A probabilistic powerdomain of evaluations
Proceedings of the Fourth Annual Symposium on Logic in computer science
Notions of computation and monads
Information and Computation
Probabilistic non-determinism
Stochastic lambda calculus and monads of probability distributions
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A Formal Approach to Probabilistic Termination
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Constructive Reals in Coq: Axioms and Categoricity
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A Universal Characterization of the Closed Euclidean Interval
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
A judgmental reconstruction of modal logic
Mathematical Structures in Computer Science
Verification of non-functional programs using interpretations in type theory
Journal of Functional Programming
Probabilistic symbolic model checking with PRISM: a hybrid approach
International Journal on Software Tools for Technology Transfer (STTT) - Special section on tools and algorithms for the construction and analysis of systems
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
A probabilistic language based upon sampling functions
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Probabilistic Guarded Commands Mechanized in HOL
Electronic Notes in Theoretical Computer Science (ENTCS)
Formalization of Continuous Probability Distributions
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Using Theorem Proving to Verify Expectation and Variance for Discrete Random Variables
Journal of Automated Reasoning
Proofs of randomized algorithms in Coq
Science of Computer Programming
A Machine-Checked Proof of the Average-Case Complexity of Quicksort in Coq
Types for Proofs and Programs
Some Domain Theory and Denotational Semantics in Coq
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Formal Reasoning about Expectation Properties for Continuous Random Variables
FM '09 Proceedings of the 2nd World Congress on Formal Methods
A framework for game-based security proofs
ICICS'07 Proceedings of the 9th international conference on Information and communications security
Improved bound for stochastic formal correctness of numerical algorithms
Innovations in Systems and Software Engineering
A probabilistic hoare-style logic for game-based cryptographic proofs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
A type theory for probability density functions
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Randomized algorithms are widely used either for finding efficiently approximated solutions to complex problems, for instance primality testing, or for obtaining good average behavior, for instance in distributed computing. Proving properties of such algorithms requires subtle reasoning both on algorithmic and probabilistic aspects of the programs. Providing tools for the mechanization of reasoning is consequently an important issue. Our paper presents a new method for proving properties of randomized algorithms in a proof assistant based on higher-order logic. It is based on the monadic interpretation of randomized programs as probabilistic distribution [1]. It does not require the definition of an operational semantics for the language nor the development of a complex formalization of measure theory, but only use functionals and algebraic properties of the unit interval. Using this model, we show the validity of general rules for estimating the probability for a randomized algorithm to satisfy certain properties, in particular in the case of general recursive functions. We apply this theory for formally proving a program implementing a Bernoulli distribution from a coin flip and the termination of a random walk. All the theories and results presented in this paper have been fully formalized and proved in the Coq proof assistant [2].