## Abstract

Action calculi are a broad class of algebraic structures, including a formulation of Petri nets as well as a formulation of the π-calculus. Each action calculus HA (K) is generated by a particular set K of operators called controls. The purpose of this paper is to extend action calculi in a uniform manner to higher-order. A special case is essentially the extension of the π-calculus to higher order by Sangiorgi. To establish a link between the interactive and functional paradigms of computation, a variety of the λ-calculus is obtained as the extension of the smallest action calculus HAC(θ).

The dynamics of higher-order action calculi is presented, blending communication -for example in process calculi- with reduction as in the λ calculus. Strong normalisation is obtained for reduction. A set of equational axioms is given for higher-order action calculi. Taking the quotient of HAC(θ) by a single extra axiom η, a cartesian-closed category is obtained.

An ultimate goal of the paper is to combine process calculi and functional calculi, both in their formulation and in their semantics.

The dynamics of higher-order action calculi is presented, blending communication -for example in process calculi- with reduction as in the λ calculus. Strong normalisation is obtained for reduction. A set of equational axioms is given for higher-order action calculi. Taking the quotient of HAC(θ) by a single extra axiom η, a cartesian-closed category is obtained.

An ultimate goal of the paper is to combine process calculi and functional calculi, both in their formulation and in their semantics.

Original language | English |
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Title of host publication | Computer Science Logic |

Subtitle of host publication | 7th Workshop, CSL '93 Swansea, United Kingdom September 13–17, 1993 Selected Papers |

Pages | 238-260 |

Number of pages | 23 |

Volume | 832 |

ISBN (Electronic) | 978-3-540-48599-5 |

DOIs | |

Publication status | Published - 1993 |