Call-by-Value Separability and Computability

The aim of this paper is to study the notion of separability in the call-by-value setting.Separability is the key notion used in the Bohm Theorem, proving that syntactically different s?-normal forms are separable in the classical ?-calculus endowed with s-reduction, i.e. in the call-by-name setting. In the case of call-by-value ?-calculus endowed with s? -reduction and ?? -reduction (see Plotkin [7]), it turns out that two syntactically different s?-normal forms are separable too, while the notion of s? -normal form and ?? -normal form is semantically meaningful.An explicit representation of Kleene's recursive functions is presented. The separability result guarantees that the representation makes sense in every consistent theory of call-by-value, i.e. theories in which not all terms are equals.