Well-Typed Logic Programs Are not Wrong
<|reference_start|>Well-Typed Logic Programs Are not Wrong: We consider prescriptive type systems for logic programs (as in Goedel 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" query are again "well-typed". This property has been called subject reduction. We show that this property can also be phrased as a property of the proof-theoretic semantics of logic programs, thus abstracting from the usual operational (top-down) semantics. This proof-theoretic view leads us to questioning a condition which is usually considered necessary for subject reduction, namely the head condition. It 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, the types of two unified terms are themselves unifiable. We discuss possible implications of this result. We also discuss the relationship between the head condition and polymorphic recursion, a concept known in functional programming.<|reference_end|>
@article{deransart2000well-typed,
    title={Well-Typed Logic Programs Are not Wrong},
    author={Pierre Deransart and Jan-Georg Smaus},
    journal={arXiv preprint arXiv:cs/0012015},
    year={2000},
    number={RR-4082},
    archivePrefix={arXiv},
    eprint={cs/0012015},
    primaryClass={cs.LO}
}