Well-typed programs are not wrong

Well-typed Programs Are not Wrong

Abstract

We consider prescriptive type systems for logic programming (as in Gödel or Mercury). In such systems, the typing is static but it guarantees an operational property: if a program is ``well-typed'', then all derivations starting in a ``well-typed'' goal are again ``well-typed''. This property has been called subject reduction. We show that this property is actually also declarative. This declarative view leads us to questioning a condition which is usually considered necessary for subject reduction, namely the head condition. This condition states that the head of each clause must have a type which is a variant (and not a proper instance) of the declared type. We provide a more general condition, thus reestablishing a certain symmetry between heads and body atoms. The condition ensures that in a derivation, only terms of identical type are unified. We discuss possible implications of this result.