The essence of functional programming
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Probabilistic non-determinism
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
PLDI '94 Proceedings of the ACM SIGPLAN 1994 conference on Programming language design and implementation
Randomized algorithms
Probabilistic models for the guarded command language
Science of Computer Programming - Special issue: on formal specifications: foundations, methods, tools and applications: selected papers from the FMTA '95 conference (29–31 May 1995, Konstancin n. Warsaw, Poland)
Termination of Probabilistic Concurrent Program
ACM Transactions on Programming Languages and Systems (TOPLAS)
A Discipline of Programming
Semantics of probabilistic programs
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Proof rules for probabilistic loops
FAC-RW'96 Proceedings of the BCS-FACS 7th conference on Refinement
Proofs of randomized algorithms in Coq
Science of Computer Programming
Probabilistic termination in B
ZB'03 Proceedings of the 3rd international conference on Formal specification and development in Z and B
A calculus for game-based security proofs
ProvSec'10 Proceedings of the 4th international conference on Provable security
Probabilistic choice, reversibility, loops, and miracles
UTP'10 Proceedings of the Third international conference on Unifying theories of programming
The open theory standard theory library
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Probabilistically accurate program transformations
SAS'11 Proceedings of the 18th international conference on Static analysis
Reasoning algebraically about probabilistic loops
ICFEM'06 Proceedings of the 8th international conference on Formal Methods and Software Engineering
Using probabilistic kleene algebra for protocol verification
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Proofs of randomized algorithms in CoQ
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Probabilistic termination of CHRiSM programs
LOPSTR'11 Proceedings of the 21st international conference on Logic-Based Program Synthesis and Transformation
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We present a probabilistic version of the while loop, in the context of our mechanised framework for verifying probabilistic programs. The while loop preserves useful program properties of measurability and independence, provided a certain condition is met. This condition is naturally interpreted as "from every starting state, the while loop will terminate with probability 1", and we compare it to other probabilistic termination conditions in the literature. For illustration, we verify in HOL two example probabilistic algorithms that necessarily rely on probabilistic termination: an algorithm to sample the Bernoulli(p) distribution using coin-flips; and the symmetric simple random walk.