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
Basic proof theory
Computability and complexity: from a programming perspective
Computability and complexity: from a programming perspective
Applicative Control and Computational Complexity
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
Intrinsic Theories and Computational Complexity
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Reasoning about functional programs and complexity classes associated with type disciplines
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
The Functions Provable by First Order Abstraction
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
A Note on Universal Measures for Weak Implicit Computational Complexity
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Implicit Computational Complexity for Higher Type Functionals
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Intrinsic reasoning about functional programs II: unipolar induction and primitive-recursion
Theoretical Computer Science - Implicit computational complexity
An arithmetic for polynomial-time computation
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
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We show that simple structural conditions on proofs of convergence of equational programs, in the intrinsic-theories verification framework of [16], correspond to resource bounds on program execution. These conditions may be construed as reflecting finitistic-predicative reasoning. The results provide a user-transparent method for certifying the computational complexity of functional programs. In particular, we define natural notions of data-positive formulas and of data-predicative derivations, and show that restricting induction to data-positive formulas captures precisely the primitive recursive functions, data-predicative derivations characterize the Kalmar-elementary functions, and the combination of both yields the poly-time functions.