The polynomial hierarchy and intuitionistic bounded arithmetic
Proc. of the conference on Structure in complexity theory
Functional interpretations of feasibly constructive arithmetic
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Lambda calculus characterizations of poly-time
Fundamenta Informaticae - Special issue: lambda calculus and type theory
A foundational delineation of poly-time
Papers presented at the IEEE symposium on Logic in computer science
A New Characterization of Type-2 Feasibility
SIAM Journal on Computing
The Expressiveness of Simple and Second-Order Type Structures
Journal of the ACM (JACM)
Calibrating Computational Feasibility by Abstraction Rank
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Termination Proofs and Complexity Certification
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
Towards a theory of type structure
Programming Symposium, Proceedings Colloque sur la Programmation
A Note on the Relation Between Polynomial Time Functionals and Constable's Class K
CSL '95 Selected Papers from the9th International Workshop on Computer Science Logic
Type two computational complexity
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
A programming language theorem which is independent of Peano Arithmetic
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Topics in computational complexity
Topics in computational complexity
On characterizations of the basic feasible functionals, Part I
Journal of Functional Programming
Polynomial and abstract subrecursive classes
Journal of Computer and System Sciences
A proof-theoretic characterization of the basic feasible functionals
Theoretical Computer Science
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In previous works we argued that second order logic with comprehension restricted to positive formulas can be viewed as the core of Feasible Mathematics. Indeed, the equational programs over strings that are provable in this logic compute precisely the poly-time computable functions.Here we investigate the provable functionals of this logic, and show that they are precisely Cook and Urquhart's basic feasible functionals, BFF. This further confirms the stability of BFF as a notion of computational feasibility in higher type.Using a formula-as-type morphism, we also show that BFF consists precisely of the functionals that are lambda representable in F2 restricted to positive type arguments (and trivially augmented with basic constructors and destructors).