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Confluence properties of weak and strong calculi of explicit substitutions

Abstract : Categorical combinators and more recently ls-calculus have been introduced to provide an explicit treatments of substitutions in the l-calculus. We reintroduce here the ingredients of these calculi in a self-contained and stepwise way, with a special emphasis on confluence properties. The main new results of the paper w.r.t. are the following : - we present a confluent weak calculus of substitutions, where no variable clashes can be feared - we solve a conjecture : ls-calculus is not confluent (it is confluent on ground terms only). This unfortunate result is "repaired" by presenting a confluent version of ls-calculus, named the lEnv-calculus called here the confluent ls-calculus.
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https://hal.inria.fr/inria-00077189
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Submitted on : Monday, May 29, 2006 - 5:16:10 PM
Last modification on : Thursday, February 3, 2022 - 11:16:40 AM
Long-term archiving on: : Friday, May 13, 2011 - 10:48:59 PM

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  • HAL Id : inria-00077189, version 1

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P.L. Curien, Thérèse Hardin, Jean-Jacques Levy. Confluence properties of weak and strong calculi of explicit substitutions. [Research Report] RR-1617, INRIA. 1992. ⟨inria-00077189⟩

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