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
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
Constructive analysis, types and exact real numbers
Mathematical Structures in Computer Science
Probabilistic Guarded Commands Mechanized in HOL
Electronic Notes in Theoretical Computer Science (ENTCS)
Proofs of randomized algorithms in CoQ
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Formal certification of code-based cryptographic proofs
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Formal Certification of ElGamal Encryption
Formal Aspects in Security and Trust
Beyond provable security verifiable IND-CCA security of OAEP
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
Proving the security of ElGamal encryption via indistinguishability logic
Proceedings of the 2011 ACM Symposium on Applied Computing
Probabilistic relational reasoning for differential privacy
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Programming language techniques for cryptographic proofs
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Probabilistic compositional reasoning for guaranteeing fault tolerance properties
OPODIS'11 Proceedings of the 15th international conference on Principles of Distributed Systems
Verified indifferentiable hashing into elliptic curves
POST'12 Proceedings of the First international conference on Principles of Security and Trust
Probabilistic Relational Reasoning for Differential Privacy
ACM Transactions on Programming Languages and Systems (TOPLAS)
Probabilistic relational verification for cryptographic implementations
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Verified indifferentiable hashing into elliptic curves
Journal of Computer Security - Security and Trust Principles
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Randomized algorithms are widely used for finding efficiently approximated solutions to complex problems, for instance primality testing and for obtaining good average behavior. Proving properties of such algorithms requires subtle reasoning both on algorithmic and probabilistic aspects of programs. Thus, providing tools for the mechanization of reasoning is an important issue. This 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 distributions (Giry, Ramsey and Pfeffer). It does not require the definition of an operational semantics for the language nor the development of a complex formalization of measure theory. Instead it uses functional and algebraic properties of unit interval. Using this model, we show the validity of general rules for estimating the probability for a randomized algorithm to satisfy specified properties. This approach addresses only discrete distributions and gives rules for analyzing general recursive functions. We apply this theory to the formal proof of a program implementing a Bernoulli distribution from a coin flip and to the (partial) termination of several programs. All the theories and results presented in this paper have been fully formalized and proved in the Coq proof assistant.