## A Monadic Probabilistic Language (2003)

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Venue: | In Proceedings of the 2003 ACM SIGPLAN international workshop on Types in languages design and implementation |

Citations: | 10 - 5 self |

### BibTeX

@INPROCEEDINGS{Park03amonadic,

author = {Sungwoo Park and Frank Pfenning and Sebastian Thrun},

title = {A Monadic Probabilistic Language},

booktitle = {In Proceedings of the 2003 ACM SIGPLAN international workshop on Types in languages design and implementation},

year = {2003},

pages = {38--49},

publisher = {ACM Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

Motivated by many practical applications that have to compute in the presence of uncertainty, we propose a monadic probabilistic language based upon the mathematical notion of sampling function. Our language provides a unified representation scheme for probability distributions, enjoys rich expressiveness, and o#ers high versatility in encoding probability distributions. We also develop a novel style of operational semantics called a horizontal operational semantics, under which an evaluation returns not a single outcome but multiple outcomes. We have preliminary evidence that the horizontal operational semantics improves the ordinary operational semantics with respect to both execution time and accuracy in representing probability distributions.

### Citations

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Citation Context ...imulation and on a real robot. The pose of a robot is 48estimated with a continuous probability distribution over three-dimensional real space. At its core, our implementation employs a Bayes filter =-=[8]-=-: Bel(p) ← ηP(o|p)Bel(p) (1) Bel(p) ← R p ′ A(p|a, p ′ )Bel(p ′ )dp ′ (2) Bel(p) is the probability for a pose p. P (o|p) is the probability that the robot at a pose p observes an observation o, and η... |

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Citation Context ...e. Furthermore we can dispense with the constant c if we approximate sampling functions with a set of weighted samples, which is known as the sample-based representation for probability distributions =-=[5]-=-. Lack of Support for Precise Reasoning The quintessential weakness of λγ is that it does not permit a precise implementation of queries on probability distributions such as expectation. In other word... |

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Citation Context ...ssigned to each element in the domain is computable. Even an unbiased coin toss construct flip suffices to express such probability distributions because it is equivalent to a binary choice construct =-=[6]-=-. The use of probability mass functions as the mathematical basis implies that discrete probability distributions are the only source of probability distributions. Certain continuous probability distr... |

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Citation Context ... ∧ σ2;Σ≼ σ log inter v Λ; Σ,σ1,σ2 ≼ σ Λ; Σ,σ1 ∧ σ2 ≼ σ log inter Λ; Σ ≼ σ1 Λ; Σ ≼ σ2 Λ; Σ ≼ σ1 ∧ σ2 log inter r Figure 6: Structural subtyping rules rule log box in our system. As Davies and Pfenning =-=[3]-=- associate □A with closed code producing a value of type A via the Curry-Howard isomorphism, we can interpret a refinement type □σ as the set of closed expressions of refinement type σ in the sense th... |

165 | Probabilistic Algorithms in Robotics
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Citation Context ... probabilistic computation. An example is an imperative language CES [19], which is an extension to C++ with probabilistic data types. The language is designed specifically for probabilistic robotics =-=[18]-=- and successfully employed in implementing typical robot control programs compactly. For instance, Thrun [19] implements a program for controlling a mail-delivery robot through gestures with only 137 ... |

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Citation Context ...resents a denotational semantics based upon the monadic structure of probability distributions and shows how to achieve an elegant implementation of common queries on probability distributions. Jones =-=[9]-=- presents a metalanguage with a binary choice construct e1 orp e2. The language syntactically distinguishes expressions denoting probability distributions from function expressions denoting functions ... |

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Citation Context ...ons or by the probloop command, which explicitly maintains dependencies among probability distributions. Our work is an attempt to design a functional probabilistic language with similar goals. Kozen =-=[11]-=- investigates the semantics of probabilistic while programs. A random assignment x := random assigns a random number to a variable x and is the source of probability distributions. The language does n... |

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Citation Context ...oacommontype. Although we include a distributivity rule for the connective □, we omit distributivity rules for the type constructors → and ⇒, the second of which is unsound in the presence of effects =-=[2]-=-: (σ →σ1) ∧ (σ →σ2) ≤ σ →(σ1 ∧ σ2) (σ ⇒σ1) ∧ (σ ⇒σ2) ≤ σ ⇒(σ1 ∧ σ2) sub lam dist sub int dist We define an equivalence relation ≡ such that σ ≡ σ ′ if and only if σ ≤ σ ′ and σ ′ ≤ σ. The following eq... |

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Citation Context ... data constructor is determined. The language employs a lazy evaluation strategy, under which certain probability distributions over infinite domains can be expressed. It is later extended by Pfeffer =-=[13]-=- with higherorder functions and a type system. His language, IBAL, generalizes the coin toss construct to a multiple choice construct dist [p1 : e1, ··· ,pn : en]. Gupta, Jagadeesan, and Panangaden [7... |

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Citation Context ... there exists σ1 such that ·; ∅⊢≤ e1 : □σ1 by Lemma 3.25. By induction hypothesis, we have t = ɛ. Cases red itl and red itr follow from Lemma 3.26 in a similar way. 4. RELATED WORK Ramsey and Pfeffer =-=[16]-=- present a stochastic lambda calculus in which any expression denotes a probability distribution. A lambda abstraction translates into a function from regular values to probability distributions. A bi... |

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Citation Context ..., a probability distribution is represented by a continuous evaluation, which returns a probability for any element in a lattice of open sets over a topological space. Koller, McAllester, and Pfeffer =-=[10]-=- present a first order functional language with a coin toss construct flip(p). A program denotes a probability distribution, and its evaluation returns a sample from the probability distribution, alth... |

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Citation Context ...ver the unit interval, a full implementation of the operational semantics requires real arithmetic at an arbitrary precision. Although there are well-developed theories for exact real arithmetic (see =-=[4]-=- for an example), we do not find it necessary to incorporate such an expensive functionality into the implementation of the operational semantics sacrificing the efficiency. The reason is that often p... |

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Citation Context ...e unwinding. All the above work essentially employs call-by-value reduction for probability distributions. Note that the lazy evaluation strategy in [10, 13] is analogous to call-by-need reduction in =-=[12]-=-, but implements the observational behavior of call-by-value reduction for probability distributions. Saheb-Djahromi [17] recognizes the importance of call-byname reduction in the formulation of a pro... |

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29 | Stochastic processes as concurrent constraint programs
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Citation Context ...3] with higherorder functions and a type system. His language, IBAL, generalizes the coin toss construct to a multiple choice construct dist [p1 : e1, ··· ,pn : en]. Gupta, Jagadeesan, and Panangaden =-=[7]-=- present Probabilistic cc, a stochastic concurrent constraint language. A probabilistic choice construct choose X from Dom in P simulates coin tosses to choose a value for a variable X from a finite s... |

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22 | Towards programming tools for robots that integrate probabilistic computation and learning
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(Show Context)
Citation Context ...s in computer science, researchers have designed new languages to facilitate the development of probabilistic programs, which model probabilistic computation. An example is an imperative language CES =-=[19]-=-, which is an extension to C++ with probabilistic data types. The language is designed specifically for probabilistic robotics [18] and successfully employed in implementing typical robot control prog... |

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10 |
Toward General Analysis of Recursive Probability Models
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Citation Context ...uage based upon LCF, which supports both call-by-value reduction and call-by-name reduction. A term of the form (p →M,q→N), where p + q =1.0, is employed as a binary choice construct. Pless and Luger =-=[15]-=- present an extended lambda calculus in which an expression of the form P i expri : pi denotes a probability distribution. The calculus is distinct from all the above work in that any expression denot... |

10 |
Probabilistic LCF
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Citation Context ...lazy evaluation strategy in [10, 13] is analogous to call-by-need reduction in [12], but implements the observational behavior of call-by-value reduction for probability distributions. Saheb-Djahromi =-=[17]-=- recognizes the importance of call-byname reduction in the formulation of a probabilistic language. The paper presents a probabilistic language based upon LCF, which supports both call-by-value reduct... |

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3 |
A judgmental reconstuction of modal logic
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Citation Context ...ar argument can be made for a general distributivity rule for the type constructor ⇒. The structural subtyping system resembles the system for the intuitionistic modal logic S4 of Pfenning and Davies =-=[14]-=-, which is presented in the style of natural deduction. Their system separates valid hypotheses from true hypotheses, and a judgment has the form ∆; Γ⊢J where the antecedent consists of ∆ for valid hy... |

2 | IBAL : A probabilistic rational programming language - Pfeer - 2001 |

1 | Operational semantics for a modal type system of e#ects - Harper, Pfenning - 2003 |