Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Using Z: specification, refinement, and proof
Using Z: specification, refinement, and proof
Stochastic lambda calculus and monads of probability distributions
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A probabilistic language based upon sampling functions
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Abstraction and refinement in probabilistic systems
ACM SIGMETRICS Performance Evaluation Review
Probabilistic λ-calculus and Quantitative Program Analysis
Journal of Logic and Computation
Probabilistic guarded commands mechanized in HOL
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
Nondeterminism in Constructive Z
Fundamenta Informaticae
Markov Chains and Stochastic Stability
Markov Chains and Stochastic Stability
PMaude: Rewrite-based Specification Language for Probabilistic Object Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
An Approach to Nondeterminism in Translation of CZ Set Theory into Martin-Löf 's Theory of Types
Electronic Notes in Theoretical Computer Science (ENTCS)
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Probabilistic techniques in computer programs are becoming more and more widely used. Therefore, there is a big interest in methods for formal specification, verification, and development of probabilistic programs. In this paper, we present a constructive framework to develop probabilistic programs formally. To achieve this goal, we first introduce a Z-based formalism that assists us to specify probabilistic programs simply. This formalism is mainly based on a new notion of Z operation schemas, called probabilistic schemas, and a new set of schema calculus operations that can be applied on probabilistic schemas as well as ordinary operation schemas. We show the resulting formalism can be used to specify any discrete-time Markov chain. We also reason how one can derive functional probabilistic programs from correctness proofs of formal specifications written in the new formalism. In this way, a completely formal solution to develop probabilistic programs will be proposed.