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Resolving inductive definitions with binders

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We study inductive definitions involving binders, in which aliasing between free and bound names is permitted. Such aliasing occurs in informal specifications of operational semantics, but is excluded by the common representation of binding as meta-level lambda-abstraction. Drawing upon ideas from functional logic programming, we represent such definitions with aliasing as recursively defined functions in a higher-order typed functional programming language that extends core ML with types for name-binding, a type of “semi-decidable propositions” and existential quantification for types with decidable equality. We show that the representation is sound and complete with respect to the language’s operational semantics, which combines the use of evaluation contexts with constraint programming. We briefly discuss the associated constraint problem, which is NP-complete, and outline a constraint solving algorithm.

This talk is part of the Semantics Lunch (Computer Laboratory) series.

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