Congruence of Bisimulation in a Non-Deterministic Call-By-Need Lambda Calculus

We present a call-by-need λ-calculus λ_ND with an erratic non-deterministic operator pick and a non-recursive let. A definition of a bisimulation is given, which has to be based on a further calculus named λ_≈, since the naïve bisimulation definition is useless. The main result is that bisimulation in λ_≈ is a congruence and coincides with the contextual equivalence. The proof is a non-trivial extension of Howe's method. This might be a step towards defining useful bisimulation relations and proving them to be congruences in calculi that extend the λ_ND-calculus.