Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
NSL '94 Proceedings of the first workshop on Non-standard logics and logical aspects of computer science
Towards the animation of proofs---testing proofs by examples
Theoretical Computer Science - Special issue on theories of types and proofs
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Towards Limit Computable Mathematics
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Classical logic, continuation semantics and abstract machines
Journal of Functional Programming
Algebraically generalized recursive function theory
IBM Journal of Research and Development
Towards Limit Computable Mathematics
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
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We will construct from every partial combinatory algebra (PCA, for short) A a PCA a-lim(A) s.t. (1) every representable numeric function ϕ(n) of a-lim(A) is exactly of the form limt ξ(t, n) with ξ(t, n) being a representable numeric function of A, and (2) A can be embedded into a-lim(A) which has a synchronous application operator. Here, a-lim(A) is A equipped with a limit structure in the sense that each element of a-lim(A) is the limit of a countable sequence of A-elements. We will discuss limit structures for A in terms of Barendregt's range property. Moreover, we will repeat the construction lim(--) transfinite times to interpret infinitary λ-calculi. Finally, we will interpret affine type-free λµ-calculus by introducing another partial applicative structure which has an asynchronous application operator and allows a parallel limit operation.