Imprecise probability generalises standard probability theory by replacing a single distribution with a convex set of possible distributions. We show that this generalisation requires no change to the standard BDD compilation and weighted model counting pipeline used by discrete probabilistic languages. An imprecise coin flip is simply a BDD variable whose weight is left free rather than fixed. We introduce Imp, a Haskell embedded DSL for imprecise probabilistic programming. A graded monad, indexed by finite sets of named sources of epistemic uncertainty, restores the commutativity that the standard convex powerset monad lacks, and GHC’s type system enforces this at compile time. Moreover, weighted model counting is parametric in the semiring, so the same compiled BDD supports exact, differentiable, and interval-bounded inference.

Tue 25 Aug

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15:30 - 17:00
Types, Semantics, and Probabilistic ProgrammingICFP Papers at IP126 Auditorium
Chair(s): Leonidas Lampropoulos University of Maryland at College Park
15:30
18m
Talk
Another Type Inference Algorithm for First-class Implicit Polymorphism
ICFP Papers
J. Garrett Morris University of Iowa
DOI
15:48
18m
Talk
Same Coeffect, Different Base: Connecting Two Dominant Approaches to Graded Types
ICFP Papers
Vilem-Benjamin Liepelt University of Kent, UK, Danielle Marshall University of Glasgow, Dominic Orchard University of Cambridge; University of Kent
DOI
16:06
18m
Talk
Towards a Higher-Order Bialgebraic Denotational Semantics
ICFP Papers
Sergey Goncharov University of Birmingham, Marco Peressotti University of Southern Denmark, Stelios Tsampas University of Southern Denmark, Henning Urbat University of Erlangen-Nuremberg, Stefano Volpe University of Southern Denmark
DOI
16:24
18m
Talk
LazyHMC: Hamiltonian Monte Carlo simulation for lazy, infinite dimensional probabilistic programs
ICFP Papers
Maria-Nicoleta Craciun University of Oxford, C.-H. Luke Ong NTU, Tom Schrijvers KU Leuven, Sam Staton University of Oxford
DOI
16:42
18m
Talk
Imprecise Probabilistic Programming, Precisely (Functional Pearl)
ICFP Papers
Jack Liell-Cock University of Oxford, Sam Staton University of Oxford
DOI