Compositional theories of truth tend to follow the Tarskian tradition, either the model-theoretic semantics for classical predicate logic or its natural generalisations to many-value and possible-worlds. Other realisations of truth, which includes computational interpretations and game semantics, have been largely ignored by truth theorists. In this talk I will present axiomatic rendering of Krivine’s “classical realisability”, a ‘truth as programs’ semantics for classical logic that validates extensions of Peano arithmetic. What sets this conception of truth apart from the Tarskian view is its treatment of falsity as primitive and truth as a derived notion. This is joint work with Daichi Hayashi (Hokkaido University, Japan).