coq-random

Interpretation of random programs. This contribution is a modelisation of random programs as measures in Coq. It started in 2004 in the context of the AVERROES project (http://www-verimag.imag.fr/AVERROES/). It is based on comon work with Philippe Audebaud (ENS Lyon). It was last updated in february 2007. It contains the following elements - an axiomatisation of the interval [0,1] and derived properties (files Ubase.v and Uprop.v); - a definition of measures on a type A as functions of type (A->[0,1])->[0,1] enjoying special stability properties (files Monads.v and Probas.v); proofs that these constructions have a monadic structure; - an interpretation of programs of type A as measures, in particular a fixpoint construction; the definition of an axiomatic semantic for deriving judgements such as ``the probability of an expression e to evaluate to a result satisfying property q belongs to an interval [p,q]'' (file Prog.v); - Proof of probabilistic termination of a linear random walk (file Iterflip.v); - Proof of a program implementing a bernoulli distribution (Proba(bernouilli(p)=true)=p) using a coin flip and the derived binomial law (Proba(binomial p n=k)=C(n,k)p^k(1-p)^{n-k}) (file Bernoulli.v); - Proof of estimation of the combination of two random executions (file Choice.v) - Proof of partial termination of parameterized random walk (file Ycart.v) - Definition of a measure on traces from a mesure on transitions steps (file Nelist.v, Transitions.v) The document random.pdf contains a short introduction to the library associated to the Gallina source code of the library.

`opam install coq-random.8.7.0`
homepage
https://github.com/coq-contribs/random