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Reports (Research Report) Year : 1994

The discriminating power of multiplicities in the $\lambda$-calculus


The $\lambda$-calculus with multiplicities is a refinement of the lazy $\lambda$-calculus where the argument in an application comes with a multiplicity, which is an upper bound to the number of its uses. This introduces potential deadlocks in the evaluation. We study the discriminating power of this calculus over the usual $\lambda$-terms. We prove in particular that the observational equivalence induced by contexts with multiplicities coincides with the equality of Lévy-Longo trees associated with $\lambda$-terms. This is a consequence of the characterization we give of the corresponding observational precongruence, as an intensional preorder involving $\eta$-expansion, namely Ong's lazy Plotkin-Scott-Engeler preorder.


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inria-00074234 , version 1 (24-05-2006)


  • HAL Id : inria-00074234 , version 1


Gérard Boudol, Laneve Cosimo. The discriminating power of multiplicities in the $\lambda$-calculus. [Research Report] RR-2441, INRIA. 1994. ⟨inria-00074234⟩
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