Book contents
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 Semantics of Probabilistic Programming: A Gentle Introduction
- 2 Probabilistic Programs as Measures
- 3 Application ofComputable Distributions to the Semantics of Probabilistic Programs
- 4 On Probabilistic λ-Calculi
- 5 Probabilistic Couplings from Program Logics
- 6 Expected Runtime Analyis by Program Verification
- 7 Termination Analysis of Probabilistic Programs with Martingales
- 8 Quantitative Analysis of Programs with Probabilities and Concentration of Measure Inequalities
- 9 The Logical Essentials of Bayesian Reasoning
- 10 Quantitative Equational Reasoning
- 11 Probabilistic Abstract Interpretation: Sound Inference and Application to Privacy
- 12 Quantitative Information Flow with Monads in Haskell
- 13 Luck: A Probabilistic Language for Testing
- 14 Tabular: Probabilistic Inference from the Spreadsheet
- 15 Programming Unreliable Hardware
1 - Semantics of Probabilistic Programming: A Gentle Introduction
Published online by Cambridge University Press: 18 November 2020
- Frontmatter
- Contents
- List of Contributors
- Preface
- 1 Semantics of Probabilistic Programming: A Gentle Introduction
- 2 Probabilistic Programs as Measures
- 3 Application ofComputable Distributions to the Semantics of Probabilistic Programs
- 4 On Probabilistic λ-Calculi
- 5 Probabilistic Couplings from Program Logics
- 6 Expected Runtime Analyis by Program Verification
- 7 Termination Analysis of Probabilistic Programs with Martingales
- 8 Quantitative Analysis of Programs with Probabilities and Concentration of Measure Inequalities
- 9 The Logical Essentials of Bayesian Reasoning
- 10 Quantitative Equational Reasoning
- 11 Probabilistic Abstract Interpretation: Sound Inference and Application to Privacy
- 12 Quantitative Information Flow with Monads in Haskell
- 13 Luck: A Probabilistic Language for Testing
- 14 Tabular: Probabilistic Inference from the Spreadsheet
- 15 Programming Unreliable Hardware
Summary
Reasoning about probabilistic programs is hard because it compounds the difficulty of classic program analysis with sometimes subtle questions of probability theory. Having precise mathematical models, or semantics, describing their behaviour is therefore particularly important. In this chapter, we review two probabilistic semantics. First, an operational semantics which models the local, step-by-step, behaviour of programs, then a denotational semantics describing global behaviour as an operator transforming probability distributions over memory states.
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- Foundations of Probabilistic Programming , pp. 1 - 42Publisher: Cambridge University PressPrint publication year: 2020
- Creative Commons
- This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY 4.0 https://creativecommons.org/cclicenses/
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