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Semantics of Probabilistic Programs. Approaches discussed in literature E 1  p E 2 => E 1 (with prob. p) => E 2 (with prob. (1-p)) Probability of a specific output is not explicit. [E 1  p E 2 ]s = (p)*[E 1 ]s + (1-p)*[E 2 ]s [E]s is a measure function from events to probabilities.

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semantics of probabilistic programs
Semantics of Probabilistic Programs
  • Approaches discussed in literature
    • E1pE2 => E1 (with prob. p)

=> E2 (with prob. (1-p))

      • Probability of a specific output is not explicit.
    • [E1pE2]s = (p)*[E1]s + (1-p)*[E2]s
      • [E]s is a measure function from events to probabilities.
      • Forward or Backward?
  • Practical Issues
    • Backward implementation is difficult. (inverses, representation of sets).
    • Need to be able to compute probabilities, expectations inside of the program.
haskell implementation
Haskell Implementation
  • Using type classes to realize a general parameterized type (Prob a).
    • Has capability to generalize to product types (a  b).
  • data (DomainClass a) => (Prob a) = …
    • (DomainClass a) is an assertion that ‘a’ must be an instance of DomainClass.
    • Still must provide ‘instance DomainClass T’ declaration, which defines functions to operate on values of type T.
  • Underlying representation
    • Dimensions: exact/interpolated countable/uncountable
    • Sample sets and functions considered.