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Subsitutions explicites, logique et normalisation

Abstract : Explicit substitutions have been introduced as a refinment of the lambda-calculus - the usual formalism
used to study the semantic of programming languages. In this thesis, we study their properties of strong
normalization and preservation of strong normalization. Several works around those normalization
properties are presented here in three parts.

The first one formalises a general proof technique of strong normalization using preservation of
strong normalization. We apply this technique to several calculi with explicit substitutions to measure
its usefulness. A benefit of this work is a new result : the strong normalization of simply typed

The second one is the study of the normalization of a symmetric non-deterministic calculus providing a
term notation for classical sequent calculus, extended with explicit substitutions. Due to the
conjunction of symmetry and explicit substitutions, usual strong normalization proofs by reducibility
technique seems to fail. We then use the technique formalised above, which requires to establish the
preservation of strong normalization of the calculus. For this purpose, we use a fragment of the theory
of perpetuality in rewriting systems.

The definition and the study of a new version of the lambda-ws-calculus with names, the lambda-wsn-calculus, is
the third part of the thesis. To prove its strong normalization by translation and simulation in linear
logic proof nets, we enrich their cut elimination procedure with a new rule. It therefore constrains us
to establish strong normalization of this new notion of reduction on proof nets.
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Contributor : Emmanuel Polonowski <>
Submitted on : Friday, January 7, 2005 - 5:28:24 PM
Last modification on : Saturday, March 28, 2020 - 2:24:28 AM
Long-term archiving on: : Thursday, September 13, 2012 - 2:10:24 PM


  • HAL Id : tel-00007962, version 1



Emmanuel Polonovski. Subsitutions explicites, logique et normalisation. Modélisation et simulation. Université Paris-Diderot - Paris VII, 2004. Français. ⟨tel-00007962⟩



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