## Categories for Imperative Semantics PLDG Seminar

### BibTeX

@MISC{Pucella_categoriesfor,

author = {Riccardo Pucella},

title = {Categories for Imperative Semantics PLDG Seminar},

year = {}

}

### OpenURL

### Abstract

The aim of these notes is to provide an introduction to category theory, and a motivation for its use in denotational semantics. I will do this by showing how to apply it to give an abstract semantics to a simple imperative language. These notes are loosely based

### Citations

3016 | Convergence of Probability Measures - Billingsley - 1968 |

921 | Categories for the working mathematician - Lane - 1998 |

440 | Computational lambda-calculus and monads - Moggi - 1989 |

394 | Category Theory for Computing Science - Barr, Wells - 1999 |

267 |
Semantics of Programming Languages: Structures and Techniques. Foundations of Computing
- Gunter
- 1992
(Show Context)
Citation Context ...ogical study of computation. But then again, category theory was originally developed to make sense of topological notions. The language IMP. 1993]. Consider the following simple imperative language [=-=Gunter 1992-=-; Winskel S ::= skip xi := E S1; S2 if B then S1 else S2 while B do S We will assume that the intuition behind the syntax is clear. Some things should be noted, however. We assume a finite set of vari... |

165 | Traced monoidal categories - Joyal, Street, et al. - 1996 |

135 | Semantics of probabilistic programs - Kozen - 1981 |

96 | A probabilistic PDL - Kozen - 1983 |

86 | Algebraic Approaches to Program Semantics - Manes, Arbib - 1986 |

60 | Varieties of iteration theories - Bloom, Esik - 1988 |

49 | Monadic Computation and iterative algebraic theories - Elgot - 1975 |

40 | A categorical approach to probability theory - Giry - 1982 |

18 |
A categorical approach to linear logic, geometry of proofs and full completeness
- Haghverdi
- 2000
(Show Context)
Citation Context ...e structure is given by defining ( ∑ {fi | i ∈ I})(x, A) = ∑ i∈I fi(x, ∑ A), as long as the result is a subprobability measure, that is, as long as i∈I fi(x, A) ≤ 1 for all x and A) [Panangaden 1999; =-=Haghverdi 2000-=-]. It turns out that SRel is also a Kleisli category for a monad related to the powerset monad. The monad (Π, η, µ), a variant of a monad originally described by Giry [1981], is defined as follows. Le... |

4 |
The category of Markov kernels
- Panangaden
- 1999
(Show Context)
Citation Context ...partially additive structure is given by defining ( ∑ {fi | i ∈ I})(x, A) = ∑ i∈I fi(x, ∑ A), as long as the result is a subprobability measure, that is, as long as i∈I fi(x, A) ≤ 1 for all x and A) [=-=Panangaden 1999-=-; Haghverdi 2000]. It turns out that SRel is also a Kleisli category for a monad related to the powerset monad. The monad (Π, η, µ), a variant of a monad originally described by Giry [1981], is define... |

1 | Control Flow Semantics - Bakker - 1996 |

1 | The essence of functional programming - unknown authors - 1992 |