Arity hierarchies

Bounded-Arity Hierarchies in Fixed-Point Logics

In this paper we prove that for each k, the expressive power of k–ary fixed–point logic, i.e. the fragment of fixed–point logic whose fixed–point operators are restricted to arity ≤ k, strictly exceeds the power of (k − 1)–ary fixed–point logic. This solves a problem that was posed by Chandra and Harel in 1982. Our proof has a rather general form that applies to several variants of fixed–point ...

Arity Hierarchies for Fixed-Point Logics

Fixed-point logic is the logic of inductively deenable relations over structures of a speciic signature. The inductive deenitions are given via expressions of the rst order logic or fragments of it. A natural question is whether we can increase the expressive power of the logic by allowing larger arities of the inductively deened relations. A number of results appeared lately that essentially s...

Some Relationships between the FOIES and S1 Arity Hierarchies

Call Arity

Higher order combinators in functional programming languages can lead to code that would be considerably more efficient if some functions’ definitions were eta-expanded, but the existing analyses are not always precise enough to allow that. In particular, this has prevented the implementation of foldl via foldr, which would allow foldl to take part in list fusion. Call Arity is an analysis that...

Arity Raising in Manticore

Compilers for polymorphic languages are required to treat values in programs in an abstract and generic way at the source level. The challenges of optimizing the boxing of raw values, flattening of argument tuples, and raising the arity of functions that handle complex structures to reduce memory usage are old ones, but take on newfound import with processors that have twice as many registers. ...