## Logic for Computational Effects: work in progress

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Citations: | 2 - 2 self |

### BibTeX

@MISC{Plotkin_logicfor,

author = {Gordon Plotkin},

title = {Logic for Computational Effects: work in progress},

year = {}

}

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### Abstract

Abstract We outline a possible logic that will allow us to give a unified approach to reasoning about computational effects. The logic is given by extending Moggi's computational *-calculus by basic types and a signature, the latter given by constant symbols, function symbols, and operation symbols, and by including a _ operator. We give both syntax and semantics for the logic except for _. We consider a number of sound and complete classes of models, all given in category-theoretic terms. We illustrate the ideas with some of our leading examples of computational effects, and we observe that operations give rise to natural modalities.

### Citations

732 | Notions of computation and monads
- Moggi
- 1991
(Show Context)
Citation Context ...ction We are attempting to develop a formal logical system for reasoning about computational effects in a unified manner. Our starting point is Eugenio Moggi's computational *-calculus or *c-calculus =-=[5, 6]-=-. The *c-calculus terms provide an underlying call-by-value functional programming language. We add basic types together with a signature consisting of constant symbols, function symbols, and operatio... |

442 | Computational lambda-calculus and monads
- Moggi
- 1988
(Show Context)
Citation Context ...ction We are attempting to develop a formal logical system for reasoning about computational effects in a unified manner. Our starting point is Eugenio Moggi's computational *-calculus or *c-calculus =-=[5, 6]-=-. The *c-calculus terms provide an underlying call-by-value functional programming language. We add basic types together with a signature consisting of constant symbols, function symbols, and operatio... |

88 | The HOL logic
- Pitts
- 1993
(Show Context)
Citation Context ...order structure, as studies such as those involved with data refinement require [3], data refinement providing an application of our logic. These modalities are different to those considered by Pitts =-=[9]-=- then Moggi [7]. They do not have the *c-calculus as an underlying language and logic, and their modalities inherently involve use of a monad, which is only implicit for us. But, subject to the reform... |

54 | Notions of computation determine monads
- Plotkin, Power
- 2002
(Show Context)
Citation Context ...equations and observations. Such operations include binary . for modelling nondeterminism, read and write for modelling interactive input/output, and lookup and update for modelling side-effects (see =-=[11, 12]-=- for details). Our techniques are inherently semantic, using category theory. We seek to give an integrated, unified analysis of a programming logic with operational and denotational semantics, that a... |

30 | Adequacy for algebraic effects
- Plotkin, Power
- 2001
(Show Context)
Citation Context ...g another operation block subject to natural axioms [11], but the most elegant way to achieve that requires further investigation. We have many examples of such signatures and associated equations in =-=[1, 2, 10, 11, 12, 13]-=-. But to date, we do not have a systematic way to generate the equations from an abstract formulation of the notion of observation. Part of our ongoing work will be devoted to providing such a formula... |

26 | Computational effects and operations: an overview
- Plotkin, Power
- 2004
(Show Context)
Citation Context ...nary nondeterminism and update and lookup for state. The equational axioms to be added to the *c-calculus are those generated by the combination of nondeterminism and global state, as for instance in =-=[11, 13]-=-. One can give a systematic account of the combination of nondeterminism and global state in these terms [1, 2]. If one adds further type constructors as mentioned above, we have semantic evidence tha... |

19 | Combining computational effects: commutativity and sum
- Hyland, Plotkin, et al.
- 2002
(Show Context)
Citation Context ...se generated by the combination of nondeterminism and global state, as for instance in [11, 13]. One can give a systematic account of the combination of nondeterminism and global state in these terms =-=[1, 2]-=-. If one adds further type constructors as mentioned above, we have semantic evidence that suggests an extension to local state by adding another operation block subject to natural axioms [11], but th... |

19 | A semantics for evaluation logic
- Moggi
- 1995
(Show Context)
Citation Context ..., as studies such as those involved with data refinement require [3], data refinement providing an application of our logic. These modalities are different to those considered by Pitts [9] then Moggi =-=[7]-=-. They do not have the *c-calculus as an underlying language and logic, and their modalities inherently involve use of a monad, which is only implicit for us. But, subject to the reformulation those p... |

18 |
Algol-like Languages
- O’Hearn, Tennent
- 1997
(Show Context)
Citation Context ...(\Gamma ) # as, in some situations, the axiom x # seems unnatural. We shall also add further type constructors such as those corresponding to symmetric monoidal structure as used in studying locality =-=[8, 11]-=-. A signature consists of (base) types, function symbols, predicate symbols for the programming language, and operation symbols. The constant, function, and predicate symbols are to be considered and ... |

4 | Adequacy for Algebraic E#ects - Plotkin, Power - 2001 |

2 |
Data Refinement in Call-by-Value Languages
- Kinoshita, Power
- 1999
(Show Context)
Citation Context ...e as we seek finitistic proof theory in order to allow for easy mechanisation, and we want to isolate our use of higher order structure, as studies such as those involved with data refinement require =-=[3]-=-, data refinement providing an application of our logic. These modalities are different to those considered by Pitts [9] then Moggi [7]. They do not have the *c-calculus as an underlying language and ... |

2 |
to appear) Algebraic Operations and Generic Effects. Applied Categorical Structures
- Plotkin, Power
(Show Context)
Citation Context ...equations and observations. Such operations include binary . for modelling nondeterminism, read and write for modelling interactive input/output, and lookup and update for modelling side-effects (see =-=[11, 12]-=- for details). Our techniques are inherently semantic, using category theory. We seek to give an integrated, unified analysis of a programming logic with operational and denotational semantics, that a... |

2 | Combining computational eects: commutativity and sum - Hyland, Plotkin, et al. - 2002 |

2 | Models of the computational λ-calculus - Power - 2001 |

1 |
Combining computational effects: sum and tensor, submitted
- Hyland, Plotkin, et al.
(Show Context)
Citation Context ...se generated by the combination of nondeterminism and global state, as for instance in [11, 13]. One can give a systematic account of the combination of nondeterminism and global state in these terms =-=[1, 2]-=-. If one adds further type constructors as mentioned above, we have semantic evidence that suggests an extension to local state by adding another operation block subject to natural axioms [11], but th... |

1 |
Models of the computational -calculus
- Power
- 2001
(Show Context)
Citation Context ...ch as those arising from locality in addressing state. 2 Syntax The syntax for the programming language that forms the *c-calculus may be taken to be identical to that for the simply typed *-calculus =-=[14]-=-. So it has type constructors oe ::= 1 j oe1 \Thetasoe2 j oe ! o/ and term constructors e ::= \Lambdasj he; e0i j ssi(e) j *x:e j e0e j x where x ranges over variables, \Lambdasis of type 1, with ssi ... |

1 | Combining computational eects: sum and tensor, submitted - Hyland, Plotkin, et al. |

1 | Data Re in Call-by-Value Languages - Kinoshita, Power - 1999 |

1 | to appear) Algebraic Operations and Generic Eects. Applied Categorical Structures - Plotkin, Power |

1 | J.(2002) Computational eects and operations: an overview - Plotkin, Power |