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Towards a denotational semantics for the rho-calculus

Germain Faure 1 Alexandre Miquel
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The rho-calculus, also called rewriting calculus, provides an integration of rewriting and lambda-calculus in which, we can abstract on arbitraty patterns. Up to now, this formalism has been studied only from the perspective of tis operational semantics. This paper is a first attempt to propose a Scott-style semantics for this formalism. After introducing the rho-calculus we define a notion of rho-model in the category of Scott domains, and prove the soudness of the reduction rules w.r.t. this notion of rho-model. We then show that any universal domain D = D -> D with a top element (including the Scott's historical D_infinity) can be given the structure of rho-model by interpreting the structure construction of the rho-calculus by binary sup. From this, we deduce that the full aCI-theory of the rho-calculus is conservative w.r.t. the beta-eta theory for normalisable lambda-terms.
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https://hal.inria.fr/inria-00100235
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Submitted on : Tuesday, September 26, 2006 - 10:15:57 AM
Last modification on : Friday, February 26, 2021 - 3:28:05 PM

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  • HAL Id : inria-00100235, version 1

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Germain Faure, Alexandre Miquel. Towards a denotational semantics for the rho-calculus. [Intern report] A04-R-464 || faure04a, 2004, 14 p. ⟨inria-00100235⟩

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