to Church's synthesis combining computer assisted proofs with automatic decisions procedures. LMSO is correct in the sense that it comes with an automata-based realizability model in which proofs are interpreted as finite-state stream transducers. It is moreover complete, in the sense that every solvable instance of Church's synthesis problem leads to a linear-constructive proof of the formula specifying the synthesis problem.

Mots clés: Monadic Second-Order Logic on Infinite Words; Game Semantics; Categorical Logic; MSO on Infinite Words; Realizability; Linear Logic

Domaines: Logique en informatique [cs.LO]

Cécilia Pradic, Colin Riba. LMSO: A Curry-Howard Approach to Church's Synthesis via Linear Logic. LICS'18, Jul 2018, Oxford, United Kingdom. ⟨hal-01698648v2⟩