A polymorphic type system for PROLOG.
Artificial Intelligence
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The Go¨del programming language
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POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
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MFCS '93 Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science
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FLOPS '99 Proceedings of the 4th Fuji International Symposium on Functional and Logic Programming
Parametric Polymorphism for Typed Prolog and lambda-Prolog
PLILP '96 Proceedings of the 8th International Symposium on Programming Languages: Implementations, Logics, and Programs
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Mode Analysis Domains for Typed Logic Programs
LOPSTR'99 Selected papers from the 9th International Workshop on Logic Programming Synthesis and Transformation
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Selected papers from the 5th LOMAPS Workshop on Analysis and Verification of Multiple-Agent Languages
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We consider prescriptive type systems for logic programs (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" 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.