Handbook of logic in computer science (vol. 1)
A new recursion-theoretic characterization of the polytime functions
Computational Complexity
A foundational delineation of poly-time
Papers presented at the IEEE symposium on Logic in computer science
Handbook of logic in artificial intelligence and logic programming
Universal Algebra, Algebraic Logic, and Databases
Universal Algebra, Algebraic Logic, and Databases
Predicative Recurrence in Finite Types
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Termination Proofs and Complexity Certification
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
Intrinsic Theories and Computational Complexity
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Linear logic and elementary time
Information and Computation - Special issue: ICC '99
Reasoning about functional programs and complexity classes associated with type disciplines
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
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Function provability in higher-order logic is a versatile and powerful framework for conceptual classification as well as verification and derivation of declarative programs. Here we show that the functions provable in second-order logic with first-order set-abstraction are precisely the elementary functions. This holds regardless of whether the logic is classical, intuitionistic, or minimal. The notion of provability here is not purely logical, as it incorporates a trivial theory of data, with axioms stating that each data object has a detectable main constructor which can be destructed. We show that this is necessary, by proving that without such rudimentary axioms the provable functions are merely the functions broadly-represented in the simply typed lambda calculus, a collection that does not even include integer subtraction.