Countable nondeterminism and random assignment
Journal of the ACM (JACM)
Observable sequentiality and full abstraction
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Bistructures, bidomains, and linear logic
Proof, language, and interaction
Uncountable limits and the lambda calculus
Nordic Journal of Computing
Stable Models of Typed lambda-Calculi
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
A Fully Abstract Game Semantics for Finite Nondeterminism
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Sequentiality in Bounded Biorders
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Dually nondeterministic functions
ACM Transactions on Programming Languages and Systems (TOPLAS)
A Relational Model of a Parallel and Non-deterministic λ -Calculus
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
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We describe a denotational semantics for a sequential functional language with random number generation over a countably infinite set (the natural numbers), and prove that it is fully abstract with respect to may-and-must testing. Our model is based on biordered sets similar to Berry's bidomains, and stable, monotone functions. However, (as in prior models of unbounded non-determinism) these functions may not be continuous. Working in a biordered setting allows us to exploit the different properties of both extensional and stable orders to construct a Cartesian closed category of sequential, discontinuous functions, with least and greatest fixpoints having strong enough properties to prove computational adequacy. We establish full abstraction of the semantics by showing that it contains a simple, first-order “universal type-object” within which all types may be embedded using functions defined by (countable) ordinal induction.